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zpravodaj ČSKI - listopad 2018
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datum: 21.11.2018 v 16:00
název: General neighborhood and Kripke semantics for modal many-valued logics
přednášející: Carles Noguera (UI)
místo konání: UI, 2.patro, místnost č.318

souhrn: Frame semantics, given by Kripke or neighborhood frames, do not give completeness theorems for all modal logics extending, respectively, K and E. Such shortcoming can be overcome by means of general frames, i.e. frames equipped with a collection of admissible sets of worlds (which is the range of possible valuations over such frame). We export this approach from the classical paradigm to modal many-valued logics by defining general A-frames over a given residuated lattice A (i.e., the usual frames with a collection of admissible A-valued sets). We describe in details the relation between general Kripke and neighborhood A-frames and prove that, if the logic of A is finitary, all extensions of the corresponding logic E of A are complete w.r.t. general neighborhood frames. Our work provides a new approach to the current research trend of generalizing relational semantics for non-classical modal logics to circumvent axiomatization problems.