Modal Boolean Connexive Logics: Semantics and Tableau Approach

Tomasz Jarmużek; Jacek Malinowski

doi:10.18778/0138-0680.48.3.05

Authors

Tomasz Jarmużek Nicolaus Copernicus University in Toruń, Poland, Department of Logic Author
Jacek Malinowski Polish Academy of Sciences, Institute of Philosophy and Sociology Author

DOI:

https://doi.org/10.18778/0138-0680.48.3.05

Keywords:

Boolean connexive logics, connexive logic, modal Boolean connexive logics, modal logics, normal modal logics, possible worlds semantics, relatedness, relating logic, relating semantics, tableau methods

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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