Probabilistic Inference and Bayesian Theorem Based on Logical Implication

Abstract

Probabilistic reasoning is an essential approach of approximated reasoning to treat uncertain knowledge. Bayes’ theorem based on the interpretation of a If-Then rule as the conditional probability is widespread in applications of probabilistic reasoning. A new type of Bayes theorem based on the interpretation of a If-Then rule as the logical implication is introduced in this paper, where addition and subtraction are employed in the probabilistic operations instead of multiplication and division employed for the conditional probability of the traditional Bayes’ theorem. Inference based on both interpretations of the If-Then rules, conditional probability and logical implication, are discussed.