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

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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 as alternative to Bayes' theorem for combining conjunctive information consistently. Dempster's rule will be shown to be a special case of the OT intersection rule. It too will be derived using probability theory. The formal connection between mass and probability presented originally by Dempster and used here in a propositional framework, makes distinctions between DST and probability theory less consequential. DST is still seen to be a generalization of the concept of probability, but it is also seen to fit within a probabilistic-propositiona) framework.

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