Belief Functions and the Possible Worlds Paradigm

This paper describes a formal framework for uncertain reasoning in the possible worlds semantic theory. It shows that the model theory of belief functions is simpler than the model theory of lower order monotonic capacities. We concentrate on finding a generalization of belief functions with the same simple model theory, which also admits a conjunction operator. We identify collections of belief functions that have a full propositional logic and present our generalization based on this result. We do not completely solve the problem of finding a conjunction operator. We describe a possible application of this research in data mining, namely the combination of evidence from multiple sources.