A Tutorial Introduction to the Logic of Parametric Probability
Abstract
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.
Cite
@article{arxiv.1201.3142,
title = {A Tutorial Introduction to the Logic of Parametric Probability},
author = {Joseph W. Norman},
journal= {arXiv preprint arXiv:1201.3142},
year = {2012}
}
Comments
39 pages including 4 page appendix; new title, additional clarifications, correction of bugs introduced into one example in the last revision