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Implicational (Semilinear) Logics I: A New Hierarchy
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SYSNO ASEP 0342136 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Implicational (Semilinear) Logics I: A New Hierarchy Tvůrce(i) Cintula, Petr (UIVT-O) RID, ORCID, SAI
Noguera, C. (ES)Zdroj.dok. Archive for Mathematical Logic. - : Springer - ISSN 0933-5846
Roč. 49, č. 4 (2010), s. 417-446Poč.str. 30 s. Jazyk dok. eng - angličtina Země vyd. DE - Německo Klíč. slova abstract algebraic logic ; hierarchy of implicational logics ; implicative logics ; Leibniz hierarchy ; linearly ordered logical matrices ; mathematical fuzzy logic ; non-classical logics ; semilinear logics Vědní obor RIV BA - Obecná matematika CEP GEICC/08/E018 GA ČR - Grantová agentura ČR CEZ AV0Z10300504 - UIVT-O (2005-2011) UT WOS 000277246000001 EID SCOPUS 84871950551 DOI 10.1007/s00153-010-0178-7 Anotace In abstract algebraic logic, the general study of propositional logics is based on the abstraction of the Lindenbaum-Tarski process, one considers the Leibniz relation of indiscernible formulae. It leads to the Leibniz hierarchy; a classification of logics based on generalized equivalences. We perform an analogous abstract study of non-classical logics based on generalized implications. It yields the hierarchy of implicational logics which expands Leibniz hierarchy. The notion of implicational semilinear logic is then naturally introduced as a property of the implication, namely a logic is an implicational semilinear logic iff it has an implication and is complete w.r.t. the matrices where this implication induces a linear order, a property which is satisfied by majority of fuzzy logics. This hierarchy is then restricted to the semilinear case obtaining a classification that encompasses almost all the known examples of fuzzy logics and suggests new directions for research. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2011
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