  The computational method of parametric probability analysis is introduced. It
is demonstrated how to embed logical formulas from the propositional calculus
into parametric probability networks, thereby enabling sound reasoning about
the probabilities of logical propositions. An alternative direct probability
encoding scheme is presented, which allows statements of implication and
quantification to be modeled directly as constraints on conditional
probabilities. Several example problems are solved, from Johnson-Laird's aces
to Smullyan's zombies. Many apparently challenging problems in logic turn out
to be simple problems in algebra and computer science: systems of polynomial
equations or linear optimization problems. This work extends the mathematical
logic and parametric probability methods invented by George Boole.
