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From Kripke to Neighborhood Semantics for Modal Fuzzy Logics
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SYSNO ASEP 0460686 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title From Kripke to Neighborhood Semantics for Modal Fuzzy Logics Author(s) Cintula, Petr (UIVT-O) RID, ORCID, SAI
Noguera, Carles (UTIA-B) RID, ORCID
Roger, J. (CH)Source Title Information Processing and Management of Uncertainty in Knowledge-Based Systems, 2. - Cham : Springer, 2016 / Carvalho J.P. ; Lesot M.-J. ; Kaymak U. ; Vieira S. ; Bouchon-Meunier B. ; Yager R.R. - ISSN 1865-0929 - ISBN 978-3-319-40581-0 Pages s. 95-107 Number of pages 13 s. Publication form Print - P Action IPMU 2016 /16./ Event date 20.06.2016-24.06.2016 VEvent location Eindhoven Country NL - Netherlands Event type WRD Language eng - English Country CH - Switzerland Keywords mathematical fuzzy logic ; modal fuzzy logics ; neighborhood frames ; Kripke semantics ; many-valued logics Subject RIV BA - 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 000387430000009 EID SCOPUS 84977159867 DOI 10.1007/978-3-319-40581-0_9 Annotation The majority of works on modal fuzzy logics consider Kripke-style possible worlds semantics as the principal semantics despite its well known axiomatizability issues when considering fuzzy accessibility relations. The present work offers the first (two) steps towards exploring a more general semantical picture, namely a fuzzified version of the classical neighborhood semantics. First we prove the fuzzy version of the classical relationship between Kripke and neighborhood semantics. Second, for any axiomatic extension of MTL (one of the main fuzzy logics), we define its modal expansion by a box-like modality, and, in the presence of some additional conditions, we prove that the resulting logic can be axiomatized by adding the E-rule to the corresponding Hilbert-style calculus of the starting logic. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2017
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