On Metric Temporal Łukasiewicz Logic

Authors:
Tommaso Flaminio;Elisa B. P. Tiezzi
Affiliations:
Department of Mathematics and Computer Science, University of Siena, Siena, Italy;Department of Mathematics and Computer Science, University of Siena, Siena, Italy
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2009

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Abstract

In this paper we present a logical framework to cope with temporal reasoning under vagueness. The calculus is obtained by extending that of bounded metric temporal logic over a dense time domain, by truth-values from the rational unit interval [0,1]@?Q, connectives and rules of the infinite-valued Lukasiewicz logic. We show that the calculus is complete with respect to rational-valued Kripke frames, and as a consequence, we also show that the cut-rule is redundant.