perm filename ANALOG.2[RDG,DBL]1 blob
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C00001 00001
C00005 00002 ∂28-Sep-81 0641 Darden at SUMEX-AIM clippings and analogies
C00008 00003 ∂12-Oct-81 0705 Darden at SUMEX-AIM analogy.properties and relations
C00014 00004 ∂13-Oct-81 0726 Darden at SUMEX-AIM Tom D on analogy.properties and relations
C00028 00005 ∂17-Oct-81 0809 Darden at SUMEX-AIM Russ on properties and relations
C00038 00006 ∂TO DARDEN 17:57 13-Oct
C00050 00007 ∂14-Oct-81 1948 Darden at SUMEX-AIM hello
C00057 00008 ∂17-Oct-81 0809 Darden at SUMEX-AIM analogy as shared abstraction
C00062 00009 ∂18-Oct-81 1311 Tom Dietterich <CSD.DIETTERICH at SU-SCORE> Direct Matching vs. Abstraction
C00073 00010 ∂27-Oct-81 0821 Darden at SUMEX-AIM analogy.implicitness
C00090 00011 ∂29-Oct-81 1614 Tom Dietterich <CSD.DIETTERICH at SU-SCORE> Notes on Mike's "shared abstractions"
C00105 00012 ∂31-Oct-81 0812 Darden at SUMEX-AIM more Russ on analogy
C00117 00013 ∂31-Oct-81 1227 Tom Dietterich <CSD.DIETTERICH at SU-SCORE> Analogy archive
C00119 00014 ∂TO DARDEN@SUMEX 13:50 2-Nov
C00122 00015 ∂TO DARDEN@SUMEX 16:07 20-Nov [after sending THESIS.MSS]
C00123 00016 ∂21-Nov-81 0849 Darden at SUMEX-AIM analogy paper
C00125 00017 ∂21-Nov-81 0931 Darden at SUMEX-AIM comments on thesis proposal
C00134 00018 ∂TO DARDEN@SUMEX 16:59 26-Nov
C00157 00019 Lindley's paper - ca 21 Nov 1981
C00215 00020 ∂TO DARDEN@SUMEX, CSD.GENESERETH@SCORE 13:24 1-Dec
C00243 00021 ∂02-Dec-81 1737 Darden at SUMEX-AIM Re: Comments on your paper
C00247 00022 ∂TO DARDEN@SUMEX, TGD, STT 14:56 3-Dec
C00262 00023 ∂TO DARDEN@SUMEX 14:59 3-Dec
C00269 00024 ∂03-Dec-81 1330 Darden at SUMEX-AIM nsf proposal
C00290 00025 ∂10-Dec-81 0603 Darden at SUMEX-AIM replies, etc.
C00306 00026 ∂13-Dec-81 1630 Darden at SUMEX-AIM references on heuristics
C00308 00027 ∂17-Dec-81 0947 Darden at SUMEX-AIM analogy exam
C00319 00028 ∂23-Jan-82 0900 Darden at SUMEX-AIM hello and happy new year
C00322 00029 ∂31-Jan-82 0747 Darden at SUMEX-AIM Re: DNA book, etc.
C00324 00030 ∂07-Feb-82 1120 Tom Dietterich <CSD.DIETTERICH at SU-SCORE> [Clancey at SUMEX-AIM: analogies & schemas]
C00330 ENDMK
C⊗;
∂28-Sep-81 0641 Darden at SUMEX-AIM clippings and analogies
To: RDG at SU-AI
cc: Darden at SUMEX-AIM
Hi, Russ. Thanks for sending the clipping on Einstein. We had John
Stachel down for a colloquium last spring. I found the article quite
interesting. It is indeed an important question about how a famous person's
papers should be handled. It's one reason to work wwith material about
100 years old, so that personalities are less likely to be important.
Thanks also for the analogy article. The idea of analogies being
misleading is something I've been told by students from physics, who were
given certain analogies, for e.g.space-time, and didn't realize what was
positive vs. negative analogy until they worked through the math.
I will indeed be interested in seeing your thesis proposal with
analogy in the title.
I'm sorry not to have been more communicative lately, but life is very hectic.
Full-time teaching always takes lots of time, even though my two classes this
fall are fun and small. I'm teaching history of modern biology, and enjoying
looking again at Darwin's use of domestic selection as an analogy for natural
selection. My discovery and analogy class unfortunately has only four students,
and only one of those has a computer science background. I'm also doing lots
of committee work and I have charge of the Philosophy Department's word
processing system.
Adding to my business is the fact that my personal life these days takes
me to Boston frequently on week-ends.
How I long for the lesiurly days of my sabbatical at Stanford.
Well, this isn't one of them and I have to get ready to go to class.
You can send me your proposal on line. I now have a nice little EPSON
printer here at home.
Bye, Lindley
-------
∂12-Oct-81 0705 Darden at SUMEX-AIM analogy.properties and relations
To: Analogy seminar:
Hi, Folks. I wonder if it is possible to revive our dormant analogy
discussions. I am teaching a course this semester at Maryland called
Discovery and Analogy in Science and going over much of the literature
that we covered so quickly at Stanford last year. The press of teaching
and administrative duties has left me little time for electronic msgs,
but new ideas are occurring to me, and I would appreciate some feedback.
We have just finished reading Mary Hesse's MODELS AND ANALOGIES and
Dedre Gentner's "Are Scientific Analogies Metaphors." I am once again
puzzling over the differences between properties and relations.
(See analogy.hesse, msg of 27-May-81 for more details.) Hesse argues
for property matches of the following sort:
Properties Properties of light
echoes reflection
loudbrightness
pitch color
detected by ear detected by eye
propagated in air propagated in "ether"
The vertical relations are causal relations, hence they transfer, if
light is of the same type of causal system as sound. The horizontal
relations are similarity relations.
Gentner criticizes Hesse for looking for property matches rather
than structural, relational matches. Gentner argues for the use of
a "propositions network of nodes and predicates" as a representation
scheme. AI question: is this a semantic network?
It seems to me that if Hesse's vertical relations must be causal,
then she is, in some sense, matching causal structures, but her
more frame-like representation scheme obscures that fact.
Here is my question for you all in AI: how are relations represented
in units and slots? The sound unit depicted above does not have an
explicit representation of the "vertical, causal relations". Does the
causal interrelatedness of slots get represented by putting it into
another slot, or some other way?
Gentner draws circles (nodes) and lines between circles (relations)
and boxes off of circles (properties) and then maps isomorphically to
an identical set of nodes and lines, though not necessarily identical
boxes (analogy as structural, but not property match). Can all this
be represented in units and slots? How?
Mary Hesse thinks good scientific analogies have property matches
as well as relational matches; Gentner thinks good scientific analogies
have relational matches and few or no property matches. At least some
of Hesse's examples of analogies involve relating two things that might
be members of the same inductive class; Gentner's are always sufficiently
dissimilar that they would never be so related.
There is a deep metaphysical problem associated with properties vs.
relations: what are our basic ontological categories? Entities and
properties or relations? There is a very strong tendency in Western
thought to see substances (entities) as basic and to analyze relations
as dependent on substances interacting. Most of our discussion of analogy
thus far has focused on finding matches between properties of entities.
See discussions about protypes, exemplars etc. in various msgs
(e.g. STT on 27-Mar-81 and especially Tom D.19-Apr-81.)
Well, enough for now. Any other thoughts about properties vs.
relations?
Bye, Lindley
-------
∂13-Oct-81 0726 Darden at SUMEX-AIM Tom D on analogy.properties and relations
To: Analogy seminar:
Mail-from: ARPANET host SU-SCORE rcvd at 12-Oct-81 1502-PDT
Date: 12 Oct 1981 1423-PDT
From: Tom Dietterich <CSD.DIETTERICH at SU-SCORE>
Subject: Re: analogy.properties and relations
To: Darden at SUMEX-AIM
cc: CSD.DIETTERICH at SU-SCORE
In-Reply-To: Your message of 12-Oct-81 0701-PDT
Lindley,
It sounds to me, at least, that the debate over relations versus
features (aka properties) is not really very important. For instance,
is COLOR a feature or a relation? We might say that an apple is red
by writing RED(x) & APPLE(x), thus asserting that x has two features,
"redness" and "appleness". Alternatively, we might say COLOR(x,RED),
thus saying that the COLOR relation holds between two entities, x and
RED.
In semantic networks, both techniques have been used. Frame
representations, however, tend to employ the COLOR(x,RED)
representation. That is, a frame is created for x, the frame has a
COLOR slot, and that slot is filled with the value RED.
There are some relations that are difficult to represent as features.
For instance, to represent stacks of toy blocks such as the following:
-----
| |
| A |
| |
-----
| |
| B |
| |
-----
| |
| C |
| |
-----
AI people usually employ the representation
ONTOP(A, B) & ONTOP(B, C) & BLOCK(A) & BLOCK(B) & BLOCK(C).
It would be possible, however, if the structure was fairly static, to
employ a representation such as
BOTTOM-OF-STACK(C) & MIDDLE-OF-STACK(B) & TOP-OF-STACK(A) &
BLOCK(A) & BLOCK(B) & BLOCK(C).
However, this representation won't suffice if we need to describe
stacks of blocks that are arbitrarily large. We can still get away
with it, though, if we can place an upper bound on the height of a
stack. If we know that all stacks are 10 blocks or less, we can
create 10 properties and use only as many of them as we need. Thus,
for a stack of only three blocks, we could use the representation
STACK1(C) & STACK2(B) & STACK3(A) & STACK4(NONE) & STACK5(NONE) & ...
& STACK10(NONE)
The NONE entity says that there is no block in that position.
In general, it is possible to convert ANY relational representation
into a feature-value representation IF the "size" of the relations can
be bounded in some way. The feature-value representation is somehow
less natural, but it has the advantage of making certain inferences,
such as matching, much faster. Thus, AI people tend to use
feature-value representations whenever they can get away with it.
Hence the popularity of frames. When you use frames in which the slot
fillers are constants (rather than variables), then the frame is being
used like a vector of features, and you can compare the two frames
slot-for-slot. The frames can be "superimposed" on one another, and
the comparisons made. When variables are used as slot fillers, then
the slot starts behaving like a "relation", and matching becomes much
more complicated. All occurences of the same variable must be found
and checked.
Virtually all frame-representations and semantic net representations
can be translated directly into first-order predicate calculus. [the
exceptions to this statement involve extended types of inference, such
as non-monotonic reasoning. Many AI researchers are working on
formalizing these non-standard inference techniques in predicate
calculus]. This is why most of us in these analogy discussions have
ignored the question of whether features or relations were being
matched and concentrated instead on the nature of the matching.
Given this introduction, let me try to answer your questions.
Unfortunately, I haven't read the relevant papers, so I may very well
be mistaken. Here goes...
A "propositions network of nodes and predicates" sure sounds like a
semantic network to me. That is, it sounds like she is using explicit
relations in her representation. But, the preceding argument would
indicate that this is not particularly important. What is important
is WHICH properties or relations are being matched? I.e., the content
of the representation, rather than its form.
If we use the following representation, in which the "vertical
relation" is represented as a single, grand relation, then, Gentner
would only match the symbol "superframe" in one case to the symbol
"superframe" in the other case:
Superframe(SOUND, echoes, loud, pitch, detected-by-ear,
propagated-in-air)
Superframe(LIGHT, reflects, bright, color, detected-by-eye,
propagated-in-ether)
whereas, it appears from your description, that Hesse would match the
constants in the representation as well, by having some way of
determining that, for example, echoes and reflects were similar (for
example, she might have definitions of echoes and reflects in terms of
bouncing off of a physical surface, so that "bouncing off" and
"physical surface" could be matched to discover the similarity.)
This superframe representation trivializes Gentner's structural
match--there is virtually no structure to be matched.
An alternate representation, closer to the standard use of frames,
might be something like:
Frame(f1) &
Slot(f1, s1) & Slot(f1, s2) & Slot(f1,s3) & slot(f1,s4) & slot(f1,s5)
& Contents(s1, echoes) & Contents(s2, loud) & Contents(s3, pitch)
& Contents(s4, detected-by-ear) & Contents(s5, propagated-in-air)
Frame(f2) &
Slot(f2, s1) & Slot(f2, s2) & Slot(f2,s3) & slot(f2,s4) & slot(f2,s5)
& Contents(s1, reflects) & Contents(s2, brightness) & Contents(s3, color)
& Contents(s4, detected-by-eye) & Contents(s5, propagated-in-ether)
Now, Gentner would match the symbols "Frame" and "Slot", and the
structural relationships among the various slots. Such a match would
be completely structural, making NO use of the "CONTENTS" predicates.
I don't think such an approach is very plausible, though, because
there are 120 possible ways of doing the match (that is, s1 can be
matched to s2, s3, s4, or s5.) However, if we appended the following
information to the above representation, then we might get something
that made sense:
& Name(s1, bounce) & Name(s2, intensity) & Name(s3, frequency)
& Name(s4, detection) & Name(s5, medium)
Now, we can MATCH the SLOT NAMES as well, and now the match can only
be done in one way--the way that makes sense. However, notice that we
have worked into our representation some of the important theoretical
terms for this area: intensity, frequency, detection, and medium. How
plausible is it to suppose that these terms already exist in our
representation before we draw this analogy?
I don't like any of the approaches that I've outlined. To me, it
seems that you need to work in a whole lot more knowledge about what
"echoes" and "loud" and "pitch" and "color" mean--perhaps in terms of
examples and sense experience. All of these other representations are
too compact--they have boiled down all of the information into a very
simple structural form in which matching is either impossible or
trivial. I need to think more about this, however. I'll send another
message in a couple of weeks.
Bottom line: the property versus relation argument is not central to
the analogy question: both properties and features need to be matched,
both are interchangable. It is usually necessary to include relations
in any representation. The important issue of WHICH features and
relations should be used in a representation, and hence, should be
matched, is a difficult one. An important constraint on hypothesizing
representations is that each representation must be learnable from
some other representation. We might call this the "evolutionary
adequacy" of a representation.
In answer to one of your other questions, YES, I think you can
represent both Gentner's and Hesse's approaches using units and slots,
just as you can use predicate calculus.
I have a question. What do you mean by "causal"? I've been thinking
a lot about causality, and haven't gotten very far. What do
philosophers thhink about causality?
I hope this made some sense.
--Tom
PS. Please forward this to everyone on the analogy list.
-------
-------
∂17-Oct-81 0809 Darden at SUMEX-AIM Russ on properties and relations
To: Analogy seminar:
Mail-from: ARPANET host SU-SCORE rcvd at 13-Oct-81 1404-PDT
Date: 13 Oct 1981 1405-PDT
From: Russell Greiner <CSD.GREINER at SU-SCORE>
Subject: Complexities of Analogies
To: darden at SUMEX-AIM
cc: rdg at SU-AI
Hi Lindley --
I had some thoughts indirectly related to the question you asked in
your recent letter.
They basically reflect my weariness of claims which are this general,
especially when they pertain to domains as "subjective" as analogizing.
Your message points out (what I feel is) one of the major problems of all
existing analogizing programs -- their heavy dependence on some particular
pre-defined formalism and on a specific, implicitly defined representation.
"... one man's relations are another man's properties ..."
Consider the clearly "structural" attribute that John likes Mary.
Using the binary "Likes" relation, one could assert that (Likes John Mary).
[In units and slots, this could be represented by storing the value Mary
in the Likes slot of the John unit -- pictorially shown as
|-------------------|
| John |
| Likes: (Mary) |
|-------------------|
(I hope that comes out pretty on your terminal,)
possibly augmented with a "back-pointer", as
|-----------------------|
| Mary |
| IsLikedBy: (John) |
|-----------------------|
]
Later on, that "another man" mentioned above will, on noting Mary's
likability and host of friends, define a unary relation, (now called a
property,) LikesMary. The assertion is now the simple (LikesMary John).
Now consider the claim that the first of statements should be carried
across a good analogy, whereas the latter statement shouldn't;
in light of the fact that they both represent (semantically) the same thing.
(Note I'm NOT addressing the "pragmatics" here --
as I feel the "connotations of property-izing a relation" should play
NO role, especially when dealing with an internal representation.)
Another example: should it really make a difference whether we say something
is red, (ie satisfies the unary Red predicate) or that it's color is Red
(ie that that object participate in the ColorOf relation with Red)?
Is "IsaPerson" more natural than "Isa"?
Or consider the meta-relations, Name vs NamedLindley... etc, etc, etc.
The standard retort here is that one encoding is more natural,
and the other but a contrived aberration. Well, maybe...
But then who should decide this issue? While there may be some
general "truths", these can (at best) only be in the form of
psychological data -- and I do not feel the criteria for specifying and
defining an analogy should be in terms of such observations...
This may be what makes analogizing both interesting and elusive.
When seeking an analogy, any individual will utilize his particular
"encoding system" in deciding what is significant.
This particular example leads to a more general claim:
that any predefined specification will be subject to this same criticism
of limited applicability, and/or general fuzziness.
Ie you would find it equally trivial to critize/caricature any particular
scheme I might come, as it would necessarily be based on my particular
prejudices.
This is why I am making a effort to divorce the process of analogizing
from the particular representation used.
In my work, I intend to start with something as "neutral" as possible
-- like Predicate Calculus.
The user will be able to enter his particular analogizing heuristics in terms
of this "unbiased" description; these are then incorporated into the
actual "analogizing module".
It is these subjective, user-dependent rules which constitute the criteria
for evaluating any given analogy, or for comparing proposed analogies --
not some sacred set of specifications which had been giveth unto it.
(Of course, the user is free to use someone else's particular criteria,
sparing him the arduous overhead task of entering such data. The point
here is that he is also permitted to change these rules if he wishes,
or to enter his own biases.)
Anyway, I say quite a bit about this in my thesis proposal; which, who knows,
may actually be released of these days.
One final point: I am NOT saying that I disagree totally with Gentner, et al.
In fact, it seems obvious that the value of finding a pair of corresponding
N-ary predicates should vary monotonically with N.
I do intend to include this heuristic in my starting collection of
suggested rules. (Indeed, much of Carbonell's
"invariance hierarchy" will be used in this same way -- as a set of particular,
defeatable suggestions.
They depend far too much on the particular decomposition of "facts
about the world" into attributes to earn the status of iron-clad,
inviolatable rules.)
Conclusion:
The analogizing process seems much too complex to be so tied to the
particular representation used!
It is this (fallacious) attitude that has led people
(including me at times) to the belief that one can form analogies
using a purely syntactic mechanism -- eg by simply matching some predefined set
of features, using some weak (ie unspecialized) method.
