Modal sequents and definability
نویسندگان
چکیده
منابع مشابه
Modal Sequents and Definability
We examine a certain modal consequence relation, and define the notion of validity of a modal sequent on a frame. We demonstrate that it is possible to define classes of frames. not definable by modal formulas, by modal sequents. Through the use of modal algebras and general frames, we obtain a characterization of modal sequent-definable classes of frames which are also first-order definable, a...
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In this paper we present a new labelled sequent calculus for modal logic. The proof method works with a more “liberal” modal language which allows inferential steps where different formulas refer to different labels without moving to a particular world and there computing if the consequence holds. World-paths can be composed, decomposed and manipulated through unification algorithms and formula...
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The main method of proving the Craig Interpolation Property (CIP) constructively uses cut-free sequent proof systems. Until now, however, no such method has been known for proving the CIP using more general sequent-like proof formalisms, such as hypersequents, nested sequents, and labelled sequents. In this paper, we start closing this gap by presenting an algorithm for proving the CIP for moda...
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We present deductive systems for various modal logics that can be obtained from the constructive variant of the normal modal logic CK by adding combinations of the axioms d, t, b, 4, and 5. This includes the constructive variants of the standard modal logics K4, S4, and S5. We use for our presentation the formalism of nested sequents and give a syntactic proof of cut elimination.
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We present cut-free deductive systems without labels for the intuitionistic variants of the modal logics obtained by extending K with a subset of the axioms d, t, b, 4, and 5. For this, we use the formalism of nested sequents. We show a uniform cut elimination argument and a terminating proof search procedure. As a corollary we get the decidability of all modal logics in the intuitionistic S5-c...
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ژورنال
عنوان ژورنال: Journal of Symbolic Logic
سال: 1987
ISSN: 0022-4812,1943-5886
DOI: 10.1017/s002248120002973x