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Workshop on Proof Theory, Modal Logic and Reflection Principles
October 18, 2017 15:00, Moscow, Steklov Mathematical Institute
 


Kripke completeness of strictly positive modal logics over meet-semilattices with operators

M. Zakharyaschev
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MP4 951.9 Mb
MP4 260.9 Mb

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M. Zakharyaschev


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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.

Language: English

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