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C00002 00002	∂09-Jul-82  1740	SCHOOLEY at RUTGERS 	a critique at last 
C00011 00003	∂TO schooley@rutgers 16:21 20-Jul-82
C00018 00004	∂TO schooley@rutgers 17:00 26-July-82
C00036 00005	∂TO schooley@rutgers 17:10 29-Jul-82
C00069 00006	-- Never mailed --
C00075 ENDMK
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∂09-Jul-82  1740	SCHOOLEY at RUTGERS 	a critique at last 
To: greiner at SU-AI

    I have finally finished reading the material you sent me ages ago.
Before I get to my comments there are a few general questions I have for you.
Both Tom Mitchell and Rich Keller (at Rutgers) would like to be included in
the Analogy BBOARD. Speaking of the BBOARD, how does one access it? Rich
Keller is working with Tom Mitchell on LEX. Paul Utgoff is working on LEX
also -- trying to find a way to alter the generalization language for the
Version Space program when the predefined generalization language proves
insufficient for the generalization task. His work may be of interest to you
in relation to your problem of defining the relevant set of properties for
forming an analogy.
    To answer your question -- my "unofficial" leave was a kindness on Rutgers
part so that they could continue to pay my RA salary. I have been having
trouble with ulcers and could not predict how long I would be out of commision.
I am finally feeling better and at least working a part-time schedule again.
   
-------
∂12-Jul-82  1254	SCHOOLEY at RUTGERS 	a critique at last 
To: greiner at SU-AI

I have finally finished reading the material which you sent to me ages ago.
Before I get to my comments I have a few general questions to ask you.
How does one access the Analogy BBOARD?  Speaking of the BBOARD, both Tom
Mitchell and Rich Keller would like to be added to the list. Rich is working
with Tom on Lex this summer -- I believe his interest is in adding analogizing
capabilities to Lex.  Paul Utgoff is also working on Lex -- attempting to 
create a new generalization language for the Version Space program when the
predefined generalization  anguage proves insufficient for the current 
generalization task. His work might be of interest to you in relation to your
problem of defining "on the fly" a set of relevant properties of the analogues
being considered.
     To answer your question -- my "unoficial" leave from Rutgers was a 
kindness on the part of the CS dept. so that they could continue to pay 
me my RA salary. I have been having troubles with ulcers and could not 
predict how long I would be out of commission. I am feeling much better 
and working again at least on a part-time schedule.
     Your list of references is more complete than mine -- your short
critiques were very helpful to me- thanks.  My interest in analogy is
focused on its use as a problem solving tool. Specifically, I am interested
in what help analogy can provide to the task of redesigning an existing
system to produce a system satisfying an altered set of specifications.
The domain I am looking at currently is digital circuit design. My current 
approach is to develop proofs that each of the specs of an existing circuit
are actually satisfied by that circuit and then to use these proofs to 
guide the redesign ala the geometry problem solver (I did send you that
paper didn't I).
    Now to my comments on your papers -- I'll list the comments by the 
page in the paper where the thought occurred to me -- hope that is 
intelligible to you.
   First, comments on Analogies and things like that , Feb.8, 1981 (hope
this is not too old a version by now)
    I liked this paper very much and found it easy to read and understand.
 Page 3 -- def of analogy- I don't see the distinction between your def
    using shared partial theory and a mapping between entities that
    preserves the relations between entities as well as the properties 
    of matched entities. The shared partial theory seems to be simply
    a statement of the properties of entities and the relations between 
    entities. If the preservation of the relations between entities is used
    to limit the allowable entity mappings aren't you accomplishing the
    same thing without the necessity for discovering some abstract common
    theory underlying each of the analogues? In fact, how else are you
    ever going to find the shared partial theory?

page 4 -- allowing users to alter the rules for analogizing seems 
    appropriate since analogies are often very subjective -- this may
    be a rather formidable task since I suspect the rules will not be 
    simple ones covering all analogy tasks. The user may be hard- put
    to come up with any valid rules of his own.

page 7 -- deciding when a sufficiently good analogy has been found can 
    also be very subjective (or can be based on what the the analogy is to 
    be used for). Do you envision automatically checking whether the analogy 
    is sufficient for its intended use?

page 9 --- I see the ability to limit the generated analogies by specifying
    constraints as essential -- Rich Keller has looked at limiting the set
    of applicable problem solving production rules by looking at the
    "context" of the current problem state. His paper may be of interest 
    to you.

page 14 --- generating a Meta-Facts KB that is any way sufficient or
    complete for finding most analogies ought to earn you a PhD all by
    itself. How do you plan to approach this problem?

