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On the independence of axioms in BL and MTL

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. 123-129
Number 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

Number of the records: 1