Reasoning about continuous change

Abstract

The problem of formalising continuous change within reasoning about action systems such as the situation calculus has recently been receiving increasing attention([Rei96] [MS96]). In this paper we show that a long-existing systems theoretic reasoning methodology, that of Zeigler’s DEVS (discrete event system specification), not only subsumes the standard situation calculus but is able to elegantly describe continuous change within a discrete description structure. We demonstrate that on the semantic level both Reiter’s recent formalisation of continuous change within the situation calculus, and Miller and Shanahan’s formalisation of continuous change within the event calculus fit neatly into a DEVS framework. Our results not only evince a significant connection between logic-based action formalisms and the algebraic formalism of systems theory, and between reasoning about action and discrete event simulation, but also provides support for using DEVS—a well-studied and rigorously implemented framework—as an underlying semantic framework for reasoning about action formalisms.