I have to leave the terminal for a bit. I'll send a critique of your
other paper in another message shortly.
 Be right back!
Pat Schooley
-------

∂TO schooley@rutgers 16:21 20-Jul-82
"Cover Letter"
Pat -
	This is just a "cover letter", overhead to the (hopefully) more
substantial messages to follow.

(1) First, I hope you are continuing to feel better (both in an "absolute"
sense, and in the "first derivative" sense -- of ongoing improvements.)

(2) Do you plan to be in AAAI this August?
I'm considering arriving there a day early, to meet with the wealth of
people I'm not seen for such a long time.  Lindley is also considering that
idea.  (If you are going,) when do you plan to arrive?

(3) Yes, I did receive your critiques on both that early thesis proposal,
and that "everything I know about analogy" paper.  Thank you for spending
the considerable time and energy needed first to plow thru them, and then
to generate your responces.
I'm now addressing/answering many of the excellent issues you raised;
I'll of course send that document on completion.

(4) I'll also mail a more recent (short) proposal.
I'm actually beginning to (seriously consider doing work towards)
implementing it.

(5) I still have a set of comments on your 702 paper, which I have to commit
to paper (as well as rethink) before mailing to you.  Soon...

(6) Lindley wants to get the analogy bboard going again. Any ideas for a starting
topic?  Perhaps something nice and well-defined, like "what is an analogy"
would be appropriate...  Stay tuned for future developments.

(7) I had an hour talk with Rick Hayes-Roth recently; not on my thesis topic
per se, as much as on the nature of theses in general.  
One point he raised was on the *real* purpose of the work:
was my thesis to be the solution to a real problem, or a labor of love?
Given that there is no solid evidence that analogies are of any value,
(beyond the usual wealth of introspective data and intuitions in general,)
I had to confess my purpose must be the latter.
Have you thought how you would catalogue your work, and answer the question
of why you are doing it?

----
Enough for now.  Do expect a horde of messages to follow,

Russ

∂23-Jul-82  0800	SCHOOLEY at RUTGERS 	Re: "Cover Letter" 
To: RDG at SU-AI
In-Reply-To: Your message of 20-Jul-82 1921-EDT

Russ,
   I am planning to attend AAI and will be arriving in the evening of 8/17.
Hope to see you there.
   You're discussion with Rick Hayes-Roth sounds similar to discussions 
we have had here at Rutgers. Trying to do a thesis on the topic of
analogy per se seems not only difficult but rather esoteric and of 
dubious practical value. I have drifted in the direction of working
on what could be labelled re-planning (if one has a working digital
circuit and a plan telling how it was designed, how can this info be
used to redesign the circuit to meet an altered set of circuit 
specifications). This appears to be a more practical problem which
is still an application of a limited form of analogy (at least it appears
that analogy is involved when humans perform such redesign tasks).
   There are several people (including me) here at Rutgers who would
be interested in reviving the Analogy BBOARD. I would be especially 
interested in seeing a discussion of the practical uses of analogy.
(i.e. some atempt at categorizing the different practical uses of 
analogy by humans and defining the differences between these uses.)
For example, is there some basic difference between the use of analogy
as a problem solving device and the use of analogy in knowledge 
acquisition?  Do let me know if the BBOARD is revived -- there is 
definitely an interest here in participating in such discussions.
    Your new proposal sounds interesting -- the thought occurred to me
that you might be interested in the work that has been done here at
Rutgers on the EXPERT system. This work involved the development
of medical diagnostic data bases. In particular, the required 
interaction with medical experts during the development of the data
bases might be of interest to you. Let me know if I can help you
get any papers from here that might be of interest.
   Hope to see you in August!
Pat Schooley
-------

∂TO schooley@rutgers 17:00 26-July-82
Responses to your comments on my paper
****
   >> from message, [∂12-Jul-82  1254  SCHOOLEY@RUTGERS   a critique at last]
   >> my response: 19-Jul
[My comments are bracketed with ****s]
****

       First, comments on Analogies and things like that , Feb.8, 1981 (hope
    this is not too old a version by now)

****
My thesis ideas have gone through several iterations since then 
-- note that my more recent thesis proposal bears only cosmetic 
similarities to the document you just read.
However, many of the comments you made were still quite relevant;
and well worth addressing.
****

	I liked this paper very much and found it easy to read and understand.

