Situation theory - a formal model of interactive processes

Abstract

Many dynamic systems may be described as collections of 'elementary activities' that are partly independent of one another. Their execution may allow a degree of concurrency, subject to precedence constraints. These systems are referred to as interactive processes. This paper presents a general set-theoretical model of interactive processes called DPC (distributed planning and control). A DPC process is described as an object with three types of feature: situations, events and residual domains (RDs). A situation is any condition that persists over an uninterrupted period of time. An event is defined by the property that it terminates a set of situations and starts a new set of situations. A RD is a set of alternative events resulting from a set of co-existing situations. It is defined by the fact that to know that it has occurred is to know that exactly one of its members will occur in the future. The paper first gives an intuitive description of DPC. It then introduces a simple notation, called feature notation (FN), that is devised for the description of large set-theoretical models. A formal model of DPC is then established in FN. Finally, DPC is briefly related to other similar models: the process calculus CCS, coloured Petri nets and the decision trees and activity networks of operations research.