Query Optimization Properties of Modified VBS

Valuation-Based System can represent knowledge in different domains including probability theory, Dempster-Shafer theory and possibility theory. More recent studies show that the framework of VBS is also appropriate for representing and solving Bayesian decision problems and optimization problems. In this paper after introducing the valuation based system (VBS) framework, we present Markov-like properties of VBS and a method for resolving queries to VBS. 1 Introduction Though graphical representation of a domain knowledge has quite long history, its full potential has not been recognized until recently. We should mention here pioneering works of J. Pearl, reported in his monography published in 1988 [ 1988] . Further development in this domain has been achieved by Shenoy and Shafer [ 1986 ] who adopted a method used in solving nonserial dynamic programming problems [ Bertele & Brioschi, 1972 ] . This trick proved to be very fruitful and gave growth to a unified framework for uncertainty representation and reasoning, called V aluation-Based System, VBS for short [ Shenoy, 1989 ] .