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C00002 00002	∂23 Jun 1981 1445-PDT	CSD.GREINER	Functors, and friends
C00004 00003	∂ 1 Jul 1981 1005-PDT	CSD.GENESERETH 	things
C00009 00004	∂TO MRG 15:14 22-Jul
C00014 00005	∂TO MRG 13:33 29-Jul
C00016 00006	∂TO MRG 16:39 30-Jul
C00019 00007	∂TO STT (CC MRG) 18:21 31-Jul
C00025 ENDMK
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∂23 Jun 1981 1445-PDT	CSD.GREINER	Functors, and friends
To: CSD.GENESERETH
cc: CSD.GREINER

I followed up on your suggestion, and meandered over to the Math/CS library,
intent on finding literature about "function generation".  Results:
in a word, blank. (<- or is that Zero Words?)  Anyway, have you any
idea of even the category in which to probe?  Functors, category theory
and various subspecies of combinatorics are all out --  or at least I
couldn't begin to understand what was being said in the various notes,
books and journals.  Under the heading of Functions were hordes of sub-
entries -- none of which seemed pertanent.  I consulted a few "organization
of the (math) world" indices; with equally little success.
	Any other suggestions?  Have you any math friends who owe you
half-a-favor?  I "enclose" below a brief statement of the issue, both
to refresh your memory (as you're probably by now "What is he talking about!"
[in your confusion you probably even got the pronoun correct]) and to forward
to that mystery friend, as well.
------
<<blurb>>

Thanks,
	Russ
-------
∂ 1 Jul 1981 1005-PDT	CSD.GENESERETH 	things
To: csd.greiner

How's the homestead?  Have you found a tenor yet?  I had an idea
the other day that may be worth pursuing.  I've been
wanting to play my lute for a while.  How about if we form a "broken consort"
of 2 recorders, lute, and viola da gamba?  Would Elizabeth join us?

mrg
-------
∂ 1 Jul 1981 1425-PDT	CSD.GREINER	Re: (ANY)things ?
To: CSD.GENESERETH
cc: CSD.GREINER
In-Reply-To: Your message of 1-Jul-81 1005-PDT

I've yet to reside there -- first my bro Seth & friend were there, and now
Elizabeth's bro, Bill, has taken over the residence.  (It seems the last
clause of my "Feel free to stay there WHILE YOU SEARCH FOR A PERMANENT
PLACE" was ignored -- and I haven't the guts to play ogre and throw the
usurper out.  Oh for some assertiveness...)

Well, what's the great new idea?

Elizabeth would probably consent (sp) to join us -- when are we'all meandering
East (E will be at Julliard starting late Sept...).

How was DIA?  And MIT in general? and Arthur?  any other Axxx females?

The ACL thing here is just winding down.  One or two good talks -- a lot
more not-so-good.  Do you know of John Barwise's work, with John Perry?
(They're some local philosphers, attempting to non-Montague-ise semantics.)
Bob Moore seems to really like it -- anyway, I felt there is something,
potentially useful there; and I do want to learn more about his stuff.
Another cute bit of (to me irrelevant)
research dealt with the famous when-are-pronoun-"referents"-resolved problem.
Nice solid work.  The conclusion (that, in most cases, they are determined
at "input" (as opposed to later q/a-ing) time) might have some indirect
value -- perhaps as another idication of the sophisticated economy of
cognitive processing of which people are capable.

One paper had "analogy" in the title (should that have been `"analogy"'?
[actually that last quoted phrase (note I hereby refuse to help resolve
this problem by actually typing its extension) probably should have been 
embedded in yet another set of quotes - yes?]) -- a bit disappointing.
It said nothing about how analogies are formed, or how they "work" --
only about how people actually generate a new context within an
analogizing clause.  Nice, but irrelevant.
Which well summarizes my feel about that conference in general.
You're welcome to borrow my proceedings for a quick look see,
if you've a yen to confirm/deny this perspective.

