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Distinguished Algebraic Semantics for t-norm Based Fuzzy Logics: Methods and Algebraic Equivalencies
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SYSNO ASEP 0323929 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Distinguished Algebraic Semantics for t-norm Based Fuzzy Logics: Methods and Algebraic Equivalencies Title Význačné algebraické sémantiky pro t-normové fuzzy logiky: metody a algebraické ekvivalence Author(s) Cintula, Petr (UIVT-O) RID, ORCID, SAI
Esteva, F. (ES)
Gispert, J. (ES)
Godo, L. (ES)
Montagna, F. (IT)
Noguera, C. (ES)Source Title Annals of Pure and Applied Logic. - : Elsevier - ISSN 0168-0072
Roč. 160, č. 1 (2009), s. 53-81Number of pages 29 s. Language eng - English Country NL - Netherlands Keywords algebraic logic ; embedding properties ; left-continuous t-norms ; mathematical fuzzy logic ; residuated lattices ; standard completeness Subject RIV BA - General Mathematics R&D Projects 1M0545 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000266648600005 EID SCOPUS 67349142165 DOI 10.1016/j.apal.2009.01.012 Annotation This paper is a contribution to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and Delta-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics, study their relationships, characterization and we survey the known completeness methods and results for prominent logics. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2010
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