     Page 3 -- def of analogy- I don't see the distinction between your def
	using shared partial theory and a mapping between entities that
	preserves the relations between entities as well as the properties 
	of matched entities. The shared partial theory seems to be simply
	a statement of the properties of entities and the relations between 
	entities. If the preservation of the relations between entities is used
	to limit the allowable entity mappings aren't you accomplishing the
	same thing without the necessity for discovering some abstract common
	theory underlying each of the analogues? In fact, how else are you
	ever going to find the shared partial theory?
****
There is a subtle, but very important distinction; one I've always 
found difficult to communicate.  Perhaps this description will be less vague
than the brief one given in that paper.  
(I've also included a few examples throughout this comment, which may help
to illustrate some of the points.)
[The "reformulation" addendum in the more recent proposal also addresses this
issue; also rather poorly.]

This "shared partial theory" approach is "model-based", rather than 
"representation-based".
Critically examine the mapping approach:
Here one maps components/relations/features/etc from one analogue to the other.
Realize these components/... do NOT depend (directly) on the analogues themselves,
but rather of the particular REPRESENTATIONS of those objects.
Hence to consider a mapping from parts of the objects,
one must first have a suitable representation/decomposition of the analogues,
one which defines these components, and their interrelations.

Realize that a single object may have many different descriptions.
[For example, there are at least two totally different ways to describe a
program -- it could be described structurally, (in terms of their internal code,
or abstractions thereof,) or behaviourally (i.e. based on what it does, I/O-wise).  
And each of the descriptions would give rise to to a different analogy-mapping --
two "structurally similar" programs may exhibit totally different behaviour,
(e.g. both MAPC and LENGTH map down along a list, performing some operation
at each position);
and vice versa -- consider a BUBBLE-SORT which deals with a linked list,
and a SHELL-SORT of an array.]

(A sillier example comes from McCarthy, who suggests that a Martian,
on encountering a room filled with people,
might figure that all 20 left arms constitute one individual,
the 20 right legs another, etc.
Hence it (the Martian - or maybe "they") would claim there were 6 individuals in
the room, 
(viz., "left arm unit", "right arm unit", "left leg unit", "right leg unit", 
"head unit" and "trunk unit")
rather than the "obviously correct" answer of 20 individual people.
We would of course expect that the analogies it would make would be
considerably different from ones you or I might compose.)

Now consider the "spt" approach.  These spt-derived analogies are NOT dependent
on any particular representation, (at least in its [unrealizable] generality). 
Such an analogy, instead, could be based on ANY set of properties of the
analogues themselves; rather than just those features which happen to be
captured in some particular description of these objects.
Hence, with this approach, two objects could still be classified as analogous,
even if, in their "universally accepted" representation they have totally
different symbols, employ totally unrelated relations, and correspond to a
totally different "cut" of the objects involved.

In terms of implementation, this distinction rapidly collapses.  While the
spt approach does allow ANY representation of the analogues to be used,
no computer (nor any person) has more than a few different descriptions of
any object.  Given this small finite number of independent representations,
one can usually just merge these perspectives.
(In the program case, this means using the representation derived by merging
the structural and behaviour descriptions.)

My point, in making that spt comment, reflected my disagreement with the
claim made (implicitly) by many researchers that there is a single 
"universally accepted" way of describing any object;
and that any analogies which uses this object as an analogue
must simply deal with the symbols used in this representation.
I feel there are times when the current representation is inadequate;
either heuristically or epistemologically.
I futher belabour this point in the "Reformulation" section of the "What's
an Analogy Like" paper.

Consider the "endocrine system is like blood" example used in my mini-proposal.
There is probably no mapping of symbols from the pre-existent 
"endocrine system theory" to the standard "blood theory" which captures
the intent of this message. The trick here is to first define new symbols 
-- such as "ThroughPut of Circuit", and other features and relations 
which pertain to both such instances of Circulating Material Flow.
Then, after this reformulation, the analogy will be simply a mapping,
from one (newly generated) representation to the other.

Does any of this make sense?  If you can see a clearer way of presenting this,
please let me know.
****

    page 4 -- allowing users to alter the rules for analogizing seems 
	appropriate since analogies are often very subjective -- this may
	be a rather formidable task since I suspect the rules will not be 
	simple ones covering all analogy tasks. The user may be hard- put
	to come up with any valid rules of his own.
****
Two comments -- 
(1) Providing the user with the facility for modifying
the rules fits into my tirade against single-representation-ness;
(also examplified above.)
I.e., s/he can not only twiddle the representation,
s/he can also re-define the rules which are "run" over these descriptions as well.

