A Case Study in Reasoning about Actions and Continuous Change

Imperial College Research Report DoC 95/20, 1995.

Rob Miller

October 1995

Latest Revision 18th April 1996


This paper shows how the Situation Calculus can be extended to deal both with 'narratives' and with domains containing real-valued parameters, whose actual values may vary continuously between the occurrences of actions. In particular, a domain is represented where action occurrences may be 'triggered' at instants in time when certain parameters reach particular values. Its formalisation requires the integration of several types of default reasoning. Hence Baker's circumscriptive solution to the frame problem is extended to reflect the assumptions that by default a given action does not occur at a given time point, that by default a given set of parameter values does not trigger a given action, and that by default a given action occurrence does not result in a discontinuity for a given parameter. Regarding the minimisation of discontinuities, the example illustrates how circumstances can arise where, at a particular time point, discontinuities in some parameters can be 'traded' for discontinuities in others. It is argued that, in general, in such cases extra domain-specific information will be necessary in order to eliminate anomalous models of the domain.

The latest (18th April 1996) revision of this paper is available over the Web in postscript form: Continuous.ps and in dvi form: Continuous.dvi

A shorter version of this paper appears in the proceedings of ECAI'96, Budapest, Hungary.

The November 1995 revision of this paper appears in the working notes of Common Sense 96, Third Symposium on Logical Formalizations of Commonsense Reasoning.

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