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Term Satisfiability in FLew-Algebras
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SYSNO ASEP 0439177 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Term Satisfiability in FLew-Algebras Author(s) Haniková, Zuzana (UIVT-O) SAI, RID, ORCID
Savický, Petr (UIVT-O) SAI, RID, ORCIDSource Title Theoretical Computer Science. - : Elsevier - ISSN 0304-3975
Roč. 631, 6 June (2016), s. 1-15Number of pages 15 s. Language eng - English Country NL - Netherlands Keywords substructural logic ; FLew-algebra ; MV-algebra ; satisfiability ; computational complexity Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GBP202/12/G061 GA ČR - Czech Science Foundation (CSF) Institutional support UIVT-O - RVO:67985807 UT WOS 000377839900001 EID SCOPUS 84977943182 DOI https://doi.org/10.1016/j.tcs.2016.03.009 Annotation 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. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2017
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