(2) There will clearly be various classes of rules, (as I see it).
Some will pertain to all manners of analogies 
(e.g. Two analogues probably belong to several of the same classes), while
others will be quite domain specific (e.g. Two diseases are considered similar
if they share a common set of symptoms.)  
Rules of the first class will probably not undergo much changes -- while the
user is allowed to modify them, they are sufficiently general and
"common-sense"-ical that they will probably stay fairly static.
(Of course this reflects only my feelings, which will soon be subjected to
various empirical tests.)  
Those other domain-dependent rules, by definition, will vary across domains.
What does it mean for two iteration descriptions to be similar?  
The above "two diseases ..." rule says nothing directly relevant to this
task.  (Indirectly, of course, it does indicate that, in some situations,
behavior is very relevant; this may hint at what types of properties to
consider when comparing two program-abstractions. Clearly we need to find
a new heuristic which is analogous to that old rule...)
****

    page 7 -- deciding when a sufficiently good analogy has been found can 
	also be very subjective (or can be based on what the the analogy is to 
	be used for). Do you envision automatically checking whether the analogy 
	is sufficient for its intended use?
****
Good idea.  This was the type of issue which led me to deal with
the Knowledge Acquisition task, shown in latest proposal.
Here the purpose to the analogy is fairly well understood,
as is the criteria for success 
(i.e. does the ES now use this new operator in solving a particular problem?).

Of course I still want to leave the user with the option of specifying
"when to stop", perhaps by defining what type of analogies are required.
It's not clear how often this facility would be used, if at all.
Anyway, I'll leave this as a research question for now.
****

    page 9 --- I see the ability to limit the generated anac1←OSKLAErAMaKGS→sS]N4∀∪G←9gieC%]ifA¬fAKgMK]iS¬X@ZZ↓%SGP↓↔KYY∃dAQCLAY←←-KHACPAYS[%iS]N↓iQJAMKh~∀%←LACAaYSG¬EYJAAe←EY∃ZAg←1mS]N↓ae←IUGiS←8AekY∃fAEr↓Y←←W%]NACPAiQJ4∀∩EG=]iKqPDA←L↓iQJA
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CMiKgh↓[CSX↓CIIe∃gfAi<A[JA%fA%	≥↓'*[¬∩@~∀(GREINER@SAIL does indeed reach me, by the way...)
1: This paper underwent a non-trivial reorganization after I mailed it to you;
	making the page numbers next to meaningless.  It would have been
	useful to see the section number as well as the page number...
2: Would you mind if I send this to Lindley, and allow her to join in this
	discussion?
****
****
Onto general comments:
1) I apparently gave an inaccurate impression of the purpose of this "magnus opus".
	My goal was basically to set down a lot of ideas running through my head;
	it was NOT to produce a definitive, final word on the topic of analogies.
	I hope to use comments, from people such as yourself, to refine and augment
	these superficial first thoughts into solid arguments.

   So, please keep your comments comings...
	and continue to point out which ideas were not effectively communicated, 
	or seem unacceptably fuzzy... [see point 3), below]

2) Your comments seem to imply that you consider two things (e.g. cases of analogy)
	to be the same if the same procedure can be used to handle both of them.
	While this is indeed one way the two things can be similar, there are
	still many other dimensions in which these objects can differ.

   My vision is of an N-dimensional space of analogies --
	in which one can locate any given instance of an analogy in
	(exactly) one place.  Here I am considering not only the
	process required to "solve this analogy problem", but also the
	situation in which this analogy occured (i.e. was only one
	individual involved, or several,) the "problem context", (whether the
	end goal was to find the other analogue, or to more completely
	describe some object, or ...), etc.

   In fact, one of the main purposes of this report was to (roughly) lay out 
	those dimensions.  Anyway, I'll elaborate on this while responding to
	your comments below.

3) In several places I puzzled over (read: challenged) some of the phrases
	you used.  Another major goal of this paper is to hone up some
	intuitive notions we all have -- to where, eventually, these vague
	fuzzy terms can be given a precise, unambiguous interpretation.

