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Implicational (semilinear) logics III: completeness properties

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    0477040 - ÚI 2019 RIV DE eng J - Journal Article
    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. E-ISSN 1432-0665
    R&D Projects: GA ČR GA13-14654S
    EU Projects: European Commission(XE) 689176 - SYSMICS
    Institutional support: RVO:67985807 ; RVO:67985556
    Keywords : abstract algebraic logic * protoalgebraic logics * implicational logics * disjunctional logics * semilinear logics * non-classical logics * completeness theorems * rational completeness
    OECD category: Pure mathematics; Pure mathematics (UTIA-B)
    Impact factor: 0.574, year: 2018

    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).
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