Interval temporal logics provide both an insight into a nature of time and a framework for temporal reasoning in various areas of computer science. In this paper we present sound and complete relational proof systems in the style of dual tableaux for relational logics associated with modal logics of temporal intervals and we prove that the systems enable us to verify validity and entailment of these temporal logics. We show how to incorporate in the systems various relations between intervals and/or (...) various time orderings. (shrink)