A Paraconsistent Linear-time Temporal Logic

Authors:
Norihiro Kamide;Heinrich Wansing
Affiliations:
(Correspd.) Waseda Institute for Advanced Study, 1-6-1 Nishi Waseda, Shinjuku-ku, Tokyo 169-8050, Japan. drnkamide08@kpd.biglobe.ne.jp;Ruhr-Universität Bochum, Department of Philosophy II, Carnap Institute for Philosophy and Science, Universitätsstr. 150, 44780 Bochum, Germany. Heinrich.Wansing@rub.de
Venue:
Fundamenta Informaticae
Year:
2011

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Abstract

Inconsistency-tolerant reasoning and paraconsistent logic are of growing importance not only in Knowledge Representation, AI and other areas of Computer Science, but also in Philosophical Logic. In this paper, a new logic, paraconsistent linear-time temporal logic (PLTL), is obtained semantically from the linear-time temporal logic LTL by adding a paraconsistent negation. Some theorems for embedding PLTL into LTL are proved, and PLTL is shown to be decidable. A Gentzentype sequent calculus PLTω for PLTL is introduced, and the completeness and cut-elimination theorems for this calculus are proved. In addition, a display calculus δPLTω for PLTL is defined.