A case study in reasoning about actions and continuous change (extended version)

This pap er 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 p oint, discontinuitie s 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