Term definable classes of Boolean functions and frame definability in modal logic
Kivelä, Jari; Hella, Lauri; Couceiro, Miguel (2008), Term definable classes of Boolean functions and frame definability in modal logic, Logic Journal of the IGPL, 16, 1, p. 43-73. http://dx.doi.org/10.1093/jigpal/jzm018
TypeArticle accepté pour publication ou publié
Journal nameLogic Journal of the IGPL
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Abstract (EN)We establish a connection between term definability of Boolean functions and definability of finite modal frames. We introduce a bijective translation between functional terms and uniform degree-1 formulas and show that a class of Boolean functions is defined by functional terms if and only if the corresponding class of Scott-Montague frames is defined by the translations of these functional terms, and vice versa. As a special case, we get that the clone Λ1 of all conjunctions corresponds to the class of all Kripke frames. We also characterize some classes of Scott-Montague frames corresponding to subclones of Λ1 by restricting the class of Kripke frames in a natural way. Furthermore, by modifying Kripke semantics, we extend our results to correspondences between linear clones and classes of Kripke frames equipped with modified semantics.
Subjects / KeywordsScott-Montague frames; Kripke frames; modal axioms; modal logic; propositional logic; clones; term definable classes; functional terms; Boolean functions
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