Parametrized modal logic I: an introduction
Résumé
In this paper, within the context of a two-typed parametrized modal language, we define a parametrized modal logic as a couple whose components are sets of formulas containing, in their respective types, all propositional tautologies and the distribution axiom and closed, in their respective types, under modus ponens, uniform substitution and generalization. We axiomatically introduce different two-typed parametrized modal logics and we prove their completeness with respect to appropriate classes of two-typed frames by means of an adaptation of the canonical model construction.
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