I certainly hope that there is something more semantic to Analogies than that.
Russ
-------
Although I got a second msg from Russ, following this one, saying that he
realized that Tom had said some of these same things about properties and
relations, I decided to go ahead and send Russ's msg around. I wonder what
it means to say that different people have different representations for
analogies? I hadn't considered that theprocess of forming analogies might
be strongly dependent on individual psychological variables.
Lindley
-------
∂TO DARDEN 17:57 13-Oct
Oops
I just noticed that Tom already sent out a note,
whose contents had a non-trivial intersection with mine.
Sorry to force you to read through that rhetoric twice.
Also, feel free to circulate any (possibly trivial) subset of my
message which you think might be relevant.
By the way, how are you these days? and things there in general?
(I realized my last letter was a little impersonal, if not downright
hostile. Sorry about that...)
I've spent the last few weeks trying desperately to answer several
groups of people's "well, where is it?" questions. (Each referring to
a different "it"...) Like the rest of us, I had incredibly
overcommitted myself. However, I did manage to reach a plateau (or
conclusion) for two of the four main projects (viz. time consuming
tasks for the student orientation committee, and some RLL-related stuff for
ISI,) leaving me with only RLL stuff for Rand and (finally) a thesis proposal
still to do. Both are well along - at the "light at the end of the tunnel"
phase.
Anyway, I plan to commit much of this week to polishing (well,
after generating) that proposal -- hopefully bringing it to a point that
I can send it out for comments, (further burdening people like you.)
By the way, I wanted to thank you again for your offers of advice --
it really is nice to have the backing and criticisms from people with
both your knowledge and enthusiasm.
It will be quite useful to find just how naive my approach really is...
Caio,
Russ
∂14-Oct-81 1948 Darden at SUMEX-AIM hello
To: rdg at SU-AI
cc: Darden at SUMEX-AIM
Hi, Russ. I didn't mind reading the relations-property stuff you sent,
even though it was quite similar to Tom's response. Obviously you all are
thinking along the same lines and it is useful for me to hear. I will be
very interested to see how you allow analogies to be formulated without
having to be committed to a prior representation scheme.
My time is filled with many things that aren't much fun at the moment:
grading history of biology papers, doing committee work for the graduate
program, etc. I would much rather have time to learn more AI, work on
a paper on analogical reasoning, and finish my work on the history of
genetics. I've been writing grant proposals to have next year in Boston
but money for philosophy of science is not easy to get. I would
like to do a book on theory construction, with the theory of the gene as
the major case study.
Did you see Doug Hofstader's article on analogy in the September
SCIENTIFIC AMERICAN? I thought it was rather shallow, but students in
my discovery and analogy class had fun with the Nancy Reagan
is to the Us as (blank) is to Britain. We've been playing with
the idea that people can recognize analogies prior to being able tosay
explicitly what the analogous relations are. I have
no idea what implication that has for AI analogy formation.
I've enjoyed the various wire service items you have sent. Keep in
touch and good luck with your proposal. It is an important topic.
Bye, Lindley
-------
∂TO DARDEN@SUMEX 15:19 16-Oct
Misc remarks
Lindley -
Yes, I did indeed read thru Doug's article, months ago; and then
offered to circulate it on the analogy bulletin board.
He decided against such "advance publicity" --
I was really disappointed to find he had no interest in getting
any feedback.
Anyway, the article did indeed touch on some of the problems with analogy:
in particular, that whole issue of how to determine the appropriate
context on which to base the comparison.
[The term "context" is based on some recent musing of mine -- it's designed
to subsume things like perspective, recent (linguistic) focus,
the speaker's model of his audience, and everything else.
One of my goals is to structure
this "general catch-all" into some well defined, and useful, entity.]
(In case neither the article nor Steve ever mentioned it:)
Two of his students - Gray [no, that's NOT a typo] and Marsha - are working
on a program, cutely (cutesy-ly?) titled "SeekWhence".
It's designed to generate analogies, and other sorts of high level mumble
jumble. An important part will deal with self-inspection -- designed
to notice when if ever some internal state is repeated.
<Compare this to Mike's position that two models are analogies if they
share a partial theory (which he calls an "abstraction").
Imagine, for argument's sake, that we each time we experience some
phenomena we internally store something like a theory of that event.
This would mean that we would store this same "neural pattern" (or whatever)
each time we had an analogous "experience".
Hence the ability to perceive such "coincidences" would be a powerful
analogizing tool.
Example: When contemplating the "leadership" organization of a company,
imagine I store (something isomorphic to) a theory of hierarchies.
I would also store a similar structure when thinking about biological trees.
[This theory of hierarchies provides the common abstract which makes
businesses and trees analogous (using Mike's definition).]
Notice this means I would be in the same internal "configuration" each
time I encountered any instance of a hierarchy.
So any time I noticed that my internal structure is in this
"storing a hierarchy configuration", (for example, when someone explains
the boss-of relation of a corporate structure,)
I should feel I'm confronting something analogous to the branchiness
of biological trees,
as I was in this same configuration when incorporating that.
....
Yes, that was a lot of handwaving. Perhaps its was merely an attempt
to force two intrinsically dissimilar ideas into an analogy...
Of course people are good at that.
End of digression, from digression.>
Any of this make sense?
That's all for now. Back to thesising.
Russ
∂17-Oct-81 0809 Darden at SUMEX-AIM analogy as shared abstraction
To: Analogy seminar:
Hi, Folks. I got a brief msg from Russ about Mike G's idea of analogy
as a shared abstraction. Russ suggests that when people perceive new
things, such as the hierarchical organization of a company, they may
store an abstraction that will then get matched to other things with
a similar structure, e.g. a biological tree.
Ihavebeen thinking a lot lately about analogies as shared abstractions
vs. analogies as direct mappings between particulars. There seem to
be advantages and disadvantages to both analyses. If one has astractions,
then the relations among analogues is identity, a much easier relations
to deal with than vague "similarity." Also, we might hope to be able to
get a typology of abstractions and use them for whatever purposes we use
analogies. In my cases, that would mean a typology of theories that could
be used when we come to construct a new theory. On the side of direct
mapping, however, is the ability to go back and make use of additional
properties of the analogue that were not exploited at the outset and that
would not (or might not)have been included in an abstraction. Mary Hesse
argues that the extendability of theories in the face of anomalies depends
on having additional neutral analogy available to exploit. I have found
(actually a student of mine found) an excellent example of this in Darwin's
use of domestic selection as an analogy for natural selection. After the
theory was already constructed, Darwin faced the problem of how neuter
insects could be perpetuated since they didn't reproduce. He went back
to the domestic slection case and said that even though we eat, e.g. a pea,
we can select the "stock" from which the good tasting peas come to plant.
So, he proposed a kind of (what we now call) "kin selection" to explian
why that stock of the neuter bees would pass on the neuter trait. The
information about choosing the stock was not part of the original match
and would not have been included in an abstraction.
One suggestion for how to build an analogy system would beto use
both shared abstractions and direct mappings: use an abstract type is
it solves a problem butkeep around the detail instances with additional
properties to be used if the abstractions fails to supply what is needed.
Thus, one would have an abstract selection model, consisting of variants,
a means of choosing among variants, and the differential reproduction of
the chosen ones. Domestic selection and natural selection would be
instantiations of this model. But when the problem of neuter insects
arises, additional details from domestic selection are examined, since
the abtract model does not aid in the solution.
Any comments?
Bye, Lindley
-------
∂18-Oct-81 1311 Tom Dietterich <CSD.DIETTERICH at SU-SCORE> Direct Matching vs. Abstraction
To: Analogy-seminar: ;
Lindley,
Your message about stored abstractions vs. direct mappings was very
interesting, and I thought I'd respond by trying to synthesize the two
views and share a few ideas about analogy that have occurred to me
recently.
Let me restate the two views in slightly exaggerated form:
DIRECT MAPPING: An analogy is a direct mapping between particulars A
and B. (A and B could be objects, situations, events, configurations,
devices, mechanisms, etc...., we will call them objects from now on.)
It specifies how A and B are the same (POSITIVE ANALOGY) and how they
are different (NEGATIVE ANALOGY), and perhaps even the ways in which
it is not known how they are the same or different (NEUTRAL ANALOGY).
I doubt that NEUTRAL ANALOGY can be explicitly represented, since a
person (or a program) cannot possibly know everything about an
object--and all of the unknown features of the object are neutral
analogy. When the analogy is set up, the person will pursue it long
enough to determine that there is a positive analogy (and thus a basis
for the analogy) and to use the analogy to map some of the neutral
analogy across. Everything else that is unknown is neutral, and can
be used at some later time to extend the analogy.
SHARED ABSTRACTION: An analogy is a mapping between a shared
abstraction S and two particulars A and B. A and B are both
recognized as being instances of S. The shared abstraction tells how
A and B are the same.
There are two issues that arise from these definitions: (a) How do we
find analogies? and (b) What do we use them for?
FINDING ANALOGIES
The shared abstraction position says that we find analogies by
recognizing instances of our pre-existing shared abstraction S. This
is very nice for mature systems, but it ignores the question of where
S comes from (i.e., it is evolutionarily inadequate).
The direct mapping position says that there is some super mapping
process that is able to compare objects and decide when (and how) two
objects are similar. This is known to be computationally expensive,
especially for "large" objects (i.e., with many subparts).
USING ANALOGIES
The direct mapping view says that analogies are used to hypothesize
ways in which A and B are similar. The neutral analogy of A and B is
hypothesized to be positive. This is a very attractive idea, because
it provides a generator of new ideas: you just think of everything
that you know about A, and hypothesize that it is true of B (and vice
versa). If your knowledge of A is unbounded, then so is your
hypothesis generator.
The shared abstraction view presumably could support the same kind of
"transfer of properties" as the direct mapping view, but there is no
supporting framework for keeping track of the negative analogy. This
is not a fatal flaw--such a framework could be provided fairly easily.
Mike Genesereth has pointed out another value of having a shared
abstraction: you can attach an efficient simulation structure
(computational partial model) to the abstraction and use it to improve
the efficiency of representation and inference. [I think this is the
main point of his Metaphors and Models paper in AAAI, isn't it?] This
is one advantage of having an explicit abstraction structure in your
representation.
COMMENTS
I think the two views can be combined as follows.
Start with the direct mapping approach. When A and B are"vound to be
similar, create a shared abstraction and look for an efficient
computational model of that abstraction. In other words, when you
discover that "maple tree" and "IBM organizational structure" are
similar, look for ways in which the shared abstraction, "hierarchy",
is similar to something in a computer, and use that similarity to
build a computational model for the abstraction.
When new objects come in, first look for similarity with existing
abstractions. If none are found, then fall back on the weaker direct
mapping approach.
Employ the POSITIVE/NEGATIVE/NEUTRAL idea to generate new hypotheses
and attempt to extend analogies.
Summary: an abstraction is a "cached analogy"
OTHER POSSIBILITIES:
Another use of analogies is to represent partial knowledge. It is
possible that a system could set up an analogy that was believed to be
true, but that had almost NO POSITIVE ANALOGY. This is just another
way of looking at analogies that stresses the role of the NEUTRAL
analogy. In learning and theory formation, it is important to
represent everything you know, even when it is very weak knowledge.
Existing systems, such as Meta-DENDRAL, usually do this by
enumeration: If there are several possibilities for the right answer,
we typically list them all. Unfortunately this requires a generator
of all of the possibilities (and an explicit representation for them).
Analogies may provide an implicit representation for partial
knowledge. We may not know exact what the answer, A, is, but we know
that it is like B (and also like C), etc. This is just a vague idea
that needs a lot more work.
The problem of finding analogies is very difficult. It may be that we
can make use of some existing abstractions in order to help guide the
matching process. We need to develop a large body of heuristics that
can guide the search for analogies. Winston proposed "causality".
Carbonell elaborated on this with his idea of an "invariance
hierarchy". Dave Smith has suggested context-dependent heuristics
that might suggest certain dimensions along which the two objects
should be compared. One might imagine a "fingerprint" heuristic:
take some unusual property of A and go looking through your knowledge
base for things sharing that same unusual property. Anyway, there is
a lot of work to be done in this area.
Actually, the shared abstraction vs. direct mapping argument is
related to the larger question of the role of memory organization vs.
inference. Are there ways of organizing memory that making it easy to
find analogies? Evidently, people have many important associative
links in their brains. Words, for instance, seem to be cataloged by
sounds (vowel sounds, initial consonant, etc.). Perhaps there is an
organizational skeleton that will simplify the matching process.
Well, that's all for now.
--Tom
-------
∂27-Oct-81 0821 Darden at SUMEX-AIM analogy.implicitness
To: Analogy seminar:
This is a reply to Tom's message of 18 October 1981 on the topic
of direct matching vs. shared abstraction as analyses of analogical
reasoning.
I agree with much of what Tom says about the advantages and
disadvantages of the two approaches. The most interesting comment in his
msg if this: "Analogies may provide an implicit representation for partial
knowledge." I have been thinking a lot lately about humans' abilities
to see that A is like B, without being able to say explicitly what the
similarity relation is; further analysis will often enable a person to
say what the relation is. Thus, the first step, by humans, in finding
analogies may be some implicit recognition of similarity. I've had fun
with my students asking them about Doug Hofstader's analogy (in the
September 81 SCIENTIFIC AMERICAN) Nancy Reagan : US :: ? :Great Britain.
I usually get immediate responses and later the students analyze what
the relevant comparisons were that they were using (sex, position).
But I have no idea how we could build a system
that would recognize implicit similarities or differences
(it sounds impossible) or make use of them. It seems to me we have to
figure out what it is that humans are doing (e.g. direct mapping vs.
finding shared abstractions), even if humans aren't consciously aware
of the process. If we can figure it out, or construct something that
will function in the same way even without knowing whether it is the way
humans do it, then we may be able to build a system to do it.
A few other comments about other parts of Tom's msg:
In discussing the use of neutral analogy to generate new ideas Tom says"
"you just think of everything that you know about A, and hyothesize that it
is true of B (and vice versa). " However, you would like to have some way
of telling ahead of time which aspects of the neutral analogy will be
likely to be positive and which negative. To solve this problem, Mary Hesse
and Winston have instroduced the idea that there should be causal relations
among the already established poistive analogy and the aspects of the
neutral analogy that you transfer. Gentner wants the relations that are
mapped over to be part of a "mutually constraining system" (whatever that
is). I think causal interrelatedness is probably too strong: few
analogies are going to provide tight causal systems. But we do need
heuristics (probably coming from the problem-context) as to what kind of
properties and relations we expect to map over, e.g. if we are looking
for analogies to the structure of the atom, we will map structrual
properties. This topic needs a lot more thought.
I don't understand Mike G's point that Tom discusses: "you can
attach an efficient simulation structure (computational
partial model)[what is this?] to the abstraction and use it to
improve the efficiency of representation and inference." [How?]
Tom, can you or Mike explain this to me?
Well, enough for now.
Bye, Lindley
-------
∂29-Oct-81 1614 Tom Dietterich <CSD.DIETTERICH at SU-SCORE> Notes on Mike's "shared abstractions"
To: Analogy-seminar: ;
Lindley,
This is a response to your request for a clarification of Mike's
"abstraction" idea. Since he is so busy these days, I thought I would
respond by attempting to set forth his position and then criticize it.
I hope I'm dong him justice. My main source is his AAAI paper
(Metaphors and Models) and my own conversations with him.
Mike's main assertion is that there exist (ideally?, or in the makeup
of the human brain?) certain computational structures, such as trees,
that can be represented compactly and reasoned about efficiently.
He calls these computational structures SIMULATION STRUCTURES (after
Weyhrauch). He goes on to make two major claims:
Claim 1. Good simulation structures are "potential wells"--sources of
many good analogies. They capture some common structure that
frequently appears in the real world.
Claim 2. The process of finding an analogy is the process of
discovering (or recognizing an instance of) one of these structures.
Theory formation is also related to finding one of these structures
(He is very vague on this).
First, let's look at an example of a simulation structure and how
Mike's program actually uses them. Then we can take up these claims.
Mike's favorite example is a tree or hierarchy. A tree can be
represented compactly as a LISP list structure. Imagine a
formalization in logic of the organizational chart of a corporation.
The formalization would include axioms like
supervises(Genesereth, Smith)
supervises(Feigenbaum, Genesereth)
supervises(Genesereth, Paulson)
...
along with axioms such as
(A x,y) supervises(x,y) -> boss(x,y)
(A x,y,z) boss(x,y) & boss(y,z) -> boss(x,z).
In LISP, we can implement the boss predicate as the CDR pointer in a
linked list:
(Feigenbaum (Genesereth (Smith
Paulson))
(Buchanan (...))
(Lenat (...)))
and we can implement the transitivity axiom by an inheritance
algorithm: to test if boss(x,y) is true, start with the y and search
upward through the tree (i.e., left-ward in the linked list) for x.
This computational implementation thus allows very efficient deduction
of the fact "boss(Feigenbaum, Paulson)". We start at Paulson and
search leftward for Feigenbaum.
In terms of formal logic, the simulation structure is a partial model
(in the Tarskian sense) of the axioms. Some inference can be done in
the model and then mapped back into the axiom system as necessary. As
Russ points out, Mike calls the axiom system an ABSTRACTION.
Mike's program, ANALOG, looks for situations in which it can use the
tree simulation structure IN PLACE OF the axiom system. He sees two
basic advantages: more compact representation and more rapid
inference. The tree representation is more compact than a set of
axioms, since only one memory location is needed to store each "fact"
of the form "supervises(x,y)". And as we have seen, inference is
quite fast as well. Mike does point out that there are disadvantages
associated with using simulation structures. Facts must converted
into a canonical form in order to be stored. Partial knowledge is
hard to represent: if we don't know who supervises Dietterich, for
example, we can't put him into the list.
When Mike's program finds a situation in which the tree structure can
be used, it converts all (or as many as it can) of the facts that were
stored in a uniform logical representation into the tree structure
representation.
Mike's program thus has two tasks: (1) to recognize the applicability
of one of its simulation structures, and (2) to actually apply the
simulation structure. The problem of recognizing the applicability of
a simulation structure is basically the problem of finding an analogy
between the situation and the simulation structure. Mike doesn't say,
in his paper, exactly how this is done. He says "there is a knowledge
base describing some of the best data representations and algorithms
known to computer science." This knowledge base is used to select one
of the existing simulation structures for use in representation.
