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Implicational (semilinear) logics III: completeness properties

  1. 1. 0477040 - UIVT-O 2019 RIV DE eng J - Článek v odborném periodiku
    Cintula, Petr - Noguera, Carles
    Implicational (semilinear) logics III: completeness properties.
    Archive for Mathematical Logic. Roč. 57, 3-4 (2018), s. 391-420 ISSN 0933-5846
    Grant CEP: GA ČR GA13-14654S
    GRANT EU: European Commission(XE) 689176 - SYSMICS
    Institucionální podpora: RVO:67985807 ; RVO:67985556
    Klíčová slova: abstract algebraic logic * protoalgebraic logics * implicational logics * disjunctional logics * semilinear logics * non-classical logics * completeness theorems * rational completeness
    Kód oboru RIV: BA - Obecná matematika; BA - Obecná matematika (UTIA-B)
    Obor OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8); Pure mathematics (UTIA-B)
    Impakt faktor: 0.519, rok: 2017

    This paper presents an abstract study of completeness properties of non-classical logics with respect to matricial semantics. Given a class of reduced matrix models we define three completeness properties of increasing strength and characterize them in several useful ways. Some of these characterizations hold in absolute generality and others are for logics with generalized implication or disjunction connectives, as considered in the previous papers. Finally, we consider completeness with respect to matrices with a linear dense order and characterize it in terms of an extension property and a syntactical metarule. This is the final part of the investigation started and developed in the papers (Cintula and Noguera in Arch Math Logic 49(4):417–446, 2010 and Arch Math Logic 53(3):353–372, 2016).
    Trvalý link: http://hdl.handle.net/11104/0273436
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