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Implicational (Semilinear) Logics II: Additional Connectives and Characterizations of Semilinearity
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SYSNO ASEP 0448459 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Implicational (Semilinear) Logics II: Additional Connectives and Characterizations of Semilinearity Author(s) Cintula, Petr (UIVT-O) RID, ORCID, SAI
Noguera, Carles (UTIA-B) RID, ORCIDSource Title Archive for Mathematical Logic. - : Springer - ISSN 0933-5846
Roč. 55, č. 3 (2016), s. 353-372Number of pages 20 s. Language eng - English Country DE - Germany Keywords abstract algebraic logic ; implicational logics ; disjunctional logics ; semilinear logics ; non-classical logics ; transfer theorems Subject RIV BA - General Mathematics R&D Projects GA13-14654S GA ČR - Czech Science Foundation (CSF) Institutional support UIVT-O - RVO:67985807 ; UTIA-B - RVO:67985556 UT WOS 000374969600001 EID SCOPUS 84945261116 DOI 10.1007/s00153-015-0452-9 Annotation This is the continuation of the paper (Cintula and Noguera in Arch Math Log 49(4):417–446, 2010). We continue the abstract study of non-classical logics based on the kind of generalized implication connectives they possess and we focus on semilinear logics, i.e. those that are complete with respect to the class of models where the implication defines a linear order. We obtain general characterizations of semilinearity in terms of the intersection-prime extension property, the syntactical semilinearity metarule and the class of finitely subdirectly irreducible models. Moreover, we consider extensions of the language with lattice connectives and generalized disjunctions, study their interplay with implication and obtain axiomatizations and further descriptions of semilinear logics in terms of disjunctions and the proof by cases property. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2017
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