To actually apply the simulation structure, Mike points out the need
for a procedure for mapping each logical assertion into its
corresponding assertion about the simulation structure. This is
basically the "analogy map" telling how the two things correspond. An
interesting thing about this map is that ALL of the simulation
structure must map to SOME of the logical axiomatization. This is an
easier matching problem than the problem of finding a partial match
between two complex entities. This match is partial for the logical
axioms but total for the simulation structure.
Now that we have seen what Mike's program does, we can summarize the
main points: (1) There are things called simulation structures that
have particularly nice properties. (2) He has built a system that can
recognize when these structures can be applied and that applies them
to improve the representational and inferential efficiency of his
system.
Now we turn to his claims about the larger issues of analogy. First,
let's take up the question of the existence of these simulation
structures. Are there only a few good simulation structures around?
Mike lists hierarchies, grids, partial orders, rings, groups, and
monoids, as examples. Computer scientists study a variety of special
graph structures such as bipartite graphs, planar graphs, and complete
graphs. Mike also mentions the trick of using a bit-string to
represent a set, by assigning one bit to each possible element of the
set. Mike lists a set of considerations that bear on the problem of
inventing new simulation structures. One approach, for example, is to
choose a particular level of analysis and represent each individual by
a single structure in the machine. Thus, with sets, we represent each
potential element in the set by a single bit in the machine. With
trees, we represent each person in the organization as a single node
in the tree. Similarly, it may be important to choose a single
relation to serve as the backbone of the simulation structure and
deduce the other relations as necessary. Thus, in the tree, we chose
the "supervises" relation to organize the tree, and computed the "boss"
relation as necessary.
From the above discussion, we can conclude that there are, indeed,
many good simulation structures around, and that there are even some
principles for designing new ones.
Now, let's take up claims 1 and 2--namely, that simulation structures
capture some pattern that frequently occurs in the world, and that
finding an analogy is the problem of finding a simulation structure.
Claim 1 is, in a sense, self-fulfulling. A good simulation structure
is one that is useful. A simulation structure is useful if it appears
often in the world. But, this isn't quite the full story. Basically,
Mike is asserting that if something is efficient computationally, then
it should be useful for representation. He even goes so far as to
suggest that the computer should "bend" reality to make it "fit" the
simulation structure. This is equivalent to asserting that the
computational structure of our brains mirrors, in some sense, the
structure of the world. He admits that this is implausible for
current computers, but asserts--rather weakly--that VLSI will change
all that by providing new computational structures.
It is an interesting assertion that the structure of our minds
influences the way we perceive the world. If claim 1 is true, then
computers will probably perceive and organize the world (i.e.,
discover abstractions and analogies) differently than people.
Still, I have my doubts about claim 1.
Claim 2 says that, SINCE simulation structures capture regularities in
the world, we can find analogies by either looking for instances of
existing simulation structures or else inventing new simulation
structures. This certainly makes sense. The only issue is whether or
not there are any other ways of finding analogies. Mike hasn't really
addressed this question. It seems to me that there are
analogies--such as the analogy underlying the "man is a wolf" style
of metaphor--for which there is no corresponding simulation structure
on current computers. Mike can counter, however, with the argument
that perhaps there is such a simple structure in the human mind.
Still, I think analogies are too common and varied to assume that some
efficient computational structure underlies each one of them.
Conclusion:
Mike's idea of efficient simulation structures is nice, and it gives
another heuristic for analogy programs: try your known efficient
simulation structures before you go looking for complex partial
matches. However, I don't think simulation structures provide a
complete account of analogies or theory formation.
--Tom
-------
∂31-Oct-81 0812 Darden at SUMEX-AIM more Russ on analogy
To: Analogy seminar:
Mail-from: ARPANET host SU-AI rcvd at 28-Oct-81 1434-PST
Date: 28 Oct 1981 1431-PST
From: Russell Greiner <RDG at SU-AI>
Subject: Third Def'n of Analogy, and other meaningless dribble
To: darden at SUMEX-AIM, TGD at SU-AI
Lindley, Tom -
Actually, I was defining analogy in (yet a) third sense:
Two "objects" are analogous if they both satisfy the same (partial) theory.
Hence TGD and RDG are both models of the "theory of Stanford CS grad students".
[Ie both (of us) satisfy the single statement
<1> (Exist (S) ((Student S) & (Location S Stanford)
& (Dept S CS) & (Level S Grad))).]
A more complicated example might involve something like the theory of groups,
or the theory of a hierarchy.
(Note that both a corporate hierarchy and a biological tree satisfy that theory.)
Mike (ab)used the term "Abstraction" to refer to that partial theory...
I find it very easy to abandon that confusing term in favor of the
more accurate and less misleading phrase, "partial theory".
In some cases one can easily concoct the Abstraction from a partial theory --
as the minimal model of that set of statements.
[I'm not sure this is always possible, or if that minimal model is well defined.
Any logicians out there?]
In the case of <1>, one could simply
define an intensional object which has just the properties required of
that existentially quantified variable x.
Hence the Abstraction for RDG and TGD would be that
theorized standard "Stanford CS grad student", hereby labeled TypicalS-CS-GS.
Note nothing is known about this entity beyond these 4 characteristics.
But what about deductions which follow, you may ask? Eg as
<2> (All (x) (Student x) => (Person x)),
can't we conclude (Person TypicalS-CS-GS)?
The answer, of course, depends on where statement <2> came from.
Answers like "obvious common sense" or "from the inheritance hierarchy"
are not allowed. Rather, if one wants to make assertions like <2>,
he may; provided he has entered such rules explicitly.
As none of these facts are hidden, it is straightforward to determine
just what the system "knows" about some object, and from this, the
type of analogies it will be able to generate.
(This is what I meant in my last message about an unbiased "neutral" starting
state.)
Anyway, there are some advantages of this partial theory approach over the
abstraction one.
The first difference (which I consider an advantage, but others may disagree)
is that it forces even "obvious" facts to be entered explicitly.
(Let me contrast this with (my cariacture of) the Shank-ian view
that the original programmer should simply build every possible
common-sense idea/rule/theme imaginable into the program itself.
From here that program has the trivial "syntactic" task of matching, ...
or whatever to achieve human performance.
The problem with this approach -- the reason I cannot imagine it actually
working -- is with the (ridiculous) assumption that there can be
some universally-accepted, unbiased initial stash.
I question whether there even is such an all-encompassing set of facts,
and even more whether any coder could possibly envision it.
As that set is so incredibly ill-defined, and subjective,
it seems a real loss to encode this, inalterably and implicitly, in a
program. End of beating-up-on-straw-man.)
As a second possible advantage, note there is no need to create that
usually artificial abstraction entity.
One can, instead, deal exclusively with its description
(in term of neutral predicate calculus statements, or whatever).
Another plus answers Lindley's question posed in her most recent message:
[The question about "an efficient simulation structure (computational
partial model)"]
One may store a set of inference procedures (and associated data structures)
with a given theory. This simulation structure will, by design,
apply to any model which satisfies that particular theory.
For example, one may have an efficient mechanism for dealing with
retrievals from a hierarchy. This set of procedures could be applied
every time we find something which fits into this framework.
(See MRG's recent paper for details...)
By the way, I think Lakoff & Johnson, in their "Metaphors We Live By",
are claiming that people too possess and use certain specific
(efficient) mechanisms for a variety of computations.
Further, (I infer that he claims that) this ability developed for use in
one particular domain, but was
later applied to some other "analogous" domain,
that is, to another model which satisfies the same theory.
[Let me tone down my claim: what follows is not obviously inconsistent with
their claims. See their article in "Cognitive Science", Vol 4, Number 2
[April-June 1980], pp 195-208.]
For example, people often refer to their emotional state in terms of
up versus down -- as in "he's feeling low today",or "she's flying high today".
Perhaps people have some special purpose "hardware" for handling
linear-orderings in general.
As (one of) its primary uses is to describe the spatial up to down continuum,
our vocabulary, for this theory, has been based on this set of spatial terms.
Now along comes some other phenomena which also deals with a linear ordering,
as say the happy-to-sad (pseudo)continuum.
Why not use this linear-ordering hardware for doing things like, say, comparisons
(using its transitivity)? For that matter, why not for communicating?
It is this second use of that hardware that prompts us to use spatial terms
for describing emotions.
Note this will work in any situation where the same theory which applies
to one domain happened to apply to another.
Here any example of a linear ordering will do -- such as quantity
("Number of books printed this year is up") or goodness
("The quality of life is high these days").
Of course there is nothing special about linear ordering -- their
Cognitive Science atricle contains a wealth of these
(oops, quantity as precious possession...).
End of digression. Of course I totally ignored the issue of indexing:
just how does one locate the relevant theory for a given new model?
There is no a priori reason to think this process would be any easier
that finding an apt abstraction, or forming a new mapping.
Any ideas?
Anyway, the efficient computational partial model would be the algorithms people
have for dealing with linear orderings, or whatever. For example, one
could represent any linear ordering as a straightline. In this model GreaterThan
would be trivial to compute: it would be true if the first value was to
the left of the second. (For comparison, consider the model which represented
each term with its english spelling. Here ">" is incredibly indirect, and
hence expensive.)
-----
That's all for now. As usual, if you think any of it makes sense, please
forward it along to the rest of analogy mailing list.
Russ
-------
∂31-Oct-81 1227 Tom Dietterich <CSD.DIETTERICH at SU-SCORE> Analogy archive
To: Analogy-seminar: ;
For the past few months, I have been maintaining a combined archive of
all of the messages from the analogy seminar on the file
[score]<csd.hpp-utilities>analogy.msgs. About once a month, I move
recent analogy messages into this file and delete old ones. Before I
delete old messages, I archive the whole file at SUMEX, so all of our
messages are saved for posterity. I don't know if anyone else out
there is maintaining an analogy archive, but I thought I'd let you all
know so that if you like, you can delete your copies of analogy
messages after you have read them, and refer to my archive file for
old messages. This is particularly relevant since we (especially I)
have been very long-winded of late, and those messages sure take up a
lot of space!! If you need to see some REALLY old messages, let me
know, and I'll restore them for you.
--Tom
-------
∂TO DARDEN@SUMEX 13:50 2-Nov
Recent NOVA
Lindley -
Did you see the latest NOVA show?
It apparently dealt with flaws (real and imagined) in Darwin's ideas.
I unfortunately missed all but the last few minutes of it last night;
I do intend to see it in its entirity when next it repeats.
(Transcripts are available for this show, if you're interested.)
Russ
∂05-Nov-81 0806 Darden at SUMEX-AIM Re: Recent NOVA
To: RDG at SU-AI
cc: Darden at SUMEX-AIM, STT at SU-AI
Yes, I saw the recent NOVA entitles "Did Darwin getit Wrong?" I thought
it was intellectually muddled. It mixed up creationist challenges to
evolution ("decent with modification) with scientific challenges to
Darwin's version of the theory of natural selection. This confusion
of the ambiguous "theory of evolution", i.e. descent with modification
and the mechanism to explain such species change, is rampant today.
Although some of the people on the show made the distinction, it was
NOT made clear to the average viewer. The views of Eldridge and Gould
on punctuated equilibria (i.e. long periods of stasis then rapid
speciation) present an important challenge to the gradualism that
Darwin postulated; but they do not deny that natural selection is an
imporant agent in selecting adapted forms. The relations between Darwin's
views and the newer scientific mechanisms were not made clear in the show.
Nonetheless, it is worth seeing to hear the interesting cases from the
paleontological record.
Bye, Lindley
-------
∂TO DARDEN@SUMEX 16:07 20-Nov [after sending THESIS.MSS]
Description of Previous Message
Hi Lindley,
That last message is an overgrown thesis proposal, strewn with
miscellaneous SCRIBE commands. I'd be very happy to hear any
comments/suggestions/concerns/... you can offer. In addition, any recent
readings, beyond those mentioned, would help me considerably. (I do still
have your reading list from last year.)
Thanks for your help,
(and sorry to burden you and your mail file with so much)
Russ
∂21-Nov-81 0849 Darden at SUMEX-AIM analogy paper
To: Analogy seminar:
Hi, folks. I have been busy writing a paper on analogy that I presented
at American Univeristy last week. It is in my directory at SUMEX:
<Darden>mss.analogy;3. I think you can print it out, since I never
figured out what protection codes I should have to prevent that. So,
if you would like to read it, see if you can get a copy. If there is
a problem wit this method, let me know and I can send it as a msg to
whoever wants it. Sorry that the references aren't typed in, but many
you all will know or have on the bibliography from our seminar last year.
If any of you think of other examples of th selection theory abstraction,
please let me know. I will be very interested in comments. This is
probably a first, first draft of the paper that I will present at th
Philosophy of Science Association meetings in Octber 82 in Philadelphia
where Bruce and I will be on a symposium entitled "Discovery, Heuristics
and AI". I would like to increase the AI component of the paper and need
your help.
Bye, Lindley
-------
---
Lindley's paper
Tom, Steve -
... is now at MSS.ANA[1,rdg]. Feel free to dover it from there.
Russ
∂21-Nov-81 0931 Darden at SUMEX-AIM comments on thesis proposal
To: Greiner at SUMEX-AIM
cc: Darden at SUMEX-AIM, Genesereth at SUMEX-AIM, Lenat at SUMEX-AIM,
Buchanan at SUMEX-AIM
Hi, Russ. I VERY MUCH enjoyed receiving a copy of your thesis proposal.
I am so happy that you have decided to work on analogy. I have jsut
finished a paper on analogy, as you know from the msg to the analogy
seminar and I will enjoy receiving your comments. Do youthink that
humans have to spend a certain amount of time thinking about new ideas
before they gell? It is curious that we spent all that time in fall, 80
talking about analogy and youand I both are just now getting around to
putting ideas into print.
Now to some specific comments: I had trouble following some of
the material, both because it is still so schematic and because I
am not familiar with some of the functions you use. Nonetheless, here
are some comments: Do you really want to take on any possible examples
of analogy (except those requiring extensive knowledge of a single
domain)? I think you should take seriously Gentner's claim that
literary and scientific analogies may be rather different--she
empahsizes differences in richness and clarity. Perhpas structural
analogies (or functional ones, or some other such dimension) might be
easiwer to deal with, or.... At any rate, I think you should consider
at the outset to which kind of set you might limit your system. Trying
to tak on all comers may be asking too much.
I got very little idea to what CONTEXT refers. Can you be more
specific? How is the context going to function to constrain "the
analogizer to generate only thoose analogies appropriate for a
particular situation"? I don't understand the relation between the
"dynamic" aspect of CONTEXT and the more ''static" aspect of the
HEURISTICS. I would have expected the user-input heuristics to
vary from analogy to analogy, but apparently it is the CONTEXT that
plays this role. I need more examples of heuristics. If I as a
naive user tried to use your (to be built) system, how would I know
what counted as a heuristic and what kinds of things I was being
asked to put in?
As to your defiintion of analogy as "shared partial theory>"
I like Mike's "shared abstraction" better since the word "theory"
is so theory-laden. In other words, "theory" is used in so many
ways in so many contexts that it may confuse some readers. "Abstraction"
has the advantage of having meaningful content. Also, I am personally
concerned wit using analogies to construct scientific theories, so
"shared partial theory" obscures things somewhat, even thought my
"abstraction for selection theories" is an abstracted portion of a
group of theories. I wanted to use the term "selection model" but
model sometimes has the opposite meaning of an example, rather than
the abstract structure.
I don't think Gentner and Hesse have the same idea of mapping from
one analogue to another. Hesse maps properties and relations; Gentner
wants to map only (abstracted) relations. I know you all don't think
that is a very clear distinction, and I have come to agree. Nonetheless,
I think Gentner's structures that are mapped are at a more general,
abstracted level than Hesse's.
How is "deep structure" going to be represented and discovered by
your analogizer? Don't you somehow have to be it in explicitly? And
if you do, then you have the "already canned" problem of looking like
you put it all in at the beginning.
I think humans have some sort of (as yet mysterious to me) ability
to recognize an analogy before they can say explicity on what grounds
the two things are similar. I had fun in my discovery and analogy
class with Doug Hof.'s example of the first lady of Britain: students
gave answers and then had some trouble defending their snap judgments.
I can't figure out how this ability to recognize but not know why
could be part of an analogy AI system. Of course, since we aren't
trying to mimic humans, we don't have to make a system function this way.
But your talk of coming to see deep structure sounded similar to me,
so I worry.
I wonder what type of heuristics could be used to abstract the
form of selection theories from domestic selection and natural selection?
Maybe my real scientific cases are going to be too complicated for
your system.
I am still working on the idea we discussed last year of types of
problems and types of solutions. The result from myselection theory
paper: if you want to explain adapted somethings (a type of problem),
then you can use either of two known abstractions: selection type
theories or tool-fashioning theories. Do you have any plan for
typologies for analogies, via types of partial theories?
Well, this is fun, but I have to stop and work on an NSF grant
proposal.
Obviously I would like to be kept posted on what you are doing.
Sorry that I am so far away. Do you have any plans to come East
this winter?
Bye, Lindley
-------
∂TO DARDEN@SUMEX 16:59 26-Nov
Comments↑2
Thanks for your quick comments! Yes it is curious that both of our
papers (well, draft in my case) appeared almost simultaneously.
By the way, your paper is indeed accessable. (I'll send you my comments
on it soon.)
------ My comments on your comments -------
0. Sorry the paper was so hard to follow.
This tree example seemed so straightforward --
but apparently only to CS people...
Paul Cohen also had a hard time with it.
1. As to your worry about its enormous breadth:
The analogizer is (currently) being designed to deal with any inquiry of this form,
"Find `analogizing common theory' given two analogues" (yes, I did finally
learn to spell that word. If it wasn't so hard to state, I'd make
a case that "Analog" (as in digital) was in fact analogous to "analogue".
Note they both refer to a some sort of direct mapping
(from say sound waves to electronic sine waves in one case,
and from one model to another in the other).
I suspose most cognates can be considered analogous, pretty much by
construction/derivation. But enough digression; back to the plot...)
The purpose of those initial "dry-lab" experiments
is to help me understand first how to input these questions,
and second, what type of rules will be required to solve these problems.
It is very likely different types of analogies (eg like Gentner's
literary versus scientific) will have to handled differently -- that is,
processed using a different body of heuristics.
Finding these categories -- the dimensions which "cut" the space of analogies
at its axes -- is a major research area.
(I'd be very interested, by the way, to learn just how you organize this space.)
Notice I do NOT intend to laboriously enter all the heuristics needed.
My goal is rather to provide the organization for these rules,
(based on that structure of analogies I mentioned above,)
together with that general analogizer.
