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Polymodal Lattices and Polymodal Logic
Author(s) -
Bell John L.
Publication year - 1996
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19960420119
Subject(s) - soundness , kripke semantics , mathematics , distributive property , extension (predicate logic) , completeness (order theory) , modal logic , intuitionistic logic , modal , calculus (dental) , pure mathematics , algebra over a field , discrete mathematics , computer science , programming language , propositional calculus , mathematical analysis , medicine , chemistry , dentistry , polymer chemistry
A polymodal lattice is a distributive lattice carrying an n ‐place operator preserving top elements and certain finite meets. After exploring some of the basic properties of such structures, we investigate their freely generated instances and apply the results to the corresponding logical systems — polymodal logics — which constitute natural generalizations of the usual systems of modal logic familiar from the literature. We conclude by formulating an extension of Kripke semantics to classical polymodal logic and proving soundness and completeness theorems. Mathematics Subject Classification: 03G10, 06D99, 03B45.