Mathematics – Logic
Scientific paper
2012-01-16
Mathematics
Logic
40 pages including 3 page appendix; minor edits for journal submission
Scientific paper
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; often just systems of polynomial equations or linear optimization problems. This work extends the mathematical logic and parametric probability methods invented by George Boole.
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