While performing this exercise I may realize the intractability
of so grandious and general a system --
e.g. there may in fact be no underlying common theme to these
diverse examples of analogy.
If they do turn out to be fundamentally different things,
each requiring a radically different type of processing,
I reserve the right to cut back the scope of my undertakings accordingly.
Side points:
First, I will clearly need to develop a bunch of "conceptual front ends" to
accomodate those nine types of analogy-problems listed in section 3.
This will probably be in the form of instructions to the user, telling him
how convert his type of question into a form of inquiry meaningful to the
analogizer.
This will be (a low priority) goal of the initial dry-labs.
Second, Tom D presented the opposite view:
he felt that the analogizer was too restrictive in terms of
the scope of problems it could handle.
For example, it cannot answer questions like
Why A is NOT like B,
or
"Find something like X",
as in "Given analogue A and a `mapping' (or partial theory) R,
find best analogue B".
BEGIN<DIGRESSION>
There is an obvious, quick and dirty solution to that second type of question,
at least when there is only a small class of B's to consider
(for example, those objects modeled in a data base).
The system could find that optimal B by
looping through those candidates, trying to find an analogy joining that B to A.
Each successful match is then checked to see if its cpt (common partial theory)
was "like" R (oh no -- will this require recursively investigating whether
that cpt is ANALOGOUS to R?).
Those analogues which pass this test are then ranked,
and the best such B is returned.
There certainly should be faster ways of finding that B, though.
Any way I'll think more about this, both later in this programme, and in point
5 below.
END<DIGRESSION>
2. Your confusion about what I must have meant by context must have stemmed from
my own confusion!
It seems clear that there is something else necessary to generate
(or even to simply understand) an analogy beyond just the pair of analogues.
The purpose of the context is to somehow encode that
"everything else which might be pertanent".
Just what does this include?
I've some ideas about some of the things which belong there --
two of those were presented in the proto-proposal,
and the digression below gives another type of contextual fact.
Finding what sorts of things go there is another big research area.
I will try to map out (well, at least preliminarily-sketch-out)
this space during those initial gedanken experiments.
BEGIN<Digression>
The context might also include things like the author of the analogy,
or at least give hints of his perspective and weltershaung.
For example, I remember once talking with a friend, X, about Oscar Wilde.
In what he considered but a minor shift of focus, he started talking about
the ancient Greek society. It was only when I realized that X
was gay that this connection (ie the abstraction common to both Wilde
and Greeks) became clear.
From his perspective this attribute was an important thing to consider.
That is, having this the "Author of this analogy is X" context helped me
understand his Wilde - Greeks analogy.
[Realize I didn't say how this a fact could actually be used by the analogizer.
Like me, it would need a rule like
"Rank highly those attributes which the author of the analogy considers relevant".
This rule would be resident in the heuristics KB.]
END<Digression>
Small points:
i. You asked how to distinguish between the context and the heuristics KB.
As you noted, one clear difference is their respective duration.
Another difference, which I guess never came out in that paper,
was the nature of those contextual things: they are facts, not heuristics.
They should each reflect some true fact about this particular analogy,
or the events which surround it (such as its author, or the type of question
it is intended to answer, etc).
ii. More on (my view of) Heuristic-DB heuristics.
First, they are fairly analogy independent.
(Realize all existing AI programs assume they are user-independent as well.)
Second, there are many classes of rules -- many were given in
the INPUT part of Section 2.2 -- each triggered at a different time,
to perform some different type of task.
One type of heuristic directly uses the contextual data, to guide the
search for the analogy. The
"Rank highly those attributes which the author of the analogy considers relevant"
rule is in this category, as is FindRelevantFactors.
Without such rules the analogizer may have different behaviour. Great!
(An ego-centric heterosexual, who never considered the source of the Wilde-Greeks
mapping, might never realize this "obvious" gay connection.)
The point here is that a contextual fact is a fact, regardless, and will be
included in the CONTEXT, independent of the rules present in Heuristics-DB.
In summary, all of the "individually" of the analogizer will be in the rules.
iii. I am curently "solving" the examples given in section 3 -- trying
to write them in the appropriate style to be answerable by the analogizer.
They have helped me considerably in understanding just what should go where --
indicating what types of heuristics I will need, what types of things should
go in the context, etc.
I'd be happy to mail you these worked through examples upon completion,
if you like.
3. It's interesting that you regard "Abstraction" as well defined,
but consider "theory" ambiguous.
Because I felt oppositely, (that Abstraction was the more loaded term,)
I switched from "theory" to "Abstraction".
Of course Mike and I are describing the same thing, just using different names.
4. I couldn't understand your question about "deep structure" until I reread my
paper. "Scare quotes" notwithstanding, I think I was (slightly) misusing
that term.
The superficial, top level formalisms imposed by some KR systems
make it very difficult to communicate some types of facts.
For example, non-binary relations are hard to express in a unit-slot-value
frame based system.
To avoid (well, minimize) this difficulty,
(i) facts are expressed in a more neutral system - predicate calculus
[Do I really mean "more NEARLY neutral"?]
(ii) the user (and the system) can define new relations, sparing both of them
the burden of rewriting a cumbersome expression each time.
(iii) the system includes machinery which allows the
inferencing engine itself to be modified.
(No, I did not discuss this in this paper. If you like I will elaborate
on this point in a follow up message.)
I feel strongly that (ii) -- the ability to define new terms --
is very important.
(By the way, an example of this is the LeadsTo relation, which was generated
as the transitive closure of a given relation.)
Of course these syntheses do not create anything which is totally new --
only combinations of other terms, using known techniques.
(Are people -- with our "hardwired" brains, and "school taught" methods for
problem solving -- really that different?
Regardless, I refuse to address that issue of "de nuvo" (sp) creation of ideas...)
However the fact that such terms were NOT present in the original description
of the problem makes this solution SEEM to have some deeper knowledge.
Continuing of this tangent one step farther:
My research programme section shows how concerned I am about "cheating",
-- how to prove that the answer wasn't already coded in.
Beyond the methodology mentioned there, I have no idea how to avoid this claim.
Do you have any suggestions of ways to circumvent this issue?
Finally, you said you were worried about my "coming to see deep structure" talk?
Could you elaborate on this? (Unless my comments above have canceled
that fear.)
5. Your point about "hard to justify analogies" is (as usual) a good one.
If this analogizer is to live up to my expectations of exhibiting "many of
the properties expected of an analogy" it should be easier for it to return
the other analogue before it can explain this answer.
[Finding the connection given the pair of analogues is, essentially, looking
for an explanation; the answer given IS a justification, and so it is meaningless
to ask how to justify those answers.]
Refering way back to point 1 above, this is one strong objection to that
quick and dirty "search thru everything" scheme -- the answer returned WILL
come complete with an explanation; which is needlessly expensive.
6. Natural selection vs Domestic selection heuristics.
Thank you for mentioning this.
It fits perfectly into the analogizer's framework
(given two analogues, find the cpt).
After mailing this letter I'll try to take your data and demonstrate
how the analogizer would address this inquiry. I think this will be
the ideal medium for us to understand one another!
------ End of my comments on your comments -------
A jumbled array of other miscellany follows:
7. Statement of personal philosophy/research methodology.
At several places during these explanations
(in particular when describing the purpose of those dry-lab experiments)
I've hinting at my perception of "the structure of the world".
To be more explicit, I'm a strong believer in axes.
I feel that almost any phenomena can be decomposed into a number of
(sorta independent or orthogonal) components,
and that finding those components/dimentions is an important first step towards
understanding that area.
(To paraphrase this research style: form before content.)
I also (apparently) assume that this structure will begin to present itself
as a few examples are worked out; and that this skeleton can be fleshed out
to its full shape by relatively straightforward extrapolation and abstraction.
Comments? In particular, do you think this will work with something as
vast and (currently) undisciplined as analogy?
8. New additions to the paper:
Since you saw the proposal I have added yet another box to that first figure --
to hold facts in general. The various inputs -- ie the inquiry and
the context -- will point to information stored there.
This will spare the user the arduous task of typing in "obvious" facts;
and also simplify some of the questions about how to encode such
information, and where to store it.
9. Minor questions:
i) Any cute suggestions for a name to replace the quinte-syllabic "analogizer"?
ii) I'm now reading thru Ortony's "Metaphor and Thought", cover to cover.
While some of it seems irrelevant (to the world at large,
not just my particular task), other sections have been very helpful
(esp Ortony's intro, and some of Searle's stuff). Any suggestions of what
I should realize when I finish this book? Lakoff's stuff? or ...
10. I just realized that you didn't have to struggle with those
@ this and that, the absense of bibliography, etc.
SCRIBE, it turns out, has a /F switch which produces a "file" version of the
text file, with pages and other nice features. If I forget to transform
my files, typing
@ R SCRIBE <cr>
* thesis.mss/F <cr>
will produce that desired readable file.
11. There actually is a good chance I will be east this winter,
vising brother Miles in MIT, after attending wedding (Jan 18) in Chicago.
I'll certainly let you know if I do go.
12. Overall comments
I got the impression that you were fairly disappointed with the proposal
as it stood. Was the problem superficial -- as in,
"I had a hard time understanding the examples"?
If so, do let me know which parts were the worst,
and I'll do my best to elaborate these. (This exercise is of considerable
importance to me, on both the long and short run.
Not only will it help me to clarify my ideas, but it will
improve my presentation skills (dramatically I hope)!
If your concern was deeper, than please be more explicit.
What would you have liked to see, for example?
Perhaps we can synthesize something which I feel is doable,
and you consider worthwhile.
Finally, please continue to be direct -- even (unlike this review) cruel.
I really do want to produce a respectably peice of research; as opposed
to only a running program.
Critical comments from people as knowledgable as you be of much guidance
in this respect.
------
That's all for now. Hope all is going well there.
(By the way, we too are having a "cold spell" here -- it's almost
dipped to freezing in the dead of night! What - no sympathy from you?)
Happy Thanksgiving!
Russ
Lindley's paper - ca 21 Nov 1981
REASONING BY ANALOGY IN THEORY CONSTRUCTION: DARWIN AND SELECTION THEORIES
by Lindley Darden
Abstract
This paper examines the hypothesis that analogies may play a role
in the generation of new ideas that are built into new explanatory theories.
Methods of theory construction by analogy, by failed analogy, and by modular
components from several analogies are discussed, as are constrasting
analyses of analogy by Mary Hesse (direct mapping) and Michael Genesereth
(shared abstraction). The case of Charles Darwin's theory of natural
selection illustrates theory construction by analogy. Finally, an
"abstraction for selection theories" is shown to be the structure of
a number of theories.
!Outline
introduction
assumption:data, empirical laws, explanatory theories (new ideas,mechanisms)
desired characteristics of analysis of reasoning in discovery
don't expect infallible logic that will yield true hypotheses
only want way of obtaining one or more plausible hypotheses to be tested
Popper, Hempel vs. Hanson
analogies as a source of new ideas
questions about analogies:
What is an analogy?
Are there types of analogies?
How do we find analogies?
How do we tell good analogies from bad ones?
How do we use analogies to construct scientific theories?
analogy as direct mapping between similar things
Hesse and Oppenheimer
modular construction using more than one analogue piecemeal
analogy as shared abstraction
AI abstractions have more semantic content than Hesse's formal analogy
Genesereth e.g. hierarchies, particles and waves
similarity in direct mapping::identity in shared abstraction
Darwin case
domestic selection-natural selection
gets idea of selector at abstract, not specific level
Malthus--generalization-specialization
need to keep analogue available--neuter insects and stocks of peas
abstraction of selection theories
variation, select among variants, increase in number of selected ones
examples of other selection processes:
clonal selection
Darwin on plant movement
social Darwinism, cultural evolution
operant conditioning
verdict still out: evolutionary epistemology
! As a historian and philospher of science, I am interested in the process
of the construction of new theories. A hypothesis with which I have been
working lately is that analogies may play an important role in the
generation of new ideas that are built into new theories. That is
the hypothesis that I will explore in this paper.
In order to make clear the locus of my discussion, I would like to
present an over-simplified view of the levels of organization of scientific
knowledge. The three levels are the following: data, empirical
generalizations, and explanatory theories. At the lowest level of generality
are the data, particular statements about particular facts. For example, if
we consider data from genetics, in a cross between a yellow pea plant and
a green pea plant, all the peas of the first generation of hybrids are
yellow; if the hybrids are self-fertilized, the second hybrid generation
has a ratio of three yellow peas to one green pea.The ratio of three
yellow to one green is a datum of genetics. For the present, I
wish to ignore any possible influence of prior theory on the data here
discussed. Next, we have the empirical generalization which can be obtained
by looking for regular patterns in the data; for example, the empirical
law that in the second hybrid generation, the ratio of dominants to
recessives is 3:1. Empirical laws contain no new concepts that cannot be
completely specified in terms of the data; a "dominant" trait simply is
that trait that appears in the hybrid. However, explanatory theories have
new concepts, not found in the data and empirical generalizations, which
serve in the explanation of those data and laws. For example, the concept
of the gene is built into the theory of the gene which serves to explain
the 3:1 ratios by postulating the segregation of genes in the formation
of germ cells.
The focus of my discussion here is not on the discovery of new data
or new empirical generalizations but on how scientists discover new concepts
and use them in the construction of new explanatory theories.
What can philosophers hope to understand about this process of
the construction of new scientific theories? A prevailing view
has been that the discovery of new theories is a matter of the individual
psychology of the scientists, that there is no "logic of discovery."
Karl Popper (1960) is a prominent proponent of this view and Carl Hempel
(1966,p.14) argued that there can be no mechanical rules for producing
the novel concepts found in theories. Although N. R. Hanson (1961)
attempted to provide a logic of discovery, which he called
"retroductive reasoning," he merely hinted at the way plausible
hypotheses actually could be constructed. Philosphers are unlikely to find,
as Hanson realized, an infallible logic of discovery. Instead, our task
should be to find patterns of reasoning that can, with some measure of
reliability, provide plausible hypotheses worthy of testing.
One idea that Hanson mentions, but does not develop in detail, is that
analogies may be useful in discovery. A series of questions need
to be answered if we are going to understand how analogies function
in theory construction.
These questions are:
1. What is an analogy?
2. Are there types of analogies?
3. How do we find analogies?
4. How do we distinguish good from bad analogies?
5. How do we use analogies to construct scientific theories?
6. How can we test a proposed pattern of reasoning by analogy to
see if it is adequate for constructing plausible hypotheses?
I will not be able to completely answer all of these questions in
this paper, but I want to begin the task. I will be drawing on literature
from the fields of philosophy of science and artificial intelligence
(for short AI) on the use of analogies in theory construction. Also,
I will discuss in some detail the structure of the analogical relations
in Charles Darwin's theory of natural selection and discuss the general
type of theory of which Darwin's is an instance.
The philosopher of science who has dealt most extensively with
these questions is Mary Hesse in her book MODELS AND ANALOGIES
IN SCIENCE (1966). Hesse's key points are best illustrated by one
of her examples. (See Fig. 1) She compares sound waves and light waves.
The properties which are similar she designates as the positive analogy;
the dissimilar properties constitute the negative analogy;
the neutral analogy involves the properties of the analogue which may
or may not be present in the subject field. In her example, the properties
of light are the subject of investigation. Light has properties that are
similar to properties of sound waves and the neutral analogy of a
medium for the waves to travel in provided a plausible, but subsequently
disproved, hypothesis about the existence of the ether. The horizontal
relations between the analogue and the subject are those of similarity;
the vertical relations among properties of the analogue should be,
according to Hesse, causal relations, in the weak sense of a "tendency to
co-occurrence." (Hesse, p.77) Hesse indicates that the analogue may
be important, not only in the original stages of theory construction,
but also later: if the theory faces anomalies, the neutral analogy
may be exploitable for further theory construction.
I find Hesse's representation scheme of lining up properties of
the analogue and subject to be a helpful one; it is much like
frame-structured representation schemas used in AI systems.(Minsky,1975)
Hesse's form of representation has the disadvantage that it does not make
clear what the causal interconnections are between which properties.
Furthermore, the relation of similarity is difficult to judge. Also, it is
difficult, in some cases, to decide whether a given property is an
example of positive, negative or neutral analogy. I will illustrate these
critiques as we look at the case study of natural selection. But Hesse's
schema for theory construction by analogy may be a productive one
when adequately similar analogues can be found.
Hesse does not tell us what we are to do when postulated causal
connections fail, such as her own example of the postulation of the
medium for light waves. The physicist Robert Oppenheimer in an
insightful paper of 1956, that Hesse does not cite in her
1966 book, discussed the role of analogies in discovering
new theories. Analyzing the stages in the construction of the wave
theory of light, Oppenheimer proposed that scientists came to the
study of light phenomena with past experience of the nature of waves.
But when the postulated medium for light waves was not found, it forced
scientists to revise their previous view of necessary connections,
to sever the notion of a wave from that of a medium. Thus, a failed
portion of the neutral analogy forced scientists to a creative new
concept.
From Hesse and Oppenheimer we can extract two methods of theory
construction by analogy: look for a relevantly similar analogue and
exploit the neutral analogy; if this process fails, consider severing
connections between properties that were previously thought to be necessary
connections.
But what if a relevantly similar analogy cannot be found, or
what if the severing of what we thought were causally correlated
properties is not sufficient for the construction of a theory?
Little discussed in the analogy literature is the possibility
of using more than one analogue, in a piecemeal or modular way, to construct
a new theory out of old, but previously unrelated, pieces.
This is an additional method of analogical reasoning that I
will discuss and illustrate in the structure of the theory of natural
selection. Thus, I hope to give meaning to the cliche that creativity
may result from putting old ideas together in new ways.
Before turning to the case study, however, I want to discuss an
alternative analysis of what an analogy is that provides us with yet
another method of theory construction. Mary Hesse's primary way
of characterizing an analogy is as a direct mapping between a subject
and its analogue based on the similar properties between the two.
Hesse does also discuss formal analogies in which two things share
only the same uninterpreted mathematical formalism. Michael Genesereth
(1980) is a computer scientist who has developed a partially
implemented AI system called ANALOG to find and use analogies.
Genesereth has an alternative analysis of what an analogy is.
According to Genesereth, "many analogies are best understood as statements
that the situations being compared share a common abstraction."(p.208)
[Is this original with Mike?]
Genesereth's abstractions are not merely Hesse's formal analogies,
since Genesereth's abstractions may have more semantic content than an un-
interpreted formalism. He continued:"For example, when one asserts that the
organization chart of a corporation is like a tree or like the taxonomy
of animals in biology, what he is saying is that they are all hierarchies.
