A new version of Bayes' equation - Applications to plausible reasoning (Q1090020)

A new version of Bayes' equation is presented which expresses the linear relationship between the posterior probability values of two propositions. This formulation is made possible by the introduction of a new kind of relevance, a relevance of one proposition to another which is defined as the difference between conditionals. The new Bayesian equations are used to analyze Polya's heuristics of plausible reasoning applied to the cases of ''examining a consequence'', ''examining a possible ground,'' ''rival or conflicting conjectures,'' and ''circumstantial evidence.'' The analysis is a simple one because of the linearities and, in contrast to Polya's heuristics, both terse and quantitative.