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A Note on Axiomatizations of Pavelka-style Complete Fuzzy Logics
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SYSNO ASEP 0436177 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A Note on Axiomatizations of Pavelka-style Complete Fuzzy Logics Author(s) Cintula, Petr (UIVT-O) RID, ORCID, SAI Source Title Fuzzy Sets and Systems. - : Elsevier - ISSN 0165-0114
Roč. 292, 1 June (2016), s. 160-174Number of pages 15 s. Language eng - English Country NL - Netherlands Keywords mathematical fuzzy logic ; Pavelka-style completeness ; MTL logic ; Lukasiewicz logics ; Product Logic ; truth constants ; Monteiro–Baaz delta Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GAP202/10/1826 GA ČR - Czech Science Foundation (CSF) Institutional support UIVT-O - RVO:67985807 UT WOS 000371786900010 EID SCOPUS 84919459308 DOI 10.1016/j.fss.2014.11.021 Annotation Pavelka-style completeness, a property relating degrees of provability and truth, was previously studied mainly in the context of logics with continuous connectives. It is known that in some other logics one can use infinitary deduction rule(s) to retain this form of completeness. The present paper offers a systematic study of this idea for fuzzy logics which expand MTL and are given by a fixed standard algebra. We explore the structure of the class of all ’reasonable’ expansions of any such logic by rational truth constants and, for several prominent cases, provide axiomatizations of particular expansions enjoying the Pavelka-style completeness. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2016
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