With this view, the problem of understanding an analogy becomes one
of recognizing the shared abstraction."(p.208)
Genesereth thus shares a view explicitly discussed by the
psychologist Dedre Gentner in an excellent paper entitled "The Structure
of Analogical Models in Science," (1980) in which she argues
that the relations between the analogue and the subject are those of
identity rather than similarity, but identity at an abstract level.
In fairness to Hesse, I should mention that she thinks in some cases
the relations between the directly mapped properties are those of identity
rather than similarity. Diagrams of interpretations of analogy via
Hesse's direct mapping vs. Genesereth's shared abstraction are in
Figure 2. [two sets of lines vs. two sets with a third above].
Conceptually what is the relation between similarity and identity?
Hesse does not provide one. Let me make a tentative suggestion:
Two things are similar if on some analysis into component properties,
some of the properties are identical, while others are not identical.
If my suggestion is correct, then direct mapping between similar things
would be decomposable into identity and difference mapping between
abstracted components.
Thus the way Hesse's and Genesereth's interpretations
would differ, if I am right here, is on whether the negative and neutral
analogy are specified (in direct mapping) or whether only the positive
analogy is part of the analysis.
I will explore the idea of reducing
similarity to identity and difference relations as we look at the Darwinian
case study.
From the idea of analogy as shared abstraction we can extract another
method of theory construction. Explicitly devise abstractions of
theories or other things that might serve as analogues in theory
construction. I suspect that humans usually are not explicitly aware
of the abstract identity relations between two things that they
recognize are similar, so formulating abstractions will require analysis.
Once one has a set of abstractions, then the first stages of theory
construction involve a search through the set of abstractions to see
if an appropriate one (according to some criteria) is found. If so,
then it could be instantiated for the case in hand. If not, then one
must fall back on direct mapping to one or more specific analogues.
The shared abstraction vs. direct mapping methods have various
advantages and disadvantages. For computer systems, identity matches
are trivial, similarity very difficult.
Since the shared abstraction has a limited number of identity matches required,
then it will be better.
However, the shared abstraction method requires that an
adequate abstraction be constructed; any given theory or object may
be analyzable into numerous different abstractions. Criteria for
abstraction construction would have to be devised. Direct mapping, for
humans at least, requires no prior analysis: a similar analogue becomes
the focus for theory construction. Direct mapping also has the advantage
of having the neutral analogy, perhaps even previously unexplored neutral
analogy, available for further steps of theory construction. We will see
an excellent example of this use of neutral analogy in the Darwin case,
as well as discuss the relative merits of direct mapping and shared
abstraction with regard to selection theories.
!CASE STUDY:DARWINIAN NATURAL SELECTION
A case of analogical reasoning in theory construction is that of
Charles Darwin's natural selection. We will here be examining not the
claim that forms have evolved, but the theory that provides the
mechanism for that evolution, namely natural selection. Historians
poreing over Darwin's detailed notebooks have come to varying conclusions
about the importance of the various components that I am about to discuss.
(Ruse, 1973a, 1973b; Herbert,19//) I have no desire to enter into
those detailed historical disputes here. The picture I am about to draw
is consistent with Darwin's autobiogrphical account of his steps of
theory construction. Since that account was written many years
later, it is of course open to question as to whether Darwin
remembered the steps correctly. However, I am actually more concerned
with the conceptual relations among the various components of the theory
and its analogue rather than with the psychological details of
Darwin's own thought processes.
Figure 3 shows the two different sources for the ideas that Darwin put
together piecemeal to make up the theory of natural selection: domestic
breeding and Malthus's ESSAY ON POPULATION. Domestic selection is an
analogy to natural selection; the relations between the components of
domestic selection and natural selection can be analyzed, I will argue,
into relations of identity and difference.
The relation between Malthus's
conclusion about human populations and a component of Darwin's theory
is that of generalization: Darwin generalized to all of natural populations
what Malthus had proposed for humans.
Figure 3 shows the structure of the interrelations between
domestic selection, natural selection and Malthus's ideas.
Darwin argued that the inherited variabilty found in domesticated animals
and plants was much like that found in nature. He was interested only in
inherited variability. As Darwin said in the ORIGIN: "Any variation which
is not inherited is unimportant for us."(Darwin,1859, p.75) He needed
variations that would be passed on to offspring as the raw material
for species change. However, he argued that domestic forms showed "greater
variablity," (Darwin,1859,p.71), which I interpret to mean than the
range of variants was greater. On this point of difference Darwin said:
"When we look to the individuals of the same variety or subvariety
of our older cultivated plants and animals, one of the first points which
strikes us is, that they generally differ much more from each other, than
do individuals of any one species or variety in a state of nature."
(Darwin, 1859, p.71).
Darwin had little understanding of the causes of variation, which
genetics was later to supply, but he argued that the causes of variation
in nature and in domestic stocks were likely to be the same.
Thus, I think it is correct to say that Darwin
believed that the variability found in domesticated stocks and in nature are
part of the same inductive class. This portion of the analogy therefore
provides evidence for the existence of the kind of variability that
Darwin's theory of natural selection required.
The relations between variability in domestication and in nature are
thus those of identity of class but difference in quantity. Presumably
Hesse would say that the relation between variability in the two cases
is that of similarity, but this anaysis shows that similarity can be
reduced to identity and difference by a decomposition into the properties
being compared.
Of selection Darwin said in his AUTOBIOGRAPHY: "I soon perceived
that selection was the keystone of man's success in making useful races
of animals and plants. But how selection could be applied to organisms
living in a state of nature remained for some time a mystery to me."
(Darwin, 1876,p.42) In Figure 3, I show the relations between domestic
selection and what is occurring in nature to be that of a positive
match at the abstracted level of some mechanism of selection operating
in the two cases. But there is a negative match on the agent of selection
and the criterion of selection. Darwin knew that the agent of selection had
to differ in nature since human breeders could not be the agents.
Also the criterion for selection had to be such that it produced forms
not adapted to human purposes but adapted to natural environments.
Hesse's categories of positive, negative and neutral analogy
do not easily apply to the relation between a selector in breeding
and the puzzle that that posed for Darwin about nature. At the abstract
level of some sort of selective mechanism there is positive analogy;
at the component level of agent and criterion we have negative analogy.
But most importantly, this part of the analogy posed a question that
was crucial for further development of the theory, namely what plays the
role of selector in nature? This role of providing for further theory
development is a role that Hesse attributes to neutral analogy.
Note the role that the analogy has played with regard to selection.
It indicated that some causal mechanism must be operating in nature
if the result, namely adapted forms, was to be achieved. But it left as
a blank what exactly the selective mechanism was.
This may be an example
of a general role played by analogues: they exhibit the same abstract
structure but differ as to how the details are to be filled in.
The result of domestic selection is the origin of new varieties
adapted to human purposes. Darwin took such varieties to be nascent species.
Conseqently, the existence of a mechanism to produce such new forms in
domestic selection provided weak evidence that some similar mechanism might
be operating in nature. His major problem came to be to find such a
mechanism.
In his AUTOBIOGRAPHY Darwin said: "In October 1838...I happened to read
Malthus on POPULATION, and being well prepared to appreciate the struggle
for existence which everywhere goes on from long-continued observation
of the habits of animals and plants, it at once struck me that under
these circumstances favourable variations would tend to be preserved and
unfavourable ones to be destroyed. The result of this would be the
formation of new species. Here, then, I had at last got a theory by
which to work...."(Darwin, 1876,pp.42-43)
The relations between Darwin's theory and Malthus's ideas is shown
in Figure 3. Malthus was discussing population phenomena. At a
high level of abstraction, this matches Darwin's concern with populations.
But Darwin was concerned with variants in a population and Malthus
ignored the variability in the populations he discussed. Malthus's major
concern was to show that human populations would soon outstip their food
supply, since humans' rate of increase was greater than their ability to
bring agricultural lands into cultivation. Malthus mentions that in
"the animal and vegetable kingdoms," more seeds are produced than nature
has room for. (Malthus,1798,pp.71-72) Darwin generalized this to an
incessant "struggle for existence" through-out nature.
Thus, the relation of struggle for existence to Malthus's key idea is
not analogical but that of specialization-generalization.
This analysis indicates that Darwin constructed his theory
piecemeal, with modules coming both from the analogy to domestic
selection and from Malthus's ideas. The relations among the components
can be analyzed into identity and difference at various levels of
abstraction as well as generalization- specialization.
Once the theory is constructed, is there any continued role for the
analogy? The Darwinian case provides an excellent example of the way the
analogy can be exploited in further theory construction to account for a
seeming anomaly, a role that Hesse argued analogies play. Darwin
was concerned with the problem of neuter insects. He said that this
problem "at first appeared...insuperable, and actually fatal to my
whole theory." (Darwin, 1859, p.257) Since neuter insects do not
reproduce, how can the characteristic of being neuter be passed on to
succeeding generations; in other words, how can natural selection operate
on the character of being neuter? Darwin went back to domestic selection to
solve this problem. He said: "...a well-flavoured vegetable is cooked,
and the individual is destroyed; but the horticulturist sows seeds of the
same stock, and confidently expects to get nearly the same variety...."
(Darwin, 1859,p.258) Darwin gave several other examples from domestic
breeding and then applied the principle to insects. An individual
is selected from the stock that has the "tendency to produce sterile
offspring" (p.259) along with fertile offspring. Thus, Darwin once
again appealed to domestic selection for an additional stage of theory
construction. The detailed analogue is here seen as having the
advantage of possessing additional properties, not considered in the
original act of theory construction, that can be used in anomaly
resolution. [Note: I thank Lars Rodseth for calling this use of domestic
selection to my attention.]
ABSTRACT FORM OF SELECTION THEORIES
Once Darwin had constructed the theory of natural selection
by direct mapping piecemeal from previously unrelated components, he
established a type of scientific theory. One way of abstracting the
components of selection theories is the following:
I. An array of variants is generated.
II. Selection of a subset of variants occurs.
III. After selection, the pool of variants is different.
Each of these abstract components has abstract subproperties. The
generator or the cause of the variants will determine the number of
variants, the number of different types of variants, how much each
variant differs from another. Different evolutionary theories have
differed in their claims about such properties of the variants.
Darwin had proposed numerous small variations, which he called "individual
differences," as the most important type of variation that natural
selection acts on. Hugo de Vries, in his MUTATION THEORY (1903,1904),
proposed an alternative to Darwinian natural selection by proposing
that large scale mutations occurred that could give rise to a new
species in a single generation. Stephen Gould (in ONTOGENY AND PHYLOGENY,
1977) has recently proposed that large scale changes in developmental
timing may be more important in evolutionary change than small scale
point mutations. Humans have many properties of baby apes: maybe a
large scale change kept our ancestors from reaching ape maturity.
If the generator of variants had the capacity to produce only
adapted variants, then the subsequent step of selection would not be
necessary in either domestic or natural selection. If the second
step is not needed, then the theory proposed is not a selection
theory. In so-called Lamarckian evolution, in which characters that
are acquired as a result of an adaptation to an envirnoment during the
life of an individual are passed on to offspring, the generator of
variants eliminates the need for selection. Mendelian genetics has shown
that no such mechanism for the generation and inheritance of
acquired characters exists. Although it failed, such a so-called
Lamarckian theory represents, nonetheless, an alternative type of
theory to the selection type: a good analogy to human activity
would be not domestic selection but human tool-making.
Fashioning a tool to fit a need is like an organism developing
a characteristic in response to an environmental demand. The
criteria that would have operated in the selection process have
been incorporated into the mechanism of generation of variants and
have eliminated to need for the selective step. Thus when faced with
a problem of explaining the orgin of new adapted somethings, either
of two abstractions could be evoked: the selection type or the
tool-fashioning type.
Subproperties under the selection mechanism include the agent
of selection (That sounds a bit anthropomorphic; perhaps a more neutral
term can be found.) and the criteria on the basis of which some variants
are selected. Contemporary controversies between neutralists (see
King and Jukes, 19←←) and selectionists have focused on whether variants
can become fixed in a population as a result of random processes that
do not result in the adapted variants tending to survive. Though
the pool of variants is different in succeeding generations in
populations where random drift has occurred, that pool does not share
a set of characteristics as a result of a criterion being applied during
a selective process.
In the final component of selection theories, namely that a different
array of variants results, a temporal dimension is apparant:
the final component is a result of the causal interaction of a
selective mechanism operating in time to produce a different state of
affairs at a subsequent time. In domestic and natural selection the
temporal dimension is the next generation of organisms; thus variability
that is passed from parent to offspring, i.e.,inherited variability,
is the only variability important for selection. But in the abstraction
of selection theories, no requirement for different generations is included.
I have chosen to express the components sufficiently abstractly so that
they apply to additional theories that do not include different
generations of organisms but only a different pool of variants at a later
time.
A surprising number of different theories are specializations of this
abstract type of selection theory. A biological theory that fits this
type beautifully is Jerne's (1955) natural selection theory of antibody
formation, subsequently modified by Burnet (1957) to the theory of clonal
selection for the production of antibodies. The problem is to explain how
the body forms antibodies that are able to deactivate large numbers of
invading, foreign substances, called antigens, while not
attacking the body's own substances. Jerne (1966), in reflecting
on the reasoning he used in the formation of the theory, said:
"three mechanisms must be assumed: (1) a random mechanism for ensuring
the limited synthesis of antibody molecules possessing all possible
combining sites, in the absence of antigen, (2) a pruging mechanism for
repressing synthesis of such antibody molecules that happen to fit
auto-antigens, and (3) a selective mechanism for promoting the synthesis
of those antibody molecules that make the best fit to any antigen
entering the animal. Thus Jerne proposed (I.) a mechanism for producing
a random array of antibodies, (II) both negative and positive selection
processes to eliminate antibodies against bodily substances and cause the
reproduction of antibodies that fit an invading antigen, with the
(III.) result that the random array of antibodies is altered to a
non-random array. Jerne's theory proposed that natural antibodies
circulating through-out the body would attach to an antigen, carry
it to a phagocytic cell and cause that cell to produce more antibodies
like the selected one. (Jerne, 1955, p.849)
Although Burnet endorsed much of Jerne's theory, he
he objected to the mechanism of positive selection and proposed
an alternative. Burnet said: the "major objection is the absence of
any precedent for, and the intrinsic unlikelihood of the suggestion, that
a molecule of partially denatured antibody could stimulate a cell
into which it had been taken, to produce a series of replicas of the
molecule....it would be more satisfactory if the replicating elements
essential to any such theory were cellular in character ab initio [italics]
rather than extracellular protein which can replicate only when taken
into an appropriate cell....[this idea is developed here] from what
might be called the 'clonal' point of view." (Burnet, 1957, p.67)
Burnet proposed that the mechanism of variation was somatic mutation,
namely changes within cells of the body. The selective mechanism operated
by antigens being recognized by molecules on the cell surface.
After a type of cell recognized an antigen it would be stimulated
to reproduce into a clone of its type. Of this theory Burnet said:
"Such a point of view is basically an attempt to apply the concept
of population genetics to the clones of mesenchymal cells within the body."
(Burnet, 1957, p.68) Thus, Burnet explicitly appealed to the analogy
between mutation with natural selection and his theory of somatic mutation
and clonal selection.
Burnet argued against a prior theory of antibody formation that
was of the tool-fashioning type. The template theory of antibody formation
proposed that the body fashions an antibody on the invading antigen
that functions as the template for the antibody's construction.
The Jerne-Burnet selection theory was subsequently confirmed and
expanded. (Golub,1981)
[Note: I would like to thank Marcia Kraft for calling
Burnet's use of analogy to my attention and for supplying me with
copies of the original articles. I look forward to Marcia's detailed
analysis of this case, which is in preparation.]
A number of other theories can be seen as selection theories.
Whether direct mapping to Darwin's theory of natural selection,
use of the abstract type of selection theories, or other methods
of theory consturction played a historical role in the construction
of these theories will require additional historical research
to determine. Here I will merely call attention to the fact that
their structure fits that of the abstraction for selection theories.
Darwin in THE POWER OF MOVEMENT IN PLANTS (1880) explained, for
example, [mine, not Darwin's] the coiling of a pea tendril around a wire as
a result of natural complete circular movement of tendril being altered
(selected) after encountering an object, so that subsequent movement is
in the direction of the wire.
The variant pool was complete circular movement,
the object encountered provided the selective agent
in that direction, and the altered pool was the subsequent movement only
in that direction. (Ghiselin, 1969,p.196)
Operant conditioning works by selectively reinforcing some
behaviors out of an original array to alter the subsequent behavior.
The rat in a maze, for example, engages in random movements. Those in
the direction of a food bar are reinforced, until the rat learns to
move non-randomly. The original array of variants is thus random
movement. Humans are the agents of selection, in the experimental case,
and the criterion for selection is movement toward the food bar. The
altered array of variants is the movement after the reinforcement.
Various attempts to apply selection theories to social phenomena
have been made as far back as social Darwinism in the nineteenth century
and as recently as sociobiology in the last few years. Whether the
mechanism for producing and transmitting types of social behavior is
genetic or environmental has been hotly debated.
A final type of selection theory, that may be of more interest to
philosophers is that of evolutionary epistemology. Stephen Toulmin
in his book HUMAN UNDERSTANDING (1972) argued for a view of the
development of knowledge as a result of "a dual process of conceptual
variation and intellectual selection." (p.200) Neither Toulmin nor
others within this epistemological tradition have had much to say about
the mechanism for the production of new concepts. I have been arguing
that use of analogical reasoning may provide a means of constrained
generation of plausible new ideas that then may be selected according
to the criteria scientists use for justifying theories. Whether
selection-type theories or tool-fashioning theories will ultimately
be of use in understanding the growth of knowledge remains to
be seen.
Recursive self-reference is proving to be a powerful technique
in artificial intelligence. Having now come full-circle to my
starting point, namely a discussion of the way analogies may be used
as a mechanism to generate new ideas, it is no doubt time to stop.
[Conclusion to be added.
