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Term Satisfiability in FLew-Algebras
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SYSNO ASEP 0439177 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Term Satisfiability in FLew-Algebras Tvůrce(i) Haniková, Zuzana (UIVT-O) SAI, RID, ORCID
Savický, Petr (UIVT-O) SAI, RID, ORCIDZdroj.dok. Theoretical Computer Science. - : Elsevier - ISSN 0304-3975
Roč. 631, 6 June (2016), s. 1-15Poč.str. 15 s. Jazyk dok. eng - angličtina Země vyd. NL - Nizozemsko Klíč. slova substructural logic ; FLew-algebra ; MV-algebra ; satisfiability ; computational complexity Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics CEP GBP202/12/G061 GA ČR - Grantová agentura ČR Institucionální podpora UIVT-O - RVO:67985807 UT WOS 000377839900001 EID SCOPUS 84977943182 DOI 10.1016/j.tcs.2016.03.009 Anotace FLew-algebras form the algebraic semantics of the full Lambek calculus with exchange and weakening. We investigate two relations, called satisfiability and positive satisfiability, between FLew-terms and FLew-algebras. For each FLew-algebra, the sets of its satisfiable and positively satisfiable terms can be viewed as fragments of its existential theory; we identify and investigate the complements as fragments of its universal theory. We offer characterizations of those algebras that (positively) satisfy just those terms that are satisfiable in the two-element Boolean algebra providing its semantics to classical propositional logic. In case of positive satisfiability, these algebras are just the nontrivial weakly contractive algebras. In case of satisfiability, we give a characterization by means of another property of the algebra, the existence of a two-element congruence. Further, we argue that (positive) satisfiability problems in FLew-algebras are computationally hard. Some previous results in the area of term satisfiabilty in MV-algebras or BL-algebras, are thus brought to a common footing with, e.g., known facts on satisfiability in Heyting algebras. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2017
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