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Implicational (Semilinear) Logics II: Additional Connectives and Characterizations of Semilinearity
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SYSNO ASEP 0448459 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Implicational (Semilinear) Logics II: Additional Connectives and Characterizations of Semilinearity Tvůrce(i) Cintula, Petr (UIVT-O) RID, ORCID, SAI
Noguera, Carles (UTIA-B) RID, ORCIDZdroj.dok. Archive for Mathematical Logic. - : Springer - ISSN 0933-5846
Roč. 55, č. 3 (2016), s. 353-372Poč.str. 20 s. Jazyk dok. eng - angličtina Země vyd. DE - Německo Klíč. slova abstract algebraic logic ; implicational logics ; disjunctional logics ; semilinear logics ; non-classical logics ; transfer theorems Vědní obor RIV BA - Obecná matematika CEP GA13-14654S GA ČR - Grantová agentura ČR Institucionální podpora UIVT-O - RVO:67985807 ; UTIA-B - RVO:67985556 UT WOS 000374969600001 EID SCOPUS 84945261116 DOI 10.1007/s00153-015-0452-9 Anotace 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. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2017
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