Methods of theory construction in order of preference:
Use interfield connections (Darden and Maull, 1977; Darden, 1980)
Use shared abstraction
Use analogy
Use failed analogy to be partial set of properties
Use piecemeal construction with several analogies]
!Figure 3, Darwin's theory of natural selection
domestic nature Malthus
selection
(1)inherited (1')inherited
variability + variability population
in a group in a group + phenomena
(1.1)greater (1.1')less
than in nature than in domestic
due to geater > stocks
variety of condi-
tions in which
stocks are raised
(1.2) internal (1.2')internal
causes of varia- + causes unknown,
bility unknown, same as in domestic
same as in nature stocks
(2)selection + (2')selection
(2.1)agent: (2.1') agent:
human breeder--------> ? generalization greater rate
struggle for <------------- increase of humans
existence than food supply;
checks on animals
in nature
(2.2)criterion: (2.2')criterion:
adapted for + adapted for
human purposes - natural
environment
(3)result: (3)result:
gradual origin gradual origin
of new forms + of new forms
adapted adapted
for human - to natural
purposes environment
mechanism:favorable
variants tend to survive;
unfavorable tend to die
∂TO DARDEN@SUMEX, CSD.GENESERETH@SCORE 13:24 1-Dec
Comments on your paper
Lindley -
Sorry to take so long to comment on your paper -- I've been
largely out of action this last week with (the fatigue associated with)
a sore throat, taking time only to finish thesis-proposing.
Anyway, it took me several readings to get (most of) the ideas you were
presenting.
You philosophers must be a quicker lot than us AI types,
being able to absorb all of that from a single hearing!
Before I tire you with a variety of little comments,
I have one major point. I differ strongly with your contention that
Thus the way Hesse's and Genesereth's interpretations would differ, if I
am right here, is on whether the negative and neutral analogy are
specified (in direct mapping) or whether only the positive analogy is part
of the analysis.
Mike's scheme is far richer in mechanisms for finding similarity between
two proposed analogues. I will present some of these additional methods
first, and then address this issue of how to deal with negative and neutral
matchings.
[Side point: Isn't calling these matched features "positive ANALOGIES",
really a type error?
(I feel similarly about calling corresponding but unmatched slots
"negative ANALOGIES", and non-corresponding slots, "neutral ANALOGIES".)]
I should preface what follows with a statement of ignorance:
I have yet to read Hesse's own description of her proposed sytem;
While I think my sources have accurately portrayed the salient features,
I may still be considerably slighting her approach.
These comments can still be taken as valid objections against any
system based only on a simple comparison of the frame representations
of the analogues.
[By frame representation I am referring to anything using only the
unit-slot-value formalism.]
Let me begin by describing what (my understanding of) Hesse's scheme can do,
expressed in the analogy-as-shared-abstraction language.
Take as an example that Tom and Russ are analogous
because they share the same values for the several slots (ie properties) --
including Gender, Occupation, General-Interest.
[The term "slot" refers to binary relation itself.
Hence the slot of (Age Russ 26) is Age.]
Hesse would line up these slots and give their values for
Tom and Russ.
Russ Tom
-----------------------------------
Gender + | Male Male
Occupation + | Student Student
GeneralInterest + | {Analogy, Beer, {Analogy, Beer,
| AnnoyingLindley, AnnoyingLindley,
| FolkDancing, ...} MovieAttending, ...}
Age - | 26 27 [<- random guess]
Advisor - | DBL BGB
ReadingCommittee ? | {DBL, MRG, ...} {BGB, DBL, ...}
The correspondences are easy to see where the values are
EQUAL, (here for Gender and Occupation);
the GeneralInterest case would be a bit trickier
-- but some sufficient-overlap rule would be probably cover this case.
Slots like Age or Advisor are considered negative aspects of this analogy.
The common abstraction would be generated, here, by just listing these
three shared properties, omitting the rest.
Hence the common theory would be the sentence
(Gender x Male) & (Occupation x Student) &
(GeneralInterests x {Analogy, Beer, AnnoyingLindley})
where x would be mapped onto Russ or Tom, respectively, when this theory
is "instantiated".
This shows two methods which can be used to form an abstraction:
(1) throwing away some slots and their values, (here Age and Advisor),
and (2) generalizing the value of a given slot
(as we did by forming
(GeneralInterests Russ {Analogy, Beer, AnnoyingLindley})
from
(GeneralInterests Russ {Analogy, Beer, AnnoyingLindley, FolkDancing, ...})
As best I can tell, these are the ONLY methods provided by Hesse's scheme.
Let me propose a few others:
[Defn:
An "n-ary proposition" is an atomic proposition containing an n-ary relation.]
(1. Certain slots may be thrown away.)
(2. The value of a given slot may be generalized)
3. Properties themselves (ie the various slots) may be generalized
4. We can
a. throw away various n-ary propositions,
b. generalize the argument values of some n-ary propositions,
c. generalize the relation itself of some n-ary propositions,
where n>2.
5. We can also deal with general (non atomic) predicate calculus expressions.
6. Such expressions can be augmented with meta-level (or 2nd-Order) statements
[Notes (a) 4a-4c would reduce to 1 - 3, if n=2.
(b) this list is NOT meant to be exhaustive. There are many other methods.
Example: The nature of a relation symbol can be "extended" --
A relation involved with one analogue can be commoned
with another symbol of another arity, in some cases.]
Now for some examples, to illustrate that (i) 3-6 are useful abstracting
mechanisms, and (ii) that they are hard to do using a standard frame based
system.
Generalizing the slot, (3,) is a useful trick is when we want to
note the similarity of
(Advisor Russ DBL)
and
(ReadingCommittee Tom DBL).
Here we need to state that
(MoreGenl Advisor ReadingCommittee),
in just the same way that that 3-ary set above was a generalization of the
4 member superset.
Notice this means that
(ReadingCommittee x DBL)
is a feature in common to both Tom and Russ.
It should be possible to indicate that an object participates
in a non-binary relation.
This is quite difficult to encode in the unit-slot-value formalism.
For example, how would Hesse encode the fact that Russ has
given his thesis-proposal to his advisor?
Of course you could have a GaveThesisProposalTo slot, whose value
is "His advisor"; or use a GaveToAdvisor slot, with the value
"Thesis proposal". Seems pretty flakey -- ie one would have to explicitly state
that GaveThesisProposalTo was similar to GaveThesisTo, GaveFrisbeeTo, or
even to GaveSomethingOrOtherTo ...
The "natural" alternative is use a statement like
(Gave Russ "thesis proposal" "advisor")
Clearly this is a useful and relevant fact
-- Russ and Tom should be more regarded as more similar,
if we know that each h has given his advisor a thesis proposal.
As with slots,
any given abstraction of Russ might or might not include this fact.
That is, as 4a claims, an abstraction could be formed by throwing away
an n-ary proposition.
Onto 4b: What if Russ had only given a "draft of thesis proposal" to this
advisor? This should still match against Tom, who gave his advisor an actual
"thesis proposal". So we might generalize that 2nd argument to the Gave
statement above, to find a form which unifies against both
(Gave Russ "draft of thesis proposal" "advisor")
(Gave Tom "thesis proposal" "advisor")
-- such as
(Gave x "version of thesis proposal" "advisor"),
where
"version of thesis proposal" is a generalization of both
"draft of thesis proposal" and "thesis proposal".
(Simiarly we might generalize "advisor" to "member of reading committee",
or "interested professor".)
Hence any of the arguments of the proposition might be generalized in the
the abstraction (or even any subset of them).
[We might want to note that both Russ and Tom gave something to someone.]
4c is just like the case for 3 above:
we can could have Generalized from Handed (or Sold, or Lent, ...) to GAVE,...
and then up to a CD like PTRANS (see Shank, etal.)
This again is useful information to use when matching.
Considering 5:
The scare quotes above were designed to postpone the issue of how
to actually say "his advisor".
Notice it is more relevant to match
(Gave Russ "thesis proposal" DBL)
with
(Gave Tom "thesis proposal" BGB)
than with
(Gave Tom "thesis proposal" DBL),
given that
(Advisor Russ DBL),
whereas
(Advisor Tom BGB).
What we really want is an abstraction like
(Exist a. ((Gave x "thesis proposal" a) & (Advisor x a))).
In predicate calculus this is easily said -- but in the more restricted world
of frames this is virtually impossible to indicate.
Note in this particular case we could have stated
(Gave x "thesis proposal" (Advisor x)),
which would work for this particular existential variable.
However we may want something like
(Exist a. ((Gave x "thesis proposal" a) & (Gave a "Research-Grant" NSF))).
-- ie x gave his thesis proposal to someone who has a Research Grant from NSF.
Note this case doesn't skolemize so nicely as the first.
[Of course we should do the same thing with that other phrase --
"thesis proposal" -- as in
(Exist a,tp. (Gave x tp a) & (Advisor x a) & (ThesisProposal x tp)),
but this requires only the same operations shown above.]
In other cases we may want universal quantification, or various embedding
quantifications, in the abstracted expression.
There may be other information associated with a proposition -- for example,
its epistemological status (of simple assertion, or default assumption,
definitional attribute, etc.)
For example, the fact that
(Color Albino White)
is a definition, whereas
(Color Swan#33 White)
is a simply an assertion, and
(Color Swan White)
is a default assertion.
Note we should consider the definitional features
(Color Albino White)
(Color Melano Black)
as a close match -- closer perhaps than
(Color Albino White)
(Color Swan White)
Without that meta-level assertion, telling the "force" of the proposition,
(as in (Definitional Albino '(Color Albino White)),)
there is no way to indicate this "closeness".
Causality, which you commented was missing from Hesse's scheme,
can also be indicating in this meta-language.
I have two final comments on this topic of sharing abstractions,
before addressing the issue of negative and neutral sub-matches:
First, names pose no (epistemological) problem:
Sharing an abstraction means both analogues satisfy the abstraction,
in a model-theoritic sense.
Hence the various terms -- such as constants, relations, etc --
can have different names. Hence it was of no concern that LinkedTo and
SproutsInto had different names -- the only important thing is the role
they serve.
Secondly, I do NOT want to imply that these matches would be impossible
using any frame based system.
My point is that it would be very awkward,
and would require many embellishments over Hesse's approach.
First, it would have to include the second order statements necessary
to describe and interrelate the relations -- for 3 and 4c.
(Note this isn't much of a problem -- for example,
the frame based RLL system already has this feature.)
Dealing with n-ary relations is a bit more troublesome -- but judicious use of
things like GivingEvents can handle it. The most difficult additional
would be the mechanism for encoding meta-level assertions.
Suffice it to say that with sufficient contortions
a frame-based system could indeed represent such information;
but it would be a struggle.
The other issue deals with the space at which the match occurs.
In the Hesse-ian case, that space must be in terms of the slots
given in objects' frames.
This limits the matching to cover only those features which someone knew
in advance to define.
The particular approach I am taking is towards fabricating new perspicuous
relations as they are needed.
[Once again this can be achieved by designing only new BINARY relation
(as RLL now does). However the real expressive power of this approach will
be more apparent if general relations can be used.]
Note this permits useful, if complex, relationships to be encoded
using a single symbol.
Matching is now more straightforward, given such designed symbols.
(For example, taking the transitive close of the LinkedTo relation gave
us just the relation we needed to say interesting things about the connectivity
of a tree.)
One of my goals it to find a large (hopefully spanning) collection of
these transformations,
powerful and general enough to reduce otherwise difficult connections
into simple, straightforward matches.
This leads into my final comment -- the price for this generality is obvious:
it costs us the elegant and simple matching algorithm Hesse discusses.
Given only binary relations, in which the first argument is necessarily the
analogue, one can readily construct those linear lists of features.
Matching here is much more difficult -- as any of the elements of a
proposition might differ from one analogue to the other --
and indeed, we might even been dealing with a non-atomic form
(eg something with boolean connectives or even quantifiers).
---- Negative and Neutral ----
Finally, some comments on how (and whether) to deal with
negative and neutral sub-matches, in this abstraction context.
(Certainly it does a good job of handling those "positive" matches
-- these are the features which both analogues share.)
Consider first those solo [ie not embedded in some logical connective, or
scoped by some quantifier] binary relations,
which are used to describe an analogue.
When the same such slot is used to describe both analogues,
we can easily do a Hesse-ian feature comparison.
(Note applying case 1 above to derive the abstraction means that deleted slot
was either a neutral or negative match;
applications of case 2 correspond to various forms of positive matching.)
What about when the analogy is based on an abstraction derived by
some other method -- eg by 3 thru 6 above?
Can this feature matching be extended to these cases?
Before pursuing possible ways of achieving this, it might be worth
asking how worthwhile this categorization really is.
Recall how confusing this +/-/? trichotomy was, even in the slot case:
Hesse's categories of positive, negative and neutral analogy
do not easily apply to the relation between a selector in breeding
and the puzzle that that posed for Darwin about nature. At the abstract
level of some sort of selective mechanism there is positive analogy;
at the component level of agent and criterion we have negative analogy.
It would be much more useful to have a description of how these things
are similar -- to preserve some justification for each part of the analogizing
match.
This is even more important when we ask what it means for a pair of
n-ary propositions to match positively.
In n=2 case, two relations were considered to match, if they used the
same slot (eg both were "Agent" properties), and the second argument
were deemed sufficiently similar. (Recall the first argument was the
analogue being considered.)
The only problem there was dealing with that single similarity.
This problem is compounded in general, for n>2.
If Tom had given his thesis proposal to his advisor, but Russ hadn't,
this would seem a negative match.
(If we were comparing Tom to a door, which (to the best of my knowledge)
have neither theses nor advisors, this non-match would presumably be
a neutral occurance.)
But now we can ask what if Russ had given his thesis to his advisor?
Or if he had given that thesis proposal to a visiting prof?
If these facts,
(Gave Russ "thesis" "advisor")
(Gave Tom "thesis proposal" "advisor")
correspond to the same abstracted sentence,
(Gave x "version of thesis" "advisor"),
should we say they match -- that is, should this be an instance
of a positive match?
To push thru Hesse's scheme, I say the answer is Yes -- two statements should
be considered a positive match if they are each an "instance" of a common
abstract sentence. In addition to this Yes response should be some indication
of how they each matches -- as in an alist of bindings.
So much for the easy case. What of "neutral analogy"? This will occur
when there issome sentence in one analogue which has no corresponding sentence
in the other. Note a definition of "corresponding" is rather tricky.
A very weak definition would mean that no such sentence is "primitively"
associated with that analogue.
That is, there is the list of facts which can be easily read off about each
analogue, without performing any deductions.
A more elaborate definition of corresponding would require finding the closure
of that set of statements, under the allowed (first and second order)
rules of inference; and then checking this extended (infinite) list.
Clearly this could be messy -- and (I contend) not all that useful.
Given problems like the one mentioned above (with Russ giving something to
someone), negative matches may not even be meaningful -- if we insist that
the existance of any abstract statement means that that match is a positive one.
Perhaps we should indicate some threshold at which a match changes from
positive to negative -- that is, establish some stronger criteria for determining
commonality of features beyond just a common abstract sentence.
Final point: realize this whole process gets even hairier when we consider
arbitrary sentences -- not just atomic propositions.
Even thing from matching and binding to that thresholding becomes more
problematical.
But enough for one day.
I do have a number of other questions/comments/suggestions, etc. on your paper.
Let me know if I should send them as well -- or if I've already overstepping
my bounds as friendly commenter...
Russ
∂02-Dec-81 1737 Darden at SUMEX-AIM Re: Comments on your paper
To: RDG at SU-AI
cc: Darden at SUMEX-AIM
In response to your message sent 01 Dec 1981 1324-PST
Hi, Russ. Thanks for your comments on my paper. By all means send along
any other comments you have. I found the ones you sent quite helpful,
especially in expanding my ideas about how generalization and abstraction
can proceed. I take it that your main arguement is that the abstraction
idea is much more powerful than the Hesse idea of direct mapping in a
frame-like representation. I think you are right. [By the way, correct
spelling: occurrence, existence] I have just been rereading Winston
and he addresses the question of where in an abstraction hierarchy
the most "meaningful" matches might occur: at something Rosch et al
call a "basic" level of class abstraction (Winston is dealing with
ako hierarchies), e.g apple is basic while fruit is higher up and
Delicious apple further down. Some sort of decisions will have to be
made about where in an abstraction hierarchy to draw the line.
I think you shouldn't discount an extremely important role
of neutral analogy: suggesting new ideas. Since I am most interested
in using analogies in thoery formation, a way of generating new
(parts of) theories is very important. If one already has some
positive analogy, and a property is causally connected with oen
of the postive analogy properties in the analogue, it is a plausible
arguement to propose that a similar property is present in the subject.
Well, I had beter send this before the system dumps me off and I lose
it, as happened to a msg I was sending Tom. Are you two talking to
each other about your thesis ideas? It is exciting to get proposals
from both of you dealing with analogy within a two week period.
Keep in touch.
Bye, Lindley
P.s. I'm not annoyed; just the opposite.
∂TO DARDEN@SUMEX, TGD, STT 14:56 3-Dec
Now for something completely different ...
... more comments.
---- 0. Overhead, and response -----
I should explain my caution by mentioning the large number of people
I've encountered who really did not want critical comments --
their ego is often so tied up with their work that any but the
most superficial of criticisms is either ignored, or considered a personal
slight. I'm glad I'll not have to worry about that reaction.
Now if only my comments were as useful as you imply...
Yes, I am familiar with Rosch's work, but hadn't realized Winston was.
Is b(i)asing his conclusion on some psychological data he has gathered,
or an "it would make sense if" type of argument?
Also, I do agree that (one of) the best possible uses of analogies
is to find "surprising" results, by somehow extending the preliminary
partial mappings found so far.
I didn't think Hesse's definition of "neutral analogies" was well-defined
even in the superficial slot case; and this problem is even more pressing
when trying to extend this notion to handle a more general form of
abstraction.
A (second) preliminary cut at this issue would begin by dividizing
analogies into two categories.
Some seem quite "closed and complete", in the sense that they
define essentially everything which connects the pair of analogues.
Others have a more open feel to them -- and seem to only suggest a deeper
connection. (Sorry to use such nebulous words -- the idea is still equally
flimsy, unfortunately.)
Anyway, that something which differentiates these two classes is undoubtedly
related (somehow) to those neutral mappings.
I'll think about formalizing these notions; and will keep you informed
of such meditations.
Continuing this old business:
I realized that my last message lacked a conclusion.
I should have summarized by stating that that overall trichotomy,
like binary linguistic features/marks of yesteryear,
is appropriate only in fairly superficial cases.
... and very few things fall into such neat categories.
I agree one should still preserve the base facts about each of the analogues;
as they may come to be useful during the further analysis required
to explain some phenomena which hadn't been considered earlier.
But the attempt to classify things into three groups, throwing away the
rationale which went into this decision, seems far too limited to
explain something as complex as analogy.
Onto new stuff.
