Abstract
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=0" defined on an initially relation-free algebra of boolean polynomials that transcends an initial domain of discourse. The conditional proposition (a|b) is assigned the conditional probability P(a|b), which is different from the probability that (a|b) is a tautology. The resulting algebraic techniques are 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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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