A Modal Calculus of Partially Ordered Events in a Logic Programming Framework

This paper proposes a modal logic reconstruction of temporal reasoning about partially ordered events in a logic programming framework. It considers two variants of Kowalski and Sergot's Event Calculus (EC): the Skeptical EC (SKEC) and the Credulous EC (CREC). In the presence of partially ordered sequences of events, SKEC and CREC derive the maximal validity intervals over which the relevant properties are necessarily and possibly true, respectively. SKEC and CREC are proved to be the operational counterparts of the modal operators of necessity and possibility in an appropriate modal logic and their properties in relation to EC are studied.