----- 1. Comments on the nature of the paper ------
I also forgot to mention that I did enjoy the paper, and agreed with many
of its conclusions.
Certainly it seems that people will draw on various sources when theorizing.
Your comparision of selection-type theories with tool-building ones hit some
resonances, which I'll discuss later on.
That sextet of questions you posed about analogy was quite enticing.
If only you'd also answered them... but that would trivialize my
entire research effort (and that of dozens of other researchers).
[Side point -- is it meaningful to classify an analogy as either good or bad?
Perhaps "useful for a given task/purpose, or not"?]
Another general comment deals with the number of things presented in
the paper.
Basically I thought that your comparison of those two definitions of analogy,
(Mike's vs Hesse's) while quite interested,
did not fit into the rest of the paper.
Was this directed at some member(s) of the audience, to counter some claim;
or was this necessay to explain your "abstraction for selection theories"
phrase, or ... ?
[By the way, I found that phrase rather hard to understand.
It was easier when I substituted "of" for "for".]
----- 2. Yet-even-more piddly points -----
[These points are arranged in order of occurEnce in the paper; NOT importance.]
Isn't a datum of genetics more like "760 green peas to 260 yellow peas, on
January 17, ..." rather than 3:1 ratio. I.e. isn't that ratio already
a generalization?
You used the phrase "adequately similar" when mentioning the cases when
Hesse's scheme would be productive. In light in the critism leveled
in the prior message, may I suggest the phrase "superficially similar"?
You stated that
But what if a relevantly similar analogy cannot be found, or
what if the severing of what we thought were causally correlated
properties is not sufficient for the construction of a theory?
Did you mean that one could construct a theory by severing some properties?
I can see how such a severence would invalidate a theory, but not how
it would aide in the generation of a replacement.
Isn't identity a special subcase of similarity?
In fairness to Hesse, I should mention that she thinks in some cases
the relations between the directly mapped properties are those of identity
rather than similarity.
I'm always looking for cute and clever ways of explaining the idea of
a shared abstraction, but couldn't see how Figure 2 could do this
(probably because your description was too sparse).
Could you elaborate your description, if appropriate?
I do pretty much agree with the definition of similarity you presented, viz.
Two things are similar if on some analysis into component properties,
some of the properties are identical, while others are not identical.
As it stands, though, it is rather vacuous.
Have you given much thought on what makes for a good decomposition,
and then which subset of properties should be identical?
Neither of these decisions is trivial, and I'd love to hear any ideas you may
have on how to do this.
Wrt
Since the shared abstraction has a limited number of identity matches required,
then it will be better.
The abstraction definition of analogy does say that two objects will be analogous
if they have the SAME abstraction.
Hence this "matching" is a triviality, given the abstraction.
The previous message shows that much matching is needed to find
the abstraction, though.
A quick comment on
This may be an example
of a general role played by analogues: they exhibit the same abstract
structure but differ as to how the details are to be filled in.
This reminded me of the phenomena of confabulation -- where a person
thinks he remembers an event, but apparently only remembers some abstraction
of it. When pressed for details (eg "how many bricks were there on the
chimney of your childhood house?"), the subject will inadvertantly
refer to the wrong instantiation -- eg retrieving their "typical chimney",
rather than the one associated with childhood house --
and thereby returns the wrong answer.
(This phenomena also suggests one explanation for deja vu, by the way.)
A(nother) minor point:
I contend that generalization is actually a case analogy -- as both the
generalization and the specialization will share a common abstraction.
This comment was prompted by:
Thus, the relation of struggle for existence to Malthus's key idea is
not analogical but that of specialization-generalization.
I had all sorts of problems understanding the next section, on
"Abstract Form of Selection Theories".
The opening paragraph was especially confusing --
I couldn't tell, the first few readings, whether you were discussing the
formation of theory of evolution, or (some abstract version of) that theory
itself.
That is, was it Darwin's reasoning process which established a new type of
scientific theory, or was it the result of that thinking,
namely the (selection) theory of evolution, which was then generalized to that
Abstract Selection Theory.
(I concluded the latter was the case.)
A specific suggestion would be to tell the reader that the result of Darwin's
fabrication was an instance of the "selection theory"; and then state that
this section will discuss an abstract version of this theory,
(called the "Abstract form of Selection Theory",) and will give other
examples of where this theory is used.
Another big confusion was with the term "variant". I first thought it refered
to something like a gene - sorta the minimal unit which could vary.
Only later did I realize it must have meant an entire individual.
Then I read
The variant pool was complete circular movement,
and was confused all over again.
Finally, does "adapted variants" refer to any modified individual, or just those
which are deemed "successful" (using some appropriate definition for success)?
Your components of a selection theory,
I. An array of variants is generated.
II. Selection of a subset of variants occurs.
III. After selection, the pool of variants is different.
reminded me of the AI workhorse, the "Plan, Generate and Test" paradigm
(see early Dendral work, or ask Bruce).
After the planner has constrained the initial search space,
the generator will produce candidates in this space.
The tester will then evaluate these -- basically weeding out unacceptable ones.
This approach is needed when the space is too hard to categorize. Otherwise,
one can put enough smarts into the generator to constrain it to produce
only viable individuals, obviating the need for the testing phase.
This seems to correspond to your "tool-fashioning type of theory", sorta.
I did like your conclusion. Let me end with a similarly self-referential
conclusion, which refers to itself only in this (cutesy) closing statement.
Russ
∂TO DARDEN@SUMEX 14:59 3-Dec
Other (mostly non-technical) things
1. First, a technical comment, wrt your comments on my proposal.
I wanted to present my tirade against frame systems before
answering your question on why I was mentioning Hesse in the same
breath with Gentner.
In my mind both were
(as I understand their respective work) mapping facts about one analogue onto
corresponding facts about the other.
Their approached differed only in terms of what was actually being mapped.
I consider a fact about to an object to be any proposition in which
that object participates.
This use is intentially very general --
and blurs the property/relation (so called) dichotomy.
Hence I consider all of the following to be properties of John:
(Married John) - unary
(Age John 26) - standard binary
(WifeOf John Mary) - Is this a property or a structural relation? Who cares?
(Believes Fred "(WifeOf John Mary)")
- even embedded clauses, with varied epistemological statuses.
[This mechanism is very useful for describing causal links, etc]
(Exist x. (AND (WifeOf John x) (MemberOf x Woman)))
- abstractions pose no problem
(OR (Bachelor John) (#Kids John 2))
- nor do disjunctions
(ShorterThan (Length (LeftLeg John))
(Length (RightLeg John)))
- this is clearly a "structural relation".
So facts can be contrasted with the properties, which are always of the
unit-slot-value flavor -- as in John's age is 26.
2. WRT that onslot of little News Service articles I've been sending:
Basically any time I see an article which might possibly be interesting,
I send it. Let me know if I should elevate my threshold for
"things of possible interest to Lindley" -- ie if I'm flooding your
mail box with more than you can possibly handle.
3. I've been attending a really interesting class on "Cognitive Structures
and Musical Perception" -- "hosted" by Roger Shepard over in the Psych dept.
Various guest lectures have covered (i) an intro to psycho-acoustics
(with an (apparently unintentional) emphasis on its flaws and limitations),
(ii) a discussion of amusia -- loss of musical ability due to brain damage
(including the controversial claim that musically trained individuals appear
left-dominant
[ie use the same brain hemisphere to process music as is used to understand
speech], whereas musically naive people use their right hemisphere),
(iii) how people do and do not categorize pitch (as in phonetic categories,
such as voiced vs unvoiced),
(iv) a group-theoretic analysis of musical intervals, and rhythmic patterns,
(v) the difficulties of computerized musical dictation
(eg the range of time durations for a sixteenth note was found to be virtually
identical with the corresponding range for an eighth note!,
dooming the prospect of discrimination based on that measure),
(vi) results of the "stretched octave" experiments, etc.
The diverse interests of the various speakers make this class fascinating.
Anyway, I bring this up because of a recent pair of papers, which discussed
the obsolense of music, as it stands today. While reading it I realized
(thanks to your class) that the author was discussing the Philosophy of
Music -- in particular, he was trying to articulate a paradigm-shift
type of metamorphisis in the field.
Is there a PofM discipline? Or have musicians figured that that was what
they themselves were doing all along?
4. I remember noticing the number of writers who writing stories about writers,
or songs written about singers, newcasters discussing reporters, etc.
I can now strongly empathize -- I keep finding analogies about analogies
(as in analogies are like problem reformulation, or abstraction, or ...)
I guess this isn't too surprising: given that my current focus of attention is
on such abstract matters, it makes sense that my examples would come from
this source as well.
5. Could you send other people's comments on your article, unless that would
be uncomfortable. I'm particularly curious to see how Mike reacted; and always
find Tom's and Steve's ideas worth seeing. Thanks.
----
Hope everything is going well there.
Russ
∂03-Dec-81 1330 Darden at SUMEX-AIM nsf proposal
To: csd.dietterich at SU-SCORE, stt at SU-AI, rdg at SU-AI
cc: Darden at SUMEX-AIM
Hi, folks. I spent today drafting an nsf proposal that I will be
revising over the weekend. If any of you have time, I would appreciate
comments to improve it. You may also be interested in learning about
the book I want to write and my preliminary conclusions about
reasoning in theory construction. Some will look familiar, but others
are new this year. I'm sending it along in the next msg.
Bye, Lindley
-------
∂03-Dec-81 1332 Darden at SUMEX-AIM nsf proposal.copy
To: csd.dietterich at SU-SCORE, stt at SU-AI, rdg at SU-AI, Maxam at SUMEX-AIM
Understanding the growth of scientific knowledge has become a
central problem in philosophy of science in the last twenty years.
Until recently, however, philosophers of science have concentrated
narrowly on only a few aspects of the growth of scientific knowledge,
namely how a fully developed theory replaces another and whether such
replacement is justified. (See F. Suppe, The Structure of Scientific
Theories, 2nd. ed., 1977, for a discussion.)
But how do new ideas arise in science, how are they used to construct
new theories, how are new components added to theories when anomalies
force modifications? These are some of the questions that recent
philosophy of science has begun to address. The pioneering work of
N. R. Hanson (in, e.g., Patterns of Discovery, 1965) is criticized
and extended in a paper by Schaffner (1970) and the more recent
work of Monk (1977), Kordig (1978), Gutting (1980) and two volumes
from a 1978 conference on the logic of discovery edited by Nickles
(1980a, 1980b)
The research proposed here is to be conducted within this current
framework of attempting to understand the reasoning in the development of
new theories. The methodology to be used is that of empirical philosophy
of science. First, philosophical questions about reasoning in
theory construction are formulated; then, a historical case is
examined to provide working hypotheses about the general patterns of
reasoning that were used, or could have been used, in that case.
Some reconstruction of hypothetical patterns is often necessary
because historical evidence as to the actual, detailed steps of
reasoning is usually not available. However, given the
an early version of the theory and a later version, as well as
background knowledge of what was known to scientists at the time,
plausible hypotheses about steps of reasoning
and stages in theory construction can be proposed.
(For further discussion of empirical philosophy of science
see McMullin, 1970; Maull, 1976; and Hausman, 1980.)
Case studies from nineteenth and twentieth century biology
have provided me with a number of working hypotheses about
reasoning in theory construction. First, it is an error to
dichotomize science into two mutually
exclusive contexts--the content of discovery and the context of
justification--which has been common in both older and newer treatments
in philosohy of science (see e.g. Popper 1960, Nickles, "Introductory
Essay," 1980a) Theories rarely, if ever, arise all at once in a
complete form, ready to be justified or falsified in toto.
Instead, theory construction is a process that takes
place over time in a piecemeal way with modular components in different
stages of development at different times. Vague ideas are sharpened;
implicit assumptions made explicit. Failed predictions necessitate changes,
sometimes in only one modular component of the theory. New data demand
new modules be added to the theory.
These general conclusions will be developed in the proposed work,
which will be a book-length analysis of general patterns of reasoning
in theory construction, drawing primarily on my case study of the
construction of the theory of the gene in the early twentieth century.
My previous NSF grant during 1978-79 allowed me to complete the
research on the development of the theory of the gene, including
visiting major archives, collecting and analyzing the major published
writings of geneticists, and writing several papers presenting partial
results. In "Theory Construction in Genetics" (1980), I discussed the
early stages of interaction between the fields of genetics and cytology
that produced the new idea that the gene was a material entity
carried by the chromosomes. In "Aspects of Theory Construction in Biology,"
(forthcoming) I looked at challenges to the theory of the gene and
proposed a pattern of reasoning for the resolution of anomalies.
In "Theory Construction and Classical Genetics" (unpublished
manuscript) I discussed a crucial experiment that decided between
two plausible ways of modifying the theory of the gene. In "Not
a Logic of Discovery but a Rationale of Theory Construction,"
(unpublished manuscript), I
argued that in the early stages, the concept of the gene was a vague
idea that gained specificity with each subsequent stage of theory
construction. In "The Role of Constraints in Theory Construction,"
(unpublished manuscript) I discussed the role that different constraints,
dependent on the different interests and expertise of different
scientists, played in various stages of theory construction.
The proposed work will allow me to pull together these partial
results, many of them unpublished, into an organized longer discussion.
Also, I plan to incorporate results from other work on other cases
from nineteenth and twentieth century biology which I completed earlier.
In "Reasoning in Scientific Change," (1976) I discussed two
nineteenth century theories of heredity and the role analogies played
in their construction. In "Discoveries and the Emergence of New
Fields in Science," (1978) I discussed the construction of the cell
theory and the enzyme theory and contrasted those discoveries of
"observable" entities with the postulation of the hypothetical genes.
The proposed work will not only break new ground philosophically
in the area of reasoning in theory construction, it will also present
a new historical account of classical genetics. My primary source
research has led me to a reexmination of many of the conclusions
of historians of genetics. The book-length histories of genetics
are now quite dated and many are out of print. L.C. Dunn's A Short
History of Genetics (1965) and A.H. Sturtevants's A History of Genetics
(1965) were both written by scientists with an out-dated (Whiggish)
approach to the history of science, namely of seeing what ideas led up
to presently accepted views without mentioning other competing ideas
that were plausible in the historical context but later disproved.
In order to understand patterns of reasoning, one must look not
only at what was subsequently confirmed, but also at other
reasonable hypotheses proposed at the time. E. A. Carlson in
The Gene:A Critical History (1966) is less guilty of a straight line to the
present approach. But his book, too, is now dated, since it does not
integrate conclusions from recent historical work on thie episode,e.g
Allen's (1978) conclusions about T.H. Morgan in his new biography
of this key figure in the development of genetics.
Also, numerous recent articles reinterpreting aspects of the
development of Mendelian genetics need attention in new work.
It is now a mystery who first discovered what has come to be called
Mendel's first law, the law of segregation, that states that paired genes
(now called "alleles")
segregate or separate as germ cells are formed. Robert Olby in
"Mendel No Mendelian?" (1979) argues (though I still haven't decided
how persuasively) that Mendel allowed the possibility of more than two
types of germ cells and thus did not have the key idea of separation
of pairs of factors. Malcolm Kottler (1979) has argued, not
convincingly I think, that Hugo de Vries did not independently discover
the law of segregation before reading Mendel's paper. In my "Hugo
de Vries's Lecture Plates and the Discovery of Segregation," (manuscript,
in preparation) I present archive evidence against one of Kottler's
claims about the date of a lecture plate used by de Vries in his
teaching in Amsterdam. So far as I know, the only claim that Carl
Correns has to be an independent discover of segregation is his own
claim (like de Vries's) to have obtained the results prior to reading
Mendel's paper. (Stern and Sherwood, 1966) Thus, the historical mystery
is this: who discovered the law of segregation? Exactly what is present
in the papers of Mendel (1866), de Vries (1900) and Correns (1900)
needs to be examined carefully.
Other recent articles need to be included in an up-dated discussion
of the history of genetics, including S. Gilbert's "The Embryological
Origins of the Gene theory," (1978), A. Baxter and J Farley's, "
"Mendel and Meiosis," (1979) and my own
"William Bateson and the Promise of Mendelism," (1977).
My work with coauthor Nancy Maull in "Interfield Theories" (1977)
has shown me that a conceptual confusion abounds in both the
older and newer historical literature. The theory of the gene,
based solely on breeding data, should be distinguished from the
chromosome theory of Mendelian heredity, which is an interfield
theory postulating a link between genes and chromosomes. (See my
review of Allen, 1978 for further discussion.)
The project is already underway. During the summer
of 1981 I wrote a chapter outline. The first chapter will discuss
the philosophical literature on reasoning in discovery and outline
the philosophical questions to be investigated. The detailed
analysis of the theory of th gene will occupy six chapters. The
seventh chapter will contain the general patterns of reasoning
found in the genetics case. A final chapter will discuss the
applicability of these patterns in other cases. The second
chapter, entitled "Mendelism in 1900" is in draft form.
I have prepared an analysis of the postulates of the Mendelian
theory in 1900 and am now at work on an adequate statement of the
changed set, based on T.H. Morgan's book of 1926 entitled the
Theory of the Gene. Sections from manuscripts discussed above will
supply portions of the other historical chapters.
Work is already underway on the seventh chapter on the
hypotheses about general patterns of reasoning in theory construction.
Preliminary results include the following: Analogies often supply
new ideas in the early stages of theory construction. However,
when they are available, connections to other fields provide
a better source of new ideas than mere analogies, since they
relate the subject field to empirically confirmed knowledge in
other fields. Over-simplifications and vagueness at the outset may be
important for getting a theory started and can be corrected as
theory construction proceeds. Theory construction is a modular
process with different postulates of the theory serving different
functions. The incompleteness of some modular
parts of the theory may be tolerated if other parts are successful.
Some of the postulates are constructed to account for specific data
that the theory is expected to explain. When anomalies arise,
it is often possible to locate the most plausible postulate to
modify. Several types of constraints guide the construction and modification
of theories, including empirical , methodological and metaphysical
types. Different sets of constraints can be used to generate
differnt hypotheses.
The final chapter, in discussing applicability to other cases,
will suggest, not only other past cases in wich these patterns of reasoning
may be found, but also contemporary work to which they may be applicable.
Such work includes current attempts to formulate theories of gene
regulation within molecular biology and attempts to build artificially
intelligent computer programs to formulate scientific hypotheses.
The proposed work will thus break new ground, both historically,
in understanding the development of the field of classical genetics,
and philosophically, in understanding general patterns of reasoning
in theory construction.
