Kripke Completeness of Strictly Positive Modal Logics over Meet-semilattices with Operators
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2017
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| _version_ | 1866908776581300224 |
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| author | Kikot, Stanislav Kurucz, Agi Tanaka, Yoshihito Wolter, Frank Zakharyaschev, Michael |
| author_facet | Kikot, Stanislav Kurucz, Agi Tanaka, Yoshihito Wolter, Frank Zakharyaschev, Michael |
| contents | Our concern is the completeness problem for spi-logics, that is, sets of implications between strictly positive formulas built from propositional variables, conjunction and modal diamond operators. Originated in logic, algebra and computer science, spi-logics have two natural semantics: meet-semilattices with monotone operators providing Birkhoff-style calculi, and first-order relational structures (aka Kripke frames) often used as the intended structures in applications. Here we lay foundations for a completeness theory that aims to answer the question whether the two semantics define the same consequence relations for a given spi-logic. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1708_03403 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Kripke Completeness of Strictly Positive Modal Logics over Meet-semilattices with Operators Kikot, Stanislav Kurucz, Agi Tanaka, Yoshihito Wolter, Frank Zakharyaschev, Michael Logic in Computer Science Our concern is the completeness problem for spi-logics, that is, sets of implications between strictly positive formulas built from propositional variables, conjunction and modal diamond operators. Originated in logic, algebra and computer science, spi-logics have two natural semantics: meet-semilattices with monotone operators providing Birkhoff-style calculi, and first-order relational structures (aka Kripke frames) often used as the intended structures in applications. Here we lay foundations for a completeness theory that aims to answer the question whether the two semantics define the same consequence relations for a given spi-logic. |
| title | Kripke Completeness of Strictly Positive Modal Logics over Meet-semilattices with Operators |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/1708.03403 |