Extension of O-theory to problems of logical inferencing

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Abstract
This article extends Operator-Uncertainty Theory (OT) to the problem of uncertainty propagation in logical inferencing systems. the OT algebra and propositional interpretations presented in previous articles are applied here to derive operators for logical inferencing in the presence of conflict and undecidability. Operators for propagating uncertainties through the logical operations of disjunction and conjunction are defined. In addition, new OT operators for implication, modus ponens and modus tollens, are also proposed. the operators derived using the OT methodology are found to give rise to a four-valued logic similar to that used in computer circuit design. This framework allows uncertainty in inferencing to be represented in the form of rules convenient for use in expert systems as well as logical networks. the theory is general enough to deal with questions of conflict and undecidability, and to propagate their effects through the most widely used inference operations.

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