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The computational method of parametric probability analysis is introduced. Itis demonstrated how to embed logical formulas from the propositional calculusinto parametric probability networks, thereby enabling sound reasoning aboutthe probabilities of logical propositions. An alternative direct probabilityencoding scheme is presented, which allows statements of implication andquantification to be modeled directly as constraints on conditionalprobabilities. Several example problems are solved, from Johnson-Laird's acesto Smullyan's zombies. Many apparently challenging problems in logic turn outto be simple problems in algebra and computer science: systems of polynomialequations or linear optimization problems. This work extends the mathematicallogic and parametric probability methods invented by George Boole.

A Tutorial Introduction to the Logic of Parametric Probability