A Theory of Conditional Information with Applications.

The development of conditional propositions, deduction between conditionals, and boolean-like operations on conditionals, and their associated probabilities are here unified in terms of boolean relations of the form B O defined on an initially relation-free algebra of boolean polynomials that transcend an initial domain of discourse. The conditional proposition ab is assigned the conditional probability Pab, which is different from the probability that ab is a tautology. The resulting algebraic techniques and demonstrated in several examples such as by simplifying a circular rule-based expert system and removing its circularity and by deriving logical and probability formulas for keeping communication lines open.