Syntax and semantics for a fuzzy temporal constraint logic

In this paper we establish the relationship between the syntax and semantics of a fuzzy temporal constraint logic (FTCL) proposed by Cárdenas et al. FTCL enables us to express interrelated events by means of fuzzy temporal constraints. Moreover, it provides a resolution principle for performing inferences which take these constraints into account. FTCL is compatible with the theoretical temporal reasoning model proposed by Marín et al. - the Fuzzy Temporal Constraint Networks (FTCN). The main contributions of this paper are, on the one hand, the proofs of the FTCL-deduction and the FTCL-refutation theorems, and, on the other, the proof of the soundness of the refutation by resolution in this formal system, together with an exhaustive study of its completeness.