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 , connectives and rules of the infinite-valued Łukasiewicz 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.
