Cut-free modal sequents for normal modal logics.
نویسندگان
چکیده
منابع مشابه
Cut Elimination in Nested Sequents for Intuitionistic Modal Logics
We present cut-free deductive systems without labels for the intuitionistic variants of the modal logics obtained by extending IK with a subset of the axioms d, t, b, 4, and 5. For this, we use the formalism of nested sequents, which allows us to give a uniform cut elimination argument for all 15 logic in the intuitionistic S5 cube.
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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.
متن کاملNested Sequents for Intuitionistic Modal Logics
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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Motivated by the fact that nearly all conditional logics are axiomatised by so-called shallow axioms (axioms with modal nesting depth ≤ 1) we investigate sequent calculi and cut elimination for modal logics of this type. We first provide a generic translation of shallow axioms to (one-sided, unlabelled) sequent rules. The resulting system is complete if we admit pseudo-analytic cut, i.e. cuts o...
متن کاملLabelled Modal Sequents
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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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1993
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1093633906