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A theorem on the consistency of circumscription

✍ Scribed by Peter L. Mott


Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
536 KB
Volume
31
Category
Article
ISSN
0004-3702

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✦ Synopsis


This paper giw's more general conditions under which McCarthy's circumscription is consistent, allowing application of the method outside the domain of universal sentences. It is shown that circumscription as presented here continues to correspond to the semantic model of minimization. Some applications are detailed.

' In fact in tile case where there are no variables Q revolved in the circumscription, A may bc almost universal, that is equivalent to a sentence VxB where no predicate P has positive occurrence within B in the scope of quantifiers occurring in B.


πŸ“œ SIMILAR VOLUMES


On the satisfiability of circumscription
✍ Vladimir Lifschitz πŸ“‚ Article πŸ“… 1986 πŸ› Elsevier Science 🌐 English βš– 476 KB

Etherington, Mercer and Reiter showed, on the basis of ideas of Bossu and Siegel, that circumscription cannot lead to inconsistency for universal formulas. We extend this result in three directions: to formulas of a more general syntactic form, to circumscr~tion with some predicate symbols allowed t

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On the Consistency of a Positive Theory
✍ Olivier Esser πŸ“‚ Article πŸ“… 1999 πŸ› John Wiley and Sons 🌐 English βš– 735 KB

## Abstract In positive theories, we have an axiom scheme of comprehension for positive formulas. We study here the β€œgeneralized positive” theory GPK~∞~^+^. Natural models of this theory are hyperuniverses. The author has shown in [2] that GPK~∞~^+^ interprets the Kelley Morse class theory. Here we