Speeding up Temporal Reasoning by Exploiting the Notion of Kernel of an Ordering Relation

In this paper, we consider the problem of expediting temporal reasoning about partially ordered events in Kowalski and Sergot's Event Calculus (EC). EC is a formalism for representing and reasoning about events and their effects in a logic programming framework [7]. Given a set of events occurring in the real world, EC is able to infer the set of maximal validity intervals (MVIs, hereinafter) over which the properties initiated and/or terminated by the events maximally hold. Event occurrences can be provided with different temporal qualifications [1]. In this paper, we suppose that for each event we either specify its relative position with respect to some other events (e.g., event e1 occurs before event e2) or leave it temporally unqualified (the only thing we know is that it occurred). Database updates in EC provide information about the occurrences of events and their times [6] and are of additive nature only. We assume here that the set of events is fixed, and the input process consists in the addition of ordering information.