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Logic and Implication: An introduction to the General Algebraic Study of Non-classical Logics

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    0524930 - ÚI 2022 RIV CH eng B - Monography
    Cintula, Petr - Noguera, Carles
    Logic and Implication: An introduction to the General Algebraic Study of Non-classical Logics.
    Cham: Springer, 2021. 465 s. ISBN 978-3-030-85674-8
    R&D Projects: GA ČR GA13-14654S; GA ČR(CZ) GA18-00113S
    Institutional support: RVO:67985807 ; RVO:67985556
    Keywords : Non-Classical Logics * Algebraic Logic * Abstract Algebraic Logic * Completeness Theorems * Logical Matrices * Weakly Implicative Logics * Substructural Logics * Generalized Disjunctions * Semilinear Logics * First-Order Logics
    OECD category: Pure mathematics; Applied mathematics (UTIA-B)

    This monograph presents a general theory of weakly implicative logics, a family covering a vast number of non-classical logics studied in the literature, concentrating mainly on the abstract study of the relationship between logics and their algebraic semantics. It can also serve as an introduction to (abstract) algebraic logic, both propositional and first-order, with special attention paid to the role of implication, lattice and residuated connectives, and generalized disjunctions. Based on their recent work, the authors develop a powerful uniform framework for the study of non-classical logics. In a self-contained and didactic style, starting from very elementary notions, they build a general theory with a substantial number of abstract results. The theory is then applied to obtain numerous results for prominent families of logics and their algebraic counterparts, in particular for superintuitionistic, modal, substructural, fuzzy, and relevant logics. The book may be of interest to a wide audience, especially students and scholars in the fields of mathematics, philosophy, computer science, or related areas, looking for an introduction to a general theory of non-classical logics and their algebraic semantics.
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