Useful Four-Valued Extension of the Temporal Logic KtT4

Vincent Degauquier

doi:10.18778/0138-0680.47.1.02

Authors

Vincent Degauquier Espace philosophique de Namur, University of Namur, Rue de Bruxelles 61, 5000 Namur – Belgium

DOI:

https://doi.org/10.18778/0138-0680.47.1.02

Keywords:

temporal logic, many-valued logic, bi-intuitionistic logic, paraconsistent logic, sequent calculus, duality, cut-redundancy

Abstract

The temporal logic K_tT4 is the modal logic obtained from the minimal temporal logic K_t by requiring the accessibility relation to be reflexive (which corresponds to the axiom T) and transitive (which corresponds to the axiom 4). This article aims, firstly, at providing both a model-theoretic and a proof-theoretic characterisation of a four-valued extension of the temporal logic K_tT4 and, secondly, at identifying some of the most useful properties of this extension in the context of partial and paraconsistent logics.

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