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Neighborhood semantics for modal many-valued logics
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SYSNO ASEP 0480886 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Neighborhood semantics for modal many-valued logics Author(s) Cintula, Petr (UIVT-O) RID, ORCID, SAI
Noguera, Carles (UTIA-B) RID, ORCIDSource Title Fuzzy Sets and Systems. - : Elsevier - ISSN 0165-0114
Roč. 345, 15 August (2018), s. 99-112Number of pages 14 s. Language eng - English Country NL - Netherlands Keywords mathematical fuzzy logic ; modal fuzzy logics ; neighborhood frames ; Kripke semantics ; many-valued logics Subject RIV BA - General Mathematics OECD category Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Subject RIV - cooperation Institute of Information Theory and Automation - General Mathematics R&D Projects GF15-34650L GA ČR - Czech Science Foundation (CSF) Institutional support UIVT-O - RVO:67985807 ; UTIA-B - RVO:67985556 UT WOS 000436569200006 EID SCOPUS 85031759745 DOI 10.1016/j.fss.2017.10.009 Annotation The majority of works on modal many-valued logics consider Kripke-style possible worlds frames as the principal semantics despite their well-known axiomatizability issues when considering non-Boolean accessibility relations. The present work explores a more general semantical picture, namely a many-valued version of the classical neighborhood semantics. We present it in two levels of generality. First, we work with modal languages containing only the two usual unary modalities, define neighborhood frames over algebras of the logic FLew with operators, and show their relation with the usual Kripke semantics (this is actually the highest level of generality where one can give a straightforward definition of the Kripke-style semantics). Second, we define generalized neighborhood frames for arbitrary modal languages over a given class of algebras for an arbitrary protoalgebraic logic and, assuming certain additional conditions, axiomatize the logic of all such frames (which generalizes the completeness theorem of the classical modal logic E with respect to classical neighborhood frames). Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2019
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