A theorem on the consistency of circumscription
β 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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β¦ 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.
π SIMILAR VOLUMES
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
## Abstract Using an idea of Sargsyan, we show how to reduce the consistency strength of the assumptions employed to establish a theorem concerning a uniform level of indestructibility for both strong and supercompact cardinals. (Β© 2008 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
## Abstract In positive theories, we have an axiom scheme of comprehension for positive formulas. We study here the βgeneralized positiveβ theory GPK~β~^+^. Natural models of this theory are hyperuniverses. The author has shown in [2] that GPK~β~^+^ interprets the Kelley Morse class theory. Here we