Tableaux for some deontic logics with the explicit permission operator

Daniela Glavaničová; Tomasz Jarmużek; Mateusz Klonowski; Piotr Kulicki

doi:10.18778/0138-0680.2022.11

Authors

Daniela Glavaničová Comenius University in Bratislava, Faculty of Arts, Department of Logic and Methodology of Sciences, 813 64, Gondova 2, Bratislava, Slovakia Author https://orcid.org/0000-0002-4189-9281
Tomasz Jarmużek Nicolaus Copernicus University in Toruń, Faculty of Philosophy and Social Sciences, Department of Logic, 87-100, Stanisława Moniuszki 16/20 Toruń, Poland Author https://orcid.org/0000-0003-3456-3859
Mateusz Klonowski Nicolaus Copernicus University in Toruń, Faculty of Philosophy and Social Sciences, Department of Logic, 87-100, Stanisława Moniuszki 16/20 Toruń, Poland Author https://orcid.org/0000-0001-8616-9189
Piotr Kulicki The John Paul II Catholic University of Lublin, Institute of Philosophy, Department of the Foundations of Computer Science, 20-950, Aleje Raclawickie 14, Lublin, Poland Author https://orcid.org/0000-0001-5413-3886

DOI:

https://doi.org/10.18778/0138-0680.2022.11

Keywords:

explicit permission, free choice, relating semantics

Abstract

In this paper we present a tableau system for deontic logics with the operator of explicit permission. By means of this system the decidability of the considered logics can be proved. We will sketch how these logics are semantically defined by means of relating semantics and how they provide a simple solution to the free choice permission problem. In short, these logics employ relating implication and a certain propositional constant. These two are in turn used to define deontic operators similarly as in Andersonian-Kangerian reduction, which uses different intensional implications and constants.

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