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Implicational (semilinear) logics III: completeness properties

  1. 1.
    SYSNO ASEP0477040
    Druh ASEPJ - Článek v odborném periodiku
    Zařazení RIVJ - Článek v odborném periodiku
    NázevImplicational (semilinear) logics III: completeness properties
    Tvůrce(i)Cintula, Petr (UIVT-O) - Noguera, Carles (UTIA-B) Korespondenční autor
    Rozsah stran391 - 420
    Zdroj.dok.Archive for Mathematical Logic - ISSN 0933-5846
    Poč.str.30 s.
    Jazyk dok.eng - angličtina
    Země vyd.DE - Německo
    Klíč. slovaabstract algebraic logic ; protoalgebraic logics ; implicational logics ; disjunctional logics ; semilinear logics ; non-classical logics ; completeness theorems ; rational completeness
    Vědní obor RIVBA - Obecná matematika
    Vědní obor RIV – spolupráceÚstav teorie informace a automatizace - Obecná matematika
    CEPGA13-14654S GA ČR - Grantová agentura ČR
    Institucionální podporaUIVT-O - RVO:67985807 ; UTIA-B - RVO:67985556
    UTISI000428317500011
    DOI10.1007/s00153-017-0577-0
    AnotaceThis 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).
    PracovištěÚstav informatiky
    KontaktTereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800
    Rok sběru2019