Modal Boolean Connexive Logics: Semantics and Tableau Approach

Bulletin of the Section of Logic 48 (3):213-243 (2019)
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Abstract

In this paper we investigate Boolean connexive logics in a language with modal operators: □, ◊. In such logics, negation, conjunction, and disjunction behave in a classical, Boolean way. Only implication is non-classical. We construct these logics by mixing relating semantics with possible worlds. This way, we obtain connexive counterparts of basic normal modal logics. However, most of their traditional axioms formulated in terms of modalities and implication do not hold anymore without additional constraints, since our implication is weaker than the material one. In the final section, we present a tableau approach to the discussed modal logics.

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Tomasz Jarmużek
Nicolaus Copernicus University

References found in this work

Philosophical basis of relatedness logic.Douglas N. Walton - 1979 - Philosophical Studies 36 (2):115 - 136.

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