A sound and complete fuzzy temporal constraint logic

In this work, we define an extended fuzzy temporal constraint logic (EFTCL) based on possibilistic logic. EFTCL allows us to handle fuzzy temporal constraints between temporal variables and, therefore, enables us to express interrelated events through fuzzy temporal constraints. EFTCL is compatible with a theoretical temporal reasoning model: the fuzzy temporal constraint networks (FTCN). The syntax, the semantics and the deduction and refutation theorems for EFTCL are similar to those defined for the sound and noncomplete fuzzy temporal constraint logic (FTCL). In this paper, a resolution principle for performing inferences which take these constraints into account is proposed for EFTCL. Moreover, we prove the soundness and the completeness of the refutation by resolution in EFTCL.