   I hope this exacting style does not come across as hostile.
	If it does, please realize that does not reflect my intent,
	but rather my evaluative purpose, and (occasionally overly-gruff)
	speaking style.
****


    Russ,
	Please forgive any garbled or incomplete messages -- I've been having  
    trouble with my home terminal. Actually, I think the problem is really with 
    the telephone lines. At any rate let me know if the first set of comments
    did not arrive in readable form.
****
I got the first few paragraphs of your previous message twice, but the
full msg only the second time.  What was sent was readily readable.
****
       Following are comments on "What's an Analogy Like?" 18 May 1982

      When you are presenting a set of axes for the space of analogies you use
    the term "orthogonal" axes. How are you defining the term "orthogonal"?
    In relation to a vector space (which the space of analogies is not) orthogonal
    implies independent. I am not convinced that even the final set of axes which
    you present are truly independent. 
****
No, this is precisely the impression I was trying to avoid.
While a grandious goal is to present a collection of truly orthogonal axes,
(is "truly orthogonal" like "slightly pregnant"?... oh well,) I
fully realize that these particular features are cearly not independent
of one another.  Sorry to have mislead you.  In my current draft,
this report declares that it will attempt to present
	... a semi-formal specfication of the space of analogies.
	Our eventual goal is a description of the properties of this space;
	this paper concludes with a first approximation to this,
	motivated and justified by the results presented in the earlier chapters.
****

      Are the "senses" of analogy which you present in 3.1 really distinct? As 
    you point out the similarity case and the proportional case can be considered
    the same. I look at the familial resemblance case as an extension of the
    binary relation "similar" to an n-ary relation. If you disagree with this,
    how do you view the familial resemblance case?
****
Two comments:
i) Let me rephrase my point --
I feel that these three senses seem to be interesting positions 
along some dimension(s) -- at least according to my intuitions.
(See General Comment #1 above.)
I had hoped that any task could be placed in exactly one of these categories.
Do you have any specific example which could belong to more than one of these,
or which fits into none of them?  
(Well, as I write thigs, I have to conceed that something like
"the jawbones of the following species resemble one another" would be difficult
to classify -- here a "proportional-like analogy" is extended to more than
two cases.)

ii) The second issue deals with the issue of what it means for two cases of
analogies to be "considered the same".
The fact that a single process may be able handle both certain types of
similarity-analogizing tasks and proportional-analogizing tasks
does not mean that I feel that "the similarity case and the proportional case
can be considered the same".
(See General Comment #2 above.)

Let me elaborate:
(I feel) a similarity-analogy is clearly a different (albeit similar) beast
from a proportional-analogy.  For example, the similarity-analogy
   [1]  "LENGTH is like MAPC"
must be different from the proportional-analogy
   [2]  "the iteration process in LENGTH is like the mapping-along process in MAPC",
even if the intent on stating [1] was, in fact, have been that [2] holds.
That is, the fact that [1] and [2] might somehow "represent the same thing"
(for example, after some initial surface-level processor,)
does not mean that they are the same.
(If nothing else they exhibit different surface-level structures.
This could easily lead to the famed "linguistic front-end" vs "deep
internal processing" quagmire, which I'll not pursue farther here.)
Perhaps this distinction should be considered a property of the analogy problem
statement, rather than of the analogy per se.

In conclusion; yes, there are some senses in which these three cases of
analogy can be considered similar (that's no doubt why the term "analogy"
applies to each of them).
However this does NOT mean that these cases should be labelled the same;
as there are dimensions in which they differ greatly.
****

      In the notes on page 15, you imply that the analogy understanding tasks 
    are involved only with the similarity analogies -- isn't this merely a 
    by-product of the way you have defined the senses of analogy? Must the senses
    of analogy be defined in terms of finding predicates? I'm not sure how these
    definitions correspond to either the mapping definition or your partial 
    theory definition of analogy.
****
Two responses:
i) No, that innocent-seeming "reasons" can encode a lot.  
I imagine being able to include the proportional aspects of the analogy
in this parameter.  Hence the proportional "Cow:Calf :: Ewe:Lamb" might be
stated as
	"Cow is like Ewe, (within the constraint)/in that
		a Cow's calf is like a Ewe's lamb",
or something like that.
(I still don't know what to do about familial case, though.)

ii) I was unable to figure what you mean by
	"Must the senses of analogy be defined in terms of finding predicates?".
Did you mean
  [1]	Why discriminate amongst the cases by virtue of the predicates found?
or
  [2]	Why *(unary) predicates* as opposed to *arbitrary (n-ary) relations*?
or
  [3]	Why *predicates* as opposed to *units and slots*?
or
  [4]	Why *finding* predicates as opposed to *applying* known predicates?
or ...

