Integrating Dempster-Shafer belief functions into a knowledge representation system based on Petri nets

Abstract

The expressive power and the epistemic adequacy of the Dempster-Shafer (DS) theory of evidence has often been acknowledged. DS theory of evidence is based on two components: a tool for representing belief for a statement, i.e. a pair of set functions (Bel, Pl) that quantify to what extent available evidence implies the statement and to what extent is available evidence consistent with the statement, respectively; and a tool for combining evidence. Thus DS theory deals with belief intervals rather than single numerical values of belief. There is an explicit differentiation between the notion of disbelief from that of lack of belief. However, as many other methodologies in the field of uncertain reasoning, DS theory addresses only the problem of representing the uncertainty of knowledge, without dealing with the problem of representing the knowledge itself. Saffiotti (1994) has proposed a framework for integrating the DS theory with a knowledge representation system. This approach introduces so-called belief bases, whose purpose is to allow embedding belief functions into a knowledge representation system which is better suited for representing the knowledge itself. Belief bases for a given knowledge representation system are built using three primitive operations, which utilize Dempster's combination rule. This paper describes an attempt at integrating appropriately modified belief bases into a knowledge representation system which utilizes Petri nets for representing knowledge.