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An Abstract Approach to Fuzzy Logics: Implicational Semilinear Logics
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SYSNO ASEP 0328031 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title An Abstract Approach to Fuzzy Logics: Implicational Semilinear Logics Title Abstraktní přístup k fuzzy logikám: implikační semilineární logiky Author(s) Cintula, Petr (UIVT-O) RID, ORCID, SAI
Noguera, C. (ES)Source Title IFSA - EUSFLAT 2009. - Granada : EUSFLAT, 2009 / Carvalho J.P. ; Dubois D. ; Kaymak U. ; Sousa J.M.C. - ISBN 978-989-95079-6-8 Pages s. 519-524 Number of pages 6 s. Publication form CD ROM - CD ROM Action IFSA - EUSFLAT 2009. International Fuzzy Systems Association World Congress 2009, European Society for Fuzzy Logic and Technology Conference 2009 Event date 20.07.2009-24.07.2009 VEvent location Lisabon Country PT - Portugal Event type WRD Language eng - English Country ES - Spain Keywords abstract algebraic logic ; implicative logics ; Leibniz hierarchy ; mathematical fuzzy logic ; semilinear logics Subject RIV BA - General Mathematics R&D Projects GEICC/08/E018 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000279170600091 EID SCOPUS 84868630521 Annotation Paper presents a new abstract framework to deal in a uniform way with the increasing variety of fuzzy logics studied in the literature. By means of notions and techniques from Abstract Algebraic Logic, we perform a study of non-classical logics based on the kind of generalized implication connectives they possess. It yields the new hierarchy of implicational logics. In this framework the notion of implicational semilinear logic can be naturally introduced as a property of the implication, namely a logic L is an implicational semilinear logic iff it has an implication such that L is complete w.r.t. the matrices where the implication induces a linear order, a property which is typically satisfied by well-known systems of fuzzy logic. The hierarchy of implicational logics is then restricted to the semilinear case obtaining a classification of implicational semilinear logics that encompasses almost all the known examples of fuzzy logics and suggests new directions for research in the field. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2010
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