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      Kripke Completeness of Strictly Positive Modal Logics over Meet-semilattices with Operators

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          Abstract

          Our concern is the completeness problem for strongly positive (SP) theories, that is, sets of implications between SP-terms built from propositional variables, conjunction and modal diamond operators. Originated in logic, algebra and computer science, SP-theories 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 of a completeness theory that aims to answer the question whether the two semantics define the same consequence relations for a given SP-theory.

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          Journal
          10 August 2017
          Article
          1708.03403
          534eee5d-4264-406e-aa5a-32c8badb4a6d

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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