Situation Calculus Specifications for Event Calculus Logic Programs

Rob Miller

Abstract

This paper compares two formalisms and two associated default reasoning techniques for reasoning about action - the Situation Calculus, using a variant of Baker's circumscriptive solution to the frame problem, and the logic-programming based Event Calculus, in which default reasoning is realised through negation-as-failure. The version of the Situation Calculus used enables information about the occurrences of actions along a time line to be represented. A course of actions identified as actually occurring is referred to as a narrative, and this formalism is referred to as the Narrative Situation Calculus. Information about a narrative might be incomplete, so that default assumptions might be required. The circumscription policy incorporated in the Narrative Situation Calculus minimises action occurrences along the time-line. The original Event Calculus incorporates an analogous default assumption - that the only action occurrences are those provable from the theory.

The paper shows that under certain circumstances the Narrative Situation Calculus may be regarded as a specification for Event Calculus style logic programs. The programs presented are described as "Event Calculus style" because of their use of Initiates and Terminates predicates to describe the effects of actions, because of the form of their persistence axioms, and because of the use of a time-line rather than the notion of a sequence or structure of situations. They differ from some other variants of the Event Calculus in that they do not assume complete knowledge of an initial state, and in that properties can hold (and persist) even if they have not been explicitly initiated by an action. Two classes of programs are discussed, both of which are "sound", for a wide class of domains, in that they only allow derivation of Holds information which is semantically entailed by their circumscriptive specifications. Programs of the second type, although more complex, have an advantage over those of the first in that they are also "complete" even where information is missing about the state of affairs before any action occurs.

In: Proceedings of the Third International Conference on Logic Programming and Non-monotonic Reasoning, Lexington, KY, USA, pub. Springer Verlag, 1995, pages 217-230.

This paper is also available over the Web in postscript form: SitEventCalc.ps and in dvi form: SitEventCalc.dvi

This research was sponsored by the EPSRC, under a research project entitled Logic for Commonsense Reasoning about Continuous Change.