Let me try to answer each of these.  If you had meant none of these,
please resubmit the question.
[1] I'm not.  I'm discriminating amongst the cases by virture of
	top level surface form; and then noting what types of predicates
	seem appropriate for each such case.
[2] I do not consider this difference relevant.
	(This follows from my model-based perspective.)
[3] They're both "turing equivalent" -- 
	I choose predicate calculus because of its clean semantics.
[4] Many of the interesting, reformulation-related challenges derive from
	generating new predicates.  If I was limited to only applying known
	predicates I would never address that collection of issues.
****

       There really a clear distinction between the tasks involved in generating
    an analogy and the tasks which use the analogy to infer information. I don't
    however see the distinctions among the generation tasks -- to find an analogue
    requires finding the analogy, likewise judging or selecting analogue(s)
    requires finding the analogy. 
****
(Actually, "requires finding the analogIES."... just a small point)

Yes, one needs to find the analogy/ies to find the analogue -- so?
Here the PURPOSE of the over-task is different; even though the internal
processing will be, as you noticed, quite similar.

This point related to General Comment #2 above.
You seem to be basing you comments only the internals of the mechanism,
and ignoring the other ways in which two analogies can be compared.
****

      The incomplete algorithms on page 17 may be easier to see if the analogy is
    considered to be a mapping of relations (predicates) as well as a mapping of
    objects. For example, in the proportional case finding the analogy involves
    finding a relation between y and B having similar properties to the relation
    between x and A (the relations need not be identical, but R<x,A> must map
    into R'<y,B> in an analogy mapping from A to B which maps x to y). The 
    given constraint is just a means of limiting the allowable mappings from
    A to B.
****
Of course one wants to reason about, and compare/contrast, the relations
associated with both analogues!
I never (meant to) say contrary!
Using the "common partial theory" approach one need not even deal
with objects described using the same language, which implies, ipso facto,
that one can readily deal with relations as well as objects.
****

       The analogy application axis is definitely not "orthogonal"(independent)
    to the analogy task axis. The two application given are not really disjoint
    as shown by the examples given. In the linguistic application, the hearer is
    expected to make inferrences not directly communicated (otherwise, the
    analogy communicates no more than what is explicitly stated). Doesn't this
    mean the linguistic application includes the deductive/predictive 
    application?  Your elaboration of the applications actually says this!
****
Once again, you're only looking at the internal processing going on;
and ignoring other features of this analogy phenomena; which here is the overall
scenario.  (See General comment #2.)

Yes, as I explicitly stated, the mechanism responsible for processing
(at least) one side of the linguistic application MUST include a mechanism
similar to the one used for the deductive/predictive application.
****

      The "conclusiveness of derivation"(page 23) axis seems to apply only to the
    "using the analogy" task -- however, the provability of inferrences derived
    from an analogy can be used to judge the usefulness ness (goodness) of the 
    analogy itself. In this sense, this dimension can apply the analogy generation
    task.
****
What would it mean for a generated analogy to be "conclusive"?
(For comparison/illustration, recall that a "conclusive use of an analogy"
is one which leads to a correct (i.e. valid) deduction.)
This would obviously depend on the definition of "analogy",
and on the inferencing process which would then uses this analogy.

Perhap you were suggesting that a "goodness or usefulness" dimension should
be included as one of the axes.
An analogies position along this dimension would correlate with the number
(and nature) of "deductions" one could derive from this analogical-connection.
I had considered this, but was unable to even begin to quantify this --
not even enough to include it in even so preliminary a draft as the one I sent out.
Perhaps you have some suggestions...

I also puzzled over the phrase 
	"provability of inferrences[SIC] derived from an analogy".
Could you elaborate what you meant by that -- what is an inference derived from
an analogy? provable in what sense? based on what methods? etc.
****

      One picky point on page 24, instance to instance analogies are not really
    cases of learning from examples where the goal is to find a generalization
    which covers the presented examples.
****
[Minor parsing problem:
I assume you are claiming that learning from examples involves
finding a generalization which covers the presented examples.
The other parsing implies that instance to instance analogies, where the goal
is to find a generalization, is not a case of learning from example.]

