A New Framework for Reasoning about Points, Intervals and Durations

Arun K. Pujari, Abdul Sattar

Abstract: We present a new framework for reasoning about points, intervals and durations--Point Interval Duration Network (PIDN). The PIDN adequately handles both qualitative and quantitaive temporal information. We show that Interval Algebra, Point Algebra, TCSP, PDN and APDN become special cases of PIDN. The underlying algebraic structure of PIDN is closed under composition and intersection. Determinig consistency of P I DN is NP-Ilard. However, we identify some tractable subclasses of PIDN. We show that path consistency is not sufficient to ensure global consistency of the tractable subclasses of PIDN. We identify a subclass for which enforcing 4-consistency suffices to ensure the global consistency, and prove that this subclass is maximal for qualitative constraints. Our approach is based on the geometric interpretation of the domains of temporal objects. Interestingly, the classical Helly's Theorem of 1923 is used to prove the complexity for the tractable subclass.