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C00002 00002	Dave Smith put your ch3. in my box, and I suppose you are soliciting my comments.
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Dave Smith put your ch3. in my box, and I suppose you are soliciting my comments.
Anyway I hope they are useful.

shoham[e86,jmc]	Comments on Shoham's 1986 July 30 draft of ch. 3 of his thesis

	1. I agree with what I take to be your view that the foundation
of non-monotonic reasoning, as with monotonic, should be semantic.  I
also agree that the ability to express preference orderings among models
looks like a good approach.  I have followed it myself in developing
circumscription and looking for variants.  So has Vladimir Lifschitz.
Indeed he resuscitated it when I had let it languish and gone to
depending on the circumscription formula itself.

	It would be good if there were more examples of useful preference
orderings - described either semantically or syntactically.

	2. In considering purely semantic formalisms, you should read
the Artificial Intelligence paper of Bossu and Siegel.  You will find
some of the ideas familiar.

	3. The reason for wanting a syntax corresponding to the semantics
as well as possible is that syntactic reasoning from premisses is readily
verified, even in its non-monotonic forms, while reasoning with the set of
models of a formula is prima facie undecidable when there are an infinity
of models and intractable when there are only a finite set.  With
additional assumptions, it is sometimes feasible to reason about the set
of models, but when this is formalized, it amounts to syntactic reasoning
in a metalanguage.

	4. Circumscription has indeed proved difficult for many people
to understand.  It took me a long time to understand Lifschitz's
pointwise circumscription.  Now that I understand it, I have come
to believe that it is a very powerful formalism, and either it is
suitable for formalizing common sense or it is on the right track.
There are several papers about how to compute the old circumscription,
and a summer student, Bob Givan, has found some important cases in
which the computation of pointwise circumscription is doable with
very similar algorithms.

	It also looks like Vladimir's latest formulation will be
rather easy to use for writing common sense axioms.  I have already
done both specialization priority (getting rid of cancellation
of inheritance) and temporal priority (Fred's doom).

	5. In criticizing circumscription (and perhaps the other
formalisms) you are shooting at a moving target, and it's likely
to make that part of your thesis soon obsolete.  My opinion is
that one can't make one's own formalism popular by shooting at
its competitors.  It is better to spend the effort doing more
examples with one's own formalism and writing it up better.
Unless it is congenial to you to put quite a bit of time in
trying out circumscription and the other formalisms, you should say less
about them.

	Similarly Drew's "Critique of Pure Reason" would be more useful if
it emphasized the specific challenges to logical formalism rather than
general arguments against it, i.e. it needs more "How do you propose to do
X?".  When you make general arguments against something, you tend to get
general arguments back, and the discussion rapidly gets too high level to
be useful.

	6. Here are some points of English.  "Lifschitz's" not "Lifschitz'".
On p. 10, you mean "ingenious" not "ingenuous".  In that same sentence,
the parenthesized phrase would better read ( both McCarthy's original
ones and Lifschitz's  more recent ones), although it would be still
better to start the whole sentence with "Both McCarthy's original
circumscription axioms and ...".

	7. I agree with you about the complexity of the formulation
involving Eq(p,q,r); I didn't understand it either.  However, the
current version with the V predicates is much easier to understand
and use.

	8. In my view, giving earlier situations priority should be
derived, when it applies, from a more general principle of giving priority
to the entities one knows about and lower priority to facts about entities
whose properties are derived from them.  Formalizing this presumably
requires more reification than has been used in papers on non-monotonic
reasoning, perhaps along the line of my "First order theories of
individual concepts and propositions".  I think the non-monotonic part can
be done with pointwise circumscription.

	9. On p.3 you say "The trick is to identify the preference
criterion that is appropriate for a given purpose."  Vladimir and
I don't agree with the most obvious interpretation of this.  If
the preference criterion is in the metamathematics, i.e. in the
program rather than in the axioms, then we haven't achieved our
goal of expressing common sense knowledge in logical formulas.
For that reason I introduced the notion of simple abnormality
theory with the idea that having decided to minimize ab, everything
specific to the purpose was included in the axioms.  Even when
I introduced it, I knew it would be inadequate in general.  Vladimir
pursued the goal of getting everything about the "given purpose" in
the axioms with his pointwise circumscription, and so far as I can
presently tell, he has succeeded.

	I look forward to comparing the various formalisms on
challenging examples when you come to Stanford.