Whose definition of "learning from example" are you citing?
Who said that it must involve finding the generalization of examples given?
Certainly not Simon, who is now claiming that a human expert has between 50-100K 
"relatively specific base cases" (my quotes) which he used in problem solving.
Quine (in his discussion of ostention,) appears to take an even more extreme
position -- in which implies that no generalization is ever acquired.
(In fact, besides Winston's early simplistic examples, and Tom Mitchell's
impressive MetaDendral (LEX?) work, I don't know of any (significant) learning
research which claims that generalization is REQUIRED to actually learn.  Please
correct this ignorance of mine...)

By the way, I'm defining "learning from example" as exhibiting superior
performance on subsequent examples, based on some prior experience with
sufficiently similar cases.  (Note this is totally behavioristic -- which
is why this entire issue, which deals exclusively with internal organization
of the facts, seems almost moot.)
****

       The degree of specificity dimension seems quite vague to me -- perhaps I
    have just missed the point completely!
****
The sentences
	"People are like birds"
and
	"John ate as many sun-flower seeds on June 24 as ..." 
are similar, in that both are discussing a comparison between humans and birds.
They are, however, somewhat different.
I propose we label this type of difference "specificity".

This dimension is still extremely qualitative -- I have no idea what the
units of specificity should be...  Suggestions?
****

       Isn't the define vs refine axis subsumed by the analogy task axis (i.e.
    analogy generation vs analogy use)
****
Yes, these two dimensions are not unrelated... but once again, you seem to only
consider the internal process needed to solve these two types of problems;
and to be ignoring the other aspects of the situation: here, the goal of the
person who posed the problem; and hence what he would consider an appropriate
answer.
****
      
       Obscure vs obvious is such a subjective distinction that I doubt its 
    usefulness in any automated analogizer where at any given time only one
    person's background (knowledge base ) can be available.
****
I totally agree.  This is related to something Doug Lenat was thinking about --
what would make an analogy humorous, as opposed to usable.
Needless to say, that topic is another issue which I never bothered to pursue,
and do not intend to.
****

       I am skeptical of the statement that any analogy can be described as a 
    modification of some parameter when the problem is stated in the correct
    representation.  (Unless the term parameter is given a meaninglessly 
    broad definition.)
****
Have you any counter-examples?  I claim I could always concoct a representation
in which the commonality of the analogues is "inherited", and the difference
is just one slot whose value differs for the two analogues.
Ahh, the joys of reformulation...

Realize, of course, that such a common unit might seem
highly artificial/strained/meaningless 
(see the obscure vs obvious discussion-ette, above).
****

       Doesn't the refined vs sloppy distinction really refer to the presence
    or absence of constraints on the analogy?  If this is so, I don't see a 
    clear distinction between this dimension and the following bounded vs
    unbounded dimension.
****
Both "sloppy" and "refined" are rather ill-defined terms.
A "refined analogy", by my way of thinking, would lead naturally 
(and "unavoidably") to a single analogy; whereas "sloppier" specifications
might not.

Certainly as we increase the constraints which are included in the
problem statement, we can only be restricting the number of "legal" analogies
which could be derived.  As such, by the definition given above, the
analogy-problem is becoming increasingly more refined.

There are, however, other ways a problem could be a refined analogy.
Perhaps the analogues belong to a sparse space, or we are working with a very
limited inferencing scheme.  (No, I'm not too happy with these either...)

Note that a "bound analogy problem" is (necessarily) more limited than the
corresponding unbound one -- and hence would be more refined.
****

       I agree that the interfield/intrafield distinction is not a very useful
    one -- however, the analogies between different fields certainly seem more
    powerful.
****
Any ideas why?  Perhaps because the useful intRAfield analogies have probably
already been noticed, and, indeed, have already included in the language for
describing that domain.
As such, they are considered obvious and self-evident.
***

       The additional dimensions stated for the metaphoric use of analogy seem
    to me to be either not very useful or subsumed by the other dimensions
    given.
**** perhaps ****

       Am I correct in assuming that the properties of analogy given in section 6
    are not meant to be further dimensions of analogy but rather characteristics
    which an automatic analogizer ought to exhibit?
****
Yes -- but not just AUTOMATIC analogiers.  I would hope that ANY analogizer,
natural or artificial, would exhibit these characteristics.
****

       I totally agree with your statements on the existence of more than one
    possible analogy between any two given analogues and the necessity for 
    reformulation in order to find the "best" analogy for the given task.
****
Reformulation is not ONLY used to find the "best" analogy; but may be needed
to find any analogy at all.
****

      I seem to recall that somewhere(can't seem to find it right now) you define
    reformulation as a transformation from one abstraction to another abstraction.
    Why isn't the transformation from the given analogue to an abstraction of 
    that analogue also an instance of reformulation? Certainly the abstraction 
    of the analogue is a different view (or representation ) of that analogue!
****
"...DIFFERENT view of that analogue."?
In my view the analogue is a model, as opposed to a theory.
It is, as such, a type error to consider the analogue as a representation
of itself.