I yakked with Hofstadter the other day, about analogies.  He had little
to say, beyond the superficial stuff presented in his paper.  Oh well...

In case you didn't know STT is beginning to MRS -- he called me in frustration
the other day - unable to figure out what happened to a few of the functions
mentioned in OUR manual...  Now that DE2 has returned he can probably
begin work in earnest.

Your grass is green, and, at last check, there are no new infestations
(besides your usual warriors).  Anything else I can check on for you?
When are you boating?

See you when you return...
	Russ

∂TO MRG 15:14 22-Jul
Thesis related stuff
	Whew... I came awfully close last Sunday to losing any chance
of ever graduating from Stanford:  
I almost missed a little notice placed in your mailbox then,
telling you, in bold terms, to remove those offending blackberries from your
front yard, or suffer all sorts of bad consequences.
Figuring you'd have a hard time signing my thesis from behind prison bars,
I took the liberty of spending Sunday morning stripping in your yard.
(Yes, I agree it seems immoral, but 'dem are 'de rules.)

<I'm tempted now to go into great detail about the pain and anguish 
I had to suffer during this arduous task;
and mention what a pathetic, wretched sight I was at its completion,
with blood spurting through each of the thousands of orifices opened
by those sharp, painful thorns on those hideous death-defying plants.
But you might feel I was exaggerating a tad, to get sympathy and perhaps
some unjustified faculty backing during subsequent thesis sorts of things.
So you're spared -- I will not now mention
those 7 long miles, thru snow and sleet, I had to trudge....>

Anyway, U No Hu U'r Friends Really R (← original subject of this message).

Other things:
They came and disconnected your phone the other day.  Boo, hiss!  I was all
set to do a full day of hacking, whilst recording.

Bill went back east for a while, so the house has been relatively vacant.
(He escaped just in time, to avoid the slow and excruciatingly painful chore
of denuding that obnoxious plant of yours.)
He apparently reglued one of your chairs, and unstopped your sink during
his stay.  All I got for playing nice guy and going out of my way
by inviting him to stay is his sister's wrath -- who's now furious at me.
I just don't understand people in general, or women in particular.

Anyway, in addition to those sorts of thesis-promoting stuff I mentioned
above, I've also spent some time assembling the start of what may eventually
become something which sorta resembles a thesis draft.
(I realize that's not the best use of my time, considering the other favors
I could be doing for people like you and Doug, but someone's got to do
this sort of dirty work...)
Hopefully this skeleton will be sufficiently fleshed out by the time you
return to permit you to peruse it...

Hope you enjoyed your sailing, and rest of your vacation.
Doesn't it feel terrible to know it's now behind you -- that you've
used up all the leisure time you're likely to get for at least a year...
(Just thought I'd rub it in...)

Russ
∂TO MRG 13:33 29-Jul
Exploring the Depths of Undying Gratitude
Mike
	E's bro Bill called, and asked how best he could express his
gratitude for the use of your "in abstentia" hospitality, and house.
After hanging up it dawned on me there was a nice, inexpensive giftee
he could supply:
Bill seems just the sort of person who would savor the opportunity to
go spelunking about your "basement".  So when he calls, if you still
desire that service, you could suggest this possibility...

(Remember this would really count as a favor FROM ME, as it was really
my magninimity(sp) he is now paying back; and by the transitivity of
favors ...)

Russ
∂TO MRG 16:39 30-Jul
"x is a variable"
Mike -
	First, your house is once again yours -- I have cleared out;
leaving only messages in my wake. (Sounds poetic, no?)
	Second, I have a question about various degrees of meta.
--- Begin Story ---
Let's say I have a variable, x, which is a member of the set, S.
I think we'll agree that x:Isa = (S)  
[or, in MRG-ise, ($ASSERT '(MEMB x S))].

