A New Modal Approach to the Logic of Intervals

In Artificial Intelligence there is a need for reasoning about continuous processes, where assertions refer to time intervals rather than time points. Taking our lead from van Benthem’s treatment of interval temporal structures and Halpern and Shoham’s work on intervals, we present a interval temporal logic with two binary relations, precedence and inclusion. We study the logic in its full generality without making any assumptions about the underlying nature of time, be it discrete or dense, linear or branching. We identify two general classes of interval temporal structures, minimal interval structures and van Benthem minimal interval structures. We show that in our interval temporal language, the two classes in fact have the same logic. We go on to prove that the logic of minimal interval structures is complete and decidable, possessing the finite model property, and that the satisfiability problem is PSPACEcomplete. In order to establish the complexity result we extend the tabl...

• Type: Journal
• Year: 2007
• Where: LOGCOM
• Authors: Altaf Hussain
• Keywords: Interval Temporal Structures, LOGCOM 2007, Minimal Interval, Minimal Interval Structures