I label that "analogue to abstraction" mapping the "abstraction process",
for want of a better name.
****

    THE END -- finally! I hope you will forgive the verbosity of this critique
    and the fact that so many of the comments seem somehow negative (I guess 
    differences between your view of analogy and mine will be more helpful to 
    you than the concurrence between our views).
****
No objections whatsoever -- I'm quite pleased that you spent so long in the
analysis; and just hope that you don't mind the verbosity and negative-ness
of my rebuttals.

Also, I'm not sure we disagree as much as simply mis-understand each other.
Hopefully we can begin to develop a common language as these discussions go on.
****

    Do send me any additional work as it is finished. I am definitely interested
    n the progress of your work.
**** will do ****

    Talk to you again soon,
			     Pat
****
I'm looking forward to hearing your reactions to these comments,
and to meeting you at AAAI.
Caio,
	Russ
****
-- Never mailed --
Pat -
	Now for the promised comments about your CS702 project
("An Investigation of the Use of Analogy as a Problem Solving Tool").
First, some general comments.

Basically, I questioned the claim of generality made on page 1,
on several grounds.  
Reason 1 is the absense of reformulation.
The analogizing algorithm you describe makes heavy use of its particular
representation -- its matcher seems geared to certain particular forms of
expressions, and specific special relations (especially Isa).
While that may lead to excellent results over certain limited applications,
I question the generality of any analogy finding process unable to 
reformulate the descriptions of analogues.
I discuss this general issue in one of the appendices of the
"What's an Analogy Like" paper.

///Statement of Position digression:
If you know that two objects (e.g. proposed analogues) belong to some
general class, they will both inherit the features associated with that class.
Often the "analogicial connection" joining those analogues will be no more than
this body of common features.
This is why I feel that if one already knows the ISA, the analogical matching
is often reduced to triviality, and is uninteresting.
(Of course it may still be quite worthwhile, suggesting new conclusions, etc ... ///

Reason 2 stems from your choice of initial domain, geometry.
This particular field has many rather nice properties which might make
it rather special; and the routines you discuss seem to exploit them.
(The nice properties include continuity, known analogues (2d - 3d), rich, precise
vocabulary, etc.)

Would it really be extendable to other domains?  How easy would this be,
both conceptually and in terms of coding it?

The third point is efficiency -- (perhaps due to the vagueness of the algorithm
specification,) the process seems inherently slow.
E.g. p4 (sec 2.4) talks about examining "all applicable defin...". 
Unless you have some clever indexing scheme in mind, this could
be very expensive...
It might even be infinite - if some set of rules are circular.
(where both A => B and B => A are included.)

A different general point is the imprecision of the paper.
(i.e. this is meta to the topic, analogy; and deals with its presentation in
this paper.)
While the algorithms were, in fact, well outlined, I got lost in the leaves
and couldn't see the forest:  Just what was the "Problem Solving Process" supposed
to do; what were its inputs and what was the form of its output.
<<her>>
 the "semantics" of
what they were intended to do was not made clear.
I never ascertained what exactly an analogy is?
or what qualifed as an analogue, ...

Related - was this actually implemented, or just dry-labbed?
Any data -- e.g. what % of all geometry problems
(or of certain well-defined set of problems) 
could this actually solve -- with and without the analogy unit.

Is analogizer subgoalable -- often it seems the soln to some analogy problem
involves resolving another analogy problem ...

-----
On to less global points:

In that description, it is not clear where analogy is used.
Or is this just how the facts are accumulated, which the analogizer will later use?

(minor point - why the name change in p5 - using (M N O P) for the rectangle,
not (A B C D)?)

Examining the diagram on p6, I wondered how it was obtained --
by brute force, checking all possible matches?  Where is pruning?

You talk of replacing all occurence of the same integer with a constant --
what if two independent terms happen to have the same value?  Don't you need
some type of meta-information, telling why certain things are causally connected?

The diagram on p7 has two relations -- are they the same? or could they just be
similar?

<<here>>
----