Now we want to state that x is a variable -- ie it makes sense to store
things like what is may be "skolemed on" on x.  So we should be able to
make a meta statement, which is
x:MyIsa = (Variables)  
[translation: ($ASSERT '(MEMB ↑x Variables))].

True so far?  After all, x doesn't know whether it's a constant or not,
but the unit representing it had better, to know certain things about
how to handle dealings with this x...

Anyway, now some joker comes along and asks us how many properties does
this x unit have.  When we say 31, he says "Aha, so x is a verbose unit",
and proceeds to make such a declaration:
x:MyIsa = (VerboseUnit)  
[or, before he was enlightened: ($ASSERT '(MEMB ↑x VerboseUnits))].
--- End of Story ---
(Don't cry -- I never said it would be a happy story...)

Doesn't this seem wrong to you?  Saying "x is a variable" seems clearly
different from "the x unit has many facts"; should both of these be lumped
together?
The 3rd assertion seems right to me, but I question the second one --
So now the question:
how do I represent the fact that x is a variable?

Russ
∂TO STT (CC MRG) 18:21 31-Jul
NonTerminal Terminology
I just yakked with Mike, and found that his terminology is quite
different from what I had thought.
He uses the term "abstraction" to refer to the mapping from an object
to a theory, and "generalization" to relate a pair of theories.

His justification was a little obscure, and had to be teased out:
he claims that any theory we might write about Fido would necessarily
contain only a subset of the possible facts about this entity --
i.e. many (significant but extraneous to the task) facts would be omitted.
Hence this "representation", T, would be a mere subtheory of the full
theory of Fido -- where that full encoding holds every possible fact
about Fido.

Now any subset of that theory, T, (call it S) is a "generalization"
of T -- ie every model of T is also a model of S.

As best I understand, it appears that Abstraction is inverse of Satisfies --
ie if the theory A is an abstraction for some object M, then M satisfies A;
and vice versa.

Comments:
1) To avoid problems of logical implication, we define theory
to refer to the deductive close of the initial axioms.
Realize that a proper generalization will therefore require removing
an infinite number of propositions to be.

2) Any Generalization of an Abstraction is still an Abstraction.

3) Note we need not, at this "epistlemological level", worry about isomorphism...
Two theories are equivalent iff they have the same models.
Hence the actual symbols used are irrelevant
-- this mapping from object to constant, etc,
is in the jurisdiction of the interpretation of the model's elements
in the theory.
[Heuristically this will clearly the bulk of the analogizing work --
finding the method of mapping from symbols in one theory into the
corresponding symbols in the other.]

The related issue of how we can "default" some relations, become irrelevant --
it just means the interpretation of this symbol is slightly 
different in this theory than in the other one.

-----
I still liked using the term abstraction to refer to the relation
connecting a pair of theories -- if 
(Abstraction A B) <=> (ForEvery (M in Models) (Satisfies M B) => (Satisfies M A)).

However this seems quite a bit harder to pin down, as this quantification over
models is a tricky business.  Comments, Mike?

Russ

-- To MRG again  20:18 1-Aug ---
∂01-Aug-81  1358	SYS  
Queued mail to csd.genesereth at SU-SCORE -- ok
The following message was received from the remote host:
Mail to csd.genesereth at SU-SCORE ready
∂TO STT, MRG 10:57 1-Aug
FollowUp
I'd even be content to consider something like

(Abstraction A B) <=> (ForEvery (M in Models).
			  (Exists (I, I' in Interpretations).
				(Satisfies M B I) =>
				(Related I I') & (Satisfies M A I'))),
where this Satisfies relation considers the Interpretation used; and
the Related relation insists that the pair of interpretations are closely
related to one another: preferably identical, but it may allow things like
the teriary R relation symbol in I to correspond to the binary relation symbol
R' in I'.  (I'm considering the interpretation I as a mapping of objects
in the domain of M into symbols in (the language of) B, such that every
relation ...)
  Has anyone defined such a type of satisfaction; or dealt with
this sort of similar interpretations?

	Russ