Implicational (Semilinear) Logics II: Additional Connectives and Characterizations of Semilinearity

0448459 - ÚI 2017 RIV DE eng J - Journal Article
Cintula, Petr - Noguera, Carles
Implicational (Semilinear) Logics II: Additional Connectives and Characterizations of Semilinearity.
Archive for Mathematical Logic. Roč. 55, č. 3 (2016), s. 353-372. ISSN 0933-5846. E-ISSN 1432-0665
R&D Projects: GA ČR GA13-14654S
EU Projects: European Commission(XE) 247584 - MATOMUVI
Institutional support: RVO:67985807 ; RVO:67985556
Keywords : abstract algebraic logic * implicational logics * disjunctional logics * semilinear logics * non-classical logics * transfer theorems
Subject RIV: BA - General Mathematics
Impact factor: 0.394, year: 2016

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.
Permanent Link: http://hdl.handle.net/11104/0250156