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On the independence of axioms in BL and MTL
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SYSNO ASEP 0370261 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On the independence of axioms in BL and MTL Author(s) Chvalovský, Karel (UIVT-O) SAI, RID, ORCID Source Title Fuzzy Sets and Systems. - : Elsevier - ISSN 0165-0114
Roč. 197, 16 June (2012), s. 123-129Number of pages 7 s. Language eng - English Country NL - Netherlands Keywords non-classical logics ; basic fuzzy logic (BL) ; monoidal t-norm based logic (MTL) ; Hilbert-style calculi ; independence of axioms Subject RIV BA - General Mathematics R&D Projects GEICC/08/E018 GA ČR - Czech Science Foundation (CSF) GD401/09/H007 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000303631200009 EID SCOPUS 84859421478 DOI 10.1016/j.fss.2011.10.018 Annotation We prove that the axiom expressing that the multiplicative conjunction of two formulae implies the first one of them is redundant in the standard Hilbert-style calculi of Hájek's basic logic BL and Esteva and Godo's monoidal t-norm based logic MTL. This proof does not use the axiom expressing that multiplicative conjunction is commutative, which is already known to be redundant. Therefore both of these axioms are simultaneously redundant. We also show that all the other axioms are independent of each other. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2013
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