# A Case Study in Reasoning about Actions and Continuous Change

## Imperial College Research Report DoC 95/20, 1995.

## October 1995

## Latest Revision 18th April 1996

## Abstract

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.**