Inducing Probability Distributions from Knowledge Bases with (In)dependence Relations

Abstract

When merging belief sets from different agents, the result is normally a consistent belief set in which the inconsistency between the original sources is not represented. As probability theory is widely used to represent uncertainty, an interesting question therefore is whether it is possible to induce a probability distribution when merging belief sets. To this end, we first propose two approaches to inducing a probability distribution on a set of possible worlds, by extending the principle of indifference on possible worlds. We then study how the (in)dependence relations between atoms can influence the probability distribution. We also propose a set of properties to regulate the merging of belief sets when a probability distribution is output. Furthermore, our merging operators satisfy the well known Konieczny and Pino-Perez postulates if we use the set of possible worlds which have the maximal induced probability values. Our study shows that taking an induced probability distribution as a merging result can better reflect uncertainty and inconsistency among the original knowledge bases.