What I need now is a sustained period of writing in order to
complete the book. I am thus requesting salary support for a one
year period. I plan to locate at Harvard University to use the
libraries in the Boston area, including the very valuable collections
at the Marine Biological Laboratoy at Woods Hole, MA. By taking
the reduced off-campus rate, a reduction in salary, no travel or
other special funds, and asking the University of Maryland for
a substantial waiver of indirect costs, I am able to stay within the
NSF Scholars Award allowance of $25,000.
-------
∂10-Dec-81 0603 Darden at SUMEX-AIM replies, etc.
To: rdg at SU-AI
cc: Darden at SUMEX-AIM
Hi, Russ, I'm just now getting around to answering your Dec.3 msg.
I've finished my NSF proposal and am now trying to finish all the
details of the last week of class.
I've enjoyed reading all the news stories you have sent. Sometimes
when I haven't read my mail in a few days my directory suddenly gets full.
But mostly it isn't a problem. I will be away from December 19-January 1
so it would be best not to send long ones during that period.
From Janaury 1-11 I will be in Boston but I'll be reading msgs there.
Have I told you that Allan Maxam (the Harvard molecular biologist to whom
Peter introduced me over SUMEX) and I are seeing a lot of each other?
We met in Boston last April when I gave a talk at BU and have been seeing
each other on weekends and holidays. I'll be visiting him in Boston in
January. I wonder is we are the first couple to meet over SUMEX? We
are still talking about hypothesis-formation in gene regulation but we
are both too busy to do much about it. Allan thinks experiments are going
to resolve the issues before an AI system could get going.
I like your idea that some analogies arecomplete and others more open.
I think that is worth trying to work out more clearly.
I suspect you are right that "goodness" of analogies is likely to
depend on the context.
As to how severence of some properties could aid in generation of
theories: consider the example of constructing the wave theory of
light. First, we propose that light is a wave with a medium, the ether.
But when the existence of the ether is not confirmed, then we have to
sever the propoerty of having a medium from being a wave. We thus construct
a new concept of the e-m wave with no medium.
As to how one decomposes in order to find identitical properties: a very
good question. Philosophers of biology have talked a lot, usually rather
loosely, about organizational levels and the lack of privileged decompositions
for biological organisms. Maybe we could let the context of the analogy
or the nature of the analogue play a key role in telling us how to decompose.
I found your ideas on confabulation interesting. I don't know that
literature.
Relations between generalization and analogy: I've been thinking a lot
about this. There is some deep relation between induction over a class of
things of a single natural kind and analogizing similar things. But I don't
think they are identical--maybe they are part of a continuum from identity
to inductively similar to analogically similar to totally differnt.
Generalization seems to be used in AI more broadly than inductive
generalization. I haven't sorted out these conceptual relations.
I too had thought about the relation between generator of variants and
tester and remarks Bruce had made about the interrelations. But I didn't
know enough about that to put it into the paper. Any suggested references?
I haven't received any other specific comments on my paper, but I'll
be happy to send them along if I get any.
I'll be looking more carefully at your detailed comments when I start
revising the analogy paper next year. I'll be presenting it at Vassar,
probably in February, and will get back to it then.
Well, this is long enough and I have lots to do today.
Bye, Lindley
---
∂TO DARDEN@SUMEX 16:20 11-Dec
Follow-Up↑N
Hi Lindley,
I'm glad things are finishing up for you, and hope you allow yourself a
(well-deserved I assume) vacation.
Digression:
I recently realized that I have two modes of activity -- both frenzied.
The first is characterized by a "gotta finish up X" attitude.
Here I work exclusively on X, ignoring all other pursuits.
This mode is productive only for short periods --
after a non-trivial accomplishment or two, I find myself "burned-out".
Even though I continue to put in the same number of hours,
nothing gets accomplished.
Busy as Mode 1 is, Mode 2 is even worse.
This occurs whenever I'm not engulfed in a single, primary obsession.
The same compulsion that I had for that one X is now applied
to finishing up EVERYTHING ELSE,
based on the lists of things I'd made during Mode 1 activities.
As a result I continue to feel pressed, even after achieving some big task.
(Yep, sounds like Type A alright.)
That X had been bound to "write initial thesis proposal";
placing me now in Mode 2.
Perhaps this explains (if not justifies) my recent compulsive letter writing, etc,
assault(sp).
Anyway, back to coments on your letter.
WRT Allan Maxam -- no, you'd not mentioned him by name,
but I did suspect there was some "alterior motive" to your hops to Boston.
I'm pleased to hear more about "this cause" (<= putting to use my recently
acquired knowledge of metonymy and other tropes);
based on profession alone there seems much you and
a Harvard molecular biologist would have in common.
Best of luck, and congratulations! (Or whatever the appropriate comment is.)
One of these days, if you're interested, I'll have to relay
my "romantic (mis)adventures".
But I digress, yet again; on to things (more nearly related to) analogy.
Further thoughts on completeness:
The complete side of the incomplete-to-complete spectrum of analogies
seems fairly easy to characterize:
Consider the proportional metaphor "ewe's calf", and ask why
it is so hard to imagine this referring to anything but "lamb".
An examination of the terms involved (ewe and calf explicitly, and
cow and lamb implicitly) begins to answer this:
they can all be completely and unambiguously specified.
Contrast this with something like "language", or "metaphor".
So a zero-th order conjecture is that an analogy can be no better described
than the terms it uses. This analysis is obviously overly-simplistic:
in particular it completely ignores issues about the complexity of the
definitions of these terms
(ie "eclipse" can also be precisely defined, but this requires many more clauses,
and additional terms, (like Sun) which themselves must be defined),
and the "connotations" of the words
(e.g. "eclipse" is loaded with many myths and misconceptions which "enhance"
(read "confuse") the otherwise straightforward use of such terms in a metaphor),
etc.
Undaunted by these obvious complications, I still feel there is some notion
like this for discussing the completeness (and hence un-interestingness)
of an analogy.
Severence:
I can see how severing a property can suggest considering a new concept,
(e.g.a medium-less wave,)
but I don't see how that severence actually "generated" this concept.
This generation requires much rethinking, and much non-trivial inferencing
(e.g. how does this new concept fit into the world, etc.)
Maybe this is just an issue of simple semantics, but I feel there is something
else here. Comments?
Decomposition:
I agree that both the context of the analogy
and the nature of the analogue can strongly suggest the appropriate space
for matching the analogues -- and hence the apt perspectives for these objects.
Confabulation:
Although I've never seen it in print, this idea seems closely tied with
the notion of (Rosch-ian) categories, only over the domain of episode/event
rather than specific tangible objects --
that is, I suspect the same internal mechanism is at work both times.
Generalization vs analogy:
I basically agree with your comments -- that there is a difference between
these two connections. My claim was that the same formalism
(and associated mechanism) [of common abstraction]
could handle both of these phenomena.
Plan-Generate-&-Test:
I'm sending over a mature Dendral paper, which sorta discusses this.
The Dendral book (does Allan has this book?)
also uses this paradigm, and pretends to define it.
I (wastefully) xeroxed the most nearly relevant pages, and mailed that as well.
Another ref might be Simon's "Science of the Artificial" --
in that he discusses the complexity of the space as a factor in designing
the solving process (as in his ant). Steve's work in program synthesis,
I think, deals with this idea as well. (IE one optimizing task is to move
a test "back" to earlier in the algorithm, and incorporate it (as a constraint)
in the generator.)
New:
1. Paivio's (in the M&T, page 162) use of "Ground",
(as in "topic, vehicle and ground")
seems to have much in common with the idea of abstraction.
[Still not exactly MRG's notion, I think, but related (analogous?).]
2. An irrelevancy:
A friend asked me what sorts of things us AI types should know, outside
AI proper. (Yes, this question could be circular, in that anything in
another field deemed relevant will be "borrwed/stolen" in some system...)
Anyway, my list would include (in no particular order)
1. Tarski - semantics
2. Whorf - "you can't think what you can't say"
3. Wittgenstein - familiar resemblence
4. Philosophy of cognition - as in Behaviourism thru Abstract Functionalism
5. emic/etic distinction (from Pike (phonetics) on)
6. the idea of conceptual categories
a) basic idea, shown in works by Bower, Rosch
[& Shepard/Halperin in music, Simon for Chess, ...]
b) Miller's 7+/-2 paper - for short term memory (of these categories)
c) Kay's basic color terms
7. Rough idea of neurophysiology
a) visual perception -- [Heubel and Weisel, Gregory, ...]
b) centers of Speech (as shown by aphasaics)
c) split brain (Sperry etal)
8. Notion of a scientific paradigm (as expounded by Kuhn, etc)
[I'm skipping many other important things which most CS people encounter anyway.
Included are
Chomsky - notion of grammar,
van Neumann - theory of games,
Shannon - information theory
superficial psychology - especially behaviour "production rules"]
----
All of these seem to say something about intelligent behaviour, or analysis
of such.
Any additions/deletions/?
Enough for now. Enjoy your trip(s).
Russ
∂13-Dec-81 1630 Darden at SUMEX-AIM references on heuristics
To: Analogy seminar:
Hi, folks. Thanks to those of you who sent comments on my analogy paper.
It is still available on my SUMEX directory if anyone else wants to
look at it. I'll be revising it in February before I present it at Vassar.
Allan Maxam, a moleuclar biologist at Harvard, and I have been talking
about an AI-molecular biology project for some time. Allan would like to
have references that list general heuristics and general introductory
literature on the concept of a heuristic and how to find them. The
only list I know is the one in Doug Lenat's thesis, about 200, some of
which are quite general, e.g. look at extremes. Are there any lists
of heuristics on line? If not, why doesn't HPP have such a list?
MY Discovery and Analogy class read Jamie Carbonelle's Cognitive Science
conference and IJCAI 81 papers on metaphor and analogy. I will send a
msg soon with our critiques. If any of you get a chance, take a look
at his attempt to get a list of propeties that transfer in an analogy; he
calls itan "invariance hierarchy." An interesting but failed attempt,
I think.
Bye, Lindley
-------
∂17-Dec-81 0947 Darden at SUMEX-AIM analogy exam
To: Analogy seminar:
Some of you may be interested in seeing the final exam for my class on
Discovery and Analogy. It is on my SUMEX directory under <Darden>anal.exam.
The course focused much more on the philosophy literature and much less
on the AI literature than I had originally intended. The only student
from computer science dropped out when the first paper was due, so all
the students were undergraduates or graduates in philosophy.
Those of you that were in the Stanford analogy seminar will see from
the exam that some of my ideas are more clearly formulated and that I
am now more familiar with the literature on analogy. Comments (or even
answers to questions) from any of you will be of interest to me.
HAPPY HOLIDAYS
Bye, Lindley
-------
Final Examination, Phil 458, Discovery and Analogy
L. Darden, University of Maryland, Fall, 1981
Answer four of the following questions.
1. State and critically analyze N.R. Hanson's schema for retroductive
inference as presented in his paper "Is There a Logic of Scientific
Discovery?" (1961) Do you agree or disagree with Hanson's claim
that reasoning in discovery differs from reasoning in justification of
scientific hypotheses?
2. Compare and contrast Mary Hesse's and Mike Genesereth's accounts of
what an analogy is. What methods would each analysis provide to answer the
following question: how can we use analogies to construct scientific
theories?
3. Discuss the role of analogy in Charles Darwin's construction of
either or both his theory of natural selection and his hereditary theory
of pangenesis. How well do Mary Hesse's categories of positive,
negative and neutral analogy apply in analyzing Darwin's use of analogy?
4. Discuss the idea suggested by Monk that theory construction begins with
a vague idea. Monk relegates the finding of the vague idea to an aha
experience but Boyd pushes the analysis back another step. Critically
analyze Boyd's proposal.
5. What is the "problem of theoretical terms"? Explain how, according
to Hesse and Boyd, analogies or metaphors can aid in the resolution of
this problem. Critically analyze their positions. How is this problem
related to the problem of theory construction?
6. State and critically analyze Dedre Gentner's criteria for a good
scientific analogy.
7. State Black's interaction view of metaphor. Explicate to the best of
your ability the following statements by Black: "a metaphorical statement
can sometimes generate new knowledge and insight by <changing> [italics]
relationships between the things designated..."(p.37, Ortony) "some
metaphors enable us to see aspects of reality that the metaphor's
production helps to constitute. But that is no longer surprising if
one believes that the world is necessarily a world <under a certain
description> [italics]--or a world seen from a certain perspective.
Some metaphors can create such a perspective."(pp.39-40, Ortony)
How, if at all, could Black's view of metaphor be useful in constructing
scientific theories?
8. The question of what aspects of an analogue map onto the subject
has been addressed by various authors, including Hesse, Gentner,
Winston, and Carbonell. Discuss the views of at least two. Explain
why the question is important. Are any of the suggestions adequate?
9. Compare and contrast the constraints in theory construction discussed
by Gutting and Monk; Monk: (1) requirements of specific content, (2)
requirements of empirical adequacy, (3) requirements of theoretical
compatibility; Gutting:(a) empirical facts to be explained, (b)
theoretical concepts and laws, (c) heuristic principles, e.g. simplicity
(d) methodological considerations, e.g. make precise predictions,
(e) cosomological principles, e.g.materialism. How could these (or
similar) types of constraints be used in finding and using analogies
in theory construction?
10. What, according to Darden and Maull, is an interfield connection?
How are interfield connections like and unlike analogical relations?
Critically analyze Darden's claim in "Theory Construction in Genetics"
(Nickles, 1980) that interfield connections provide a better source of
new ideas for theory construction than do analogies.
11. Discuss the work of Patrick Winston on reasoning by analogy in AI
systems. Pay particular attention to the use of abstraction in
achieving matches. Discuss possible ways in which Winston's work
could be useful in building a system to formulate scientific hypotheses.
12. Discuss the best answers you know to the following questions:
(i) what is an analogy?
(ii) are there types of analogies?
(iii) how can we distinguish good from bad analogies?
(iv) how can we use analogies to construct new scientific theories?
(v) what are the prospects for building AI systems to use analogies
(or interfield connections) to construct scientific theories?
∂23-Jan-82 0900 Darden at SUMEX-AIM hello and happy new year
To: STT at SU-AI, RDG at SU-AI, Dietterich at SU-SCORE
cc: Darden at SUMEX-AIM
Hi, folks. I am back from holiday travels and teaching two courses
(history of molecular biology and recombinant DNA research and
philosophy of biology) and doing various administrative work.
How are you all doing?
I have the sad feeling that I am loosing touch with AI and I've
been trying to think of ways to keep that from happening. If any of
you come accross recent articles that you think I would be interested
in, please send copies. If youhave nothing else to do and want to send
me bullitins on new and interesting developments in the field, I would
very much appreciate them. I am trying to decide what journals I should
subscribe to, since getting over across campus to the computer science
library is difficult. What is the most useful thing that you do to keep
up with things, other than being at Stanford, of course.
I have applied for various fellowships that would allow me to be
in Boston next year. Do any of you know people at MIT that I should
look up?
Bye for now,
Lindley
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∂31-Jan-82 0747 Darden at SUMEX-AIM Re: DNA book, etc.
To: RDG at SU-AI
cc: Darden at SUMEX-AIM
In response to your message sent 29 Jan 1982 1341-PST
Hi, Russ. Thanks for sending the news article on the DNA book and research.
I am teaching a course on the hsitory of molecular biology and recombinatnt
DNA research and am just today making up a book list--good timing.
How is your thesis coming?
I have the sad feeling that I am losing touch with you all at Stanford
and with the AI work. I plan to subscribe to the journal Artificial
Intelligence, despite its high cost, and try to keep in touch.
I'm about to revise my analogy paper and appreciate the comments you sent
some time back.
Bye, Lindley
-------
∂07-Feb-82 1120 Tom Dietterich <CSD.DIETTERICH at SU-SCORE> [Clancey at SUMEX-AIM: analogies & schemas]
To: Analogy-seminar: ;
Here is a message from Bill Clancey that I thought you might like
to see. He is pointing out that when people are trying to understand
something new, they first try VERY hard to fit that new thing into
some existing abstraction class. Analogies seem to play a smaller role
than we may have been thinking? Reactions?
--Tom
---------------
Mail-from: ARPANET site SUMEX-AIM rcvd at 26-Jan-82 1120-PST
Date: 26 Jan 1982 1116-PST
From: Clancey at SUMEX-AIM
Subject: analogies & schemas
To: csd.dietterich at SU-SCORE, bennett at SUMEX-AIM
Dave Kieras of Arizona gave a talk at an ONR meeting last week that
may interest you.
Dave is investigating how to write procedures for operating devices, taking
into account prior knowledge that people might have about how the device
functions.
He did an exploratory experiment to determine what knowledge people have
about devices. He asked subjects to describe devices that they were given
to handle. There were 7 devices: an alarm clock, a radio, a tape recorder,
an ohm meter, an audiofrequency attenuator, a 4 line scrambler for rat
shock experiments, and a flasher for phi-phenomenon experiments.
All subjects were video-taped.
The results were what other experiments in schema-based understanding would
suggest: features acted as cues to trigger general abstract categories
(e.g., "signal generating device") which suggested other features to look
for. For example, subjects were generally disturbed that the "second hand"
of the clock was missing. Some would spend considerable time looking on
the table and floor to see if it had dropped off. Subjects expected devices
to require power and would always comment ("here's the power cord and here's
the light to tell you that it's on"). One subject kept looking for the
eject button on the recorder; she was surprised that one simply had to lift
the lid. The commentary was also feature-driven, with an attempt to explain
the purpose of each switch or dial on the front panel.
Looking inside one device, the subject commented: "tubes are like light
bulbs, but are more complex... they use current ... they have different
functions." They would also point out what they thought might be important,
but could not explain. There seemed to be more attempts to fit the
devices to known abstract categories, rather than to form analogies to
other kinds of devices: "this is a psychological generating device like
an audiotester for hearing."
Generic features of devices were mentioned: "There's a switch, but I'm not
sure what for." "There're two outputs at some rate with phase between
them altered." "Most likely something goes in and something else comes out."
More knowledgable subjects picked up subtle cues from the fact that a device
was not commercial, but built locally. "Experts" would spend a lot of time
on details, like checking the fuse, and only later come back to the question
of determining the purpose of the device.
It was not clear why subjects would decide to reject a given hypothesis
("signal measuring device") and shift to another.
I was mainly impressed by how similar the reasoning process was to medical
diagnosis, with concentration on abstract categories such as "measuring
device" rather than making analogies with particular kinds of measuring
devices.
Bill
P.S. forward this msg if you think others might be interested.
This work is not written up yet, but I'll let you know when a tech report
arrives.