From Frame Properties to Hypersequent Rules in Modal Logics
We provide a general method for generating cutfree and/or analytic hypersequent Gentzen-type calculi for a variety of normal modal logics. The method applies to all modal logics characterized by Kripke frames, transitive Kripke frames, or symmetric Kripke frames satisfying some properties, given by...
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| Vydáno v: | 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science s. 408 - 417 |
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| Hlavní autor: | |
| Médium: | Konferenční příspěvek |
| Jazyk: | angličtina |
| Vydáno: |
IEEE
01.06.2013
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| Témata: | |
| ISBN: | 1479904139, 9781479904136 |
| ISSN: | 1043-6871 |
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| Abstract | We provide a general method for generating cutfree and/or analytic hypersequent Gentzen-type calculi for a variety of normal modal logics. The method applies to all modal logics characterized by Kripke frames, transitive Kripke frames, or symmetric Kripke frames satisfying some properties, given by first-order formulas of a certain simple form. This includes the logics KT, KD, S4, S5, K4D, K4.2, K4.3, KBD, KBT, and other modal logics, for some of which no Gentzen calculi was presented before. Cut-admissibility (or analyticity in the case of symmetric Kripke frames) is proved semantically in a uniform way for all constructed calculi. The decidability of each modal logic in this class immediately follows. |
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| AbstractList | We provide a general method for generating cutfree and/or analytic hypersequent Gentzen-type calculi for a variety of normal modal logics. The method applies to all modal logics characterized by Kripke frames, transitive Kripke frames, or symmetric Kripke frames satisfying some properties, given by first-order formulas of a certain simple form. This includes the logics KT, KD, S4, S5, K4D, K4.2, K4.3, KBD, KBT, and other modal logics, for some of which no Gentzen calculi was presented before. Cut-admissibility (or analyticity in the case of symmetric Kripke frames) is proved semantically in a uniform way for all constructed calculi. The decidability of each modal logic in this class immediately follows. |
| Author | Lahav, Ori |
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| Snippet | We provide a general method for generating cutfree and/or analytic hypersequent Gentzen-type calculi for a variety of normal modal logics. The method applies... |
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| StartPage | 408 |
| SubjectTerms | Calculus Computer science Context cut-admissibility Educational institutions frame properties hypersequent calculi modal logic proof theory Semantics Syntactics |
| Title | From Frame Properties to Hypersequent Rules in Modal Logics |
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