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C00002 00002	circum[f82,jmc]		Mathematical questions of circumscription
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circum[f82,jmc]		Mathematical questions of circumscription

	1. Is there an elimination theorem?  Suppose we minimize
prev-can-fly x  treating the predicate  can-fly x  as a variable
that can be given whatever extension will minimize  prev-can-fly.
Can we express the resulting conditions on  prev-can-fly  without
using  can-fly?  Is this related somehow to the Craig interpolation
theorem?  ANS: It isn't possible even in monotonic logic.

	2. Circumscription and forcing?

	3. When do minimal models exist?

	4. When is the result of circumscription expressible by
a single formula?

	5. What can be said in general about the relation between
the syntax of circumscription and minimal models?  When does the
circumscription formula fully characterize the minimal model?

	6. Study the syntactic counterpart of the Bossu-Siegel
inferior implication.

The talk at the math. society meeting should concentrate on AI
issues, but the mathematical questions should be phrased as
precisely as possible.  The theorem proving aspects should also
be mentioned.

	7. How to invent predicates for circumscription?

	8. Note that bird uses only pointwise minima.

	9. How do we express our priorities for minimization?

	10. Lagrange multipliers?  Derivative = 0?  Perhaps the
gradient gives for each element  x  where  E[x]  is true - a disjunction
saying what must go up if  E[x] is to become false.

	11. Is there a monadic decidable case?

	12. What are the conditions for disregarding certain sentences
in making the circumscription?  The simplest example includes the
sentences that are in no way connected even through others with
the expression being circumscribed.

	13. Is there a notion of a circumscriptive theory, i.e. a set of
axioms and prescriptions for circumscription?  Such a theory should have a
circumscriptive completion - an ordinary theory.  The notion is
non-monotonic in that the completion of a theory can contain sentences not
in the completion of an extended theory.

	14. Is there a need for having contingent facts directly determine
circumscription priorities or can everything be done by suitable object
level axioms?  The policeman named Evelyn.