A PROBABILISTIC-PROPOSITIONAL FRAMEWORK FOR THE O-THEORY INTERSECTION RULE

Abstract

In a previous paper, O-theory (OT), a hybrid uncertainly theory was proposed for dealing with problems of uncertainty in logical inference. The foundations of one of the concepts introduced, the OT intersection operator, are explored in this paper. The developments rely solely on set-theoretic and probability notions which are the distinguishing features of this operator's role in the theory. The OT intersection rule has as its basis Dempster's rule of combination which ties it closely to Dempster-Shafer theory. In this paper the OT rule will be shown to be based more fundamentally on classical probability theory. To demonstrate this, possibility sets are interpreted in a propositional framework and mass assignments are converted to the probabilistic form originally proposed by Dempster. These changes are used to show that the OT intersection rule can be derived from first principles in a probability theory of propositions. Since this derivation does not require conditional probabilities, it can be used a...