0448459 20250112205916.020151013235959.9 84945261116 000374969600001 10.1007/s00153-015-0452-9 20 s. cav_un_epca*02561860933-5846553 (2016)353-372Springer abstract algebraic logic implicational logics disjunctional logics semilinear logics non-classical logics transfer theorems cav_un_auth*0100737 Cintula Petr UIVT-O Oddělení teoretické informatiky Department of Theoretical Computer Science Department of Theoretical Computer Science Ústav informatiky AV ČR, v. v. i. cav_un_auth*0293476 Noguera Carles UTIA-B Matematická teorie rozhodování Department of Decision Making Theory MTR MTR Department of Decision Making Theory K Ústav teorie informace a automatizace AV ČR, v. v. i. GA13-14654S GA ČR cav_un_auth*0292719 247584 EC XE cav_un_auth*0323440 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. BA 2017 4 A R 4a 4r 20231122141211.2 20250112205916.0 RVO:67985807 RVO:67985556 http://hdl.handle.net/11104/0250156 S n.a. Article Mathematics|Logic LOGIC|MATHEMATICS 0.414 0.018 999.9 0.00164 0.458 398 0.605 Q1 0.343 56 Q4 40.038 21.4 Q3 Q2 26.19 2016 Soubory v repozitáři: dodatecne_citace_k_0448459.pdf, a0448459.pdf, 0448459.pdf 84945261116 SCOPUS 000374969600001 WOS cav_un_epca*0256186 Archive for Mathematical Logic 0933-5846 1432-0665 Roč. 55 č. 3 2016 353 372 Springer