Titlebook: Logic and Implication; An Introduction to t Petr Cintula,Carles Noguera Book 2021 Springer Nature Switzerland AG 2021 Non-Classical Logics.

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Fortify

Weakly Implicative Logics,f these logics such as (variants of) the deduction theorem and the proof by cases property; these properties are later, in Chapters 4 and 5, studied in a much more abstract setting..Next, we start introducing basic semantical notions. The fundamental one is that of a logical matrix, which is an arbi

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Completeness Properties,the Leibniz congruence and obtain an important semantical characterization of the notion of conservative expansions and of the class of algebraically implicative logics. Our next tools are the subdirect products and subdirectly irreducible matrices. We show that each finitary logic is strongly compl

Judicious

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Generalized Disjunctions,ules. This characterization is then used to study the preservation of the proof by cases property in expansions and to prove its transfer to the general matrix semantics in terms of generated filters. The second group of characterizations is based on various generalized distributivity properties of

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Semilinear Logics,ction and the results obtained in the previous chapter to prove better characterizations of semilinearity leading to axiomatizations of the least semilinear extension of a given logic. Finally, we focus on completeness with respect to the subclass of linear models in which the order is dense and dis

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