Conditional logic and the Principle of Entropy

Abstract

The conditional three-valued logic of Calabrese is applied to the language L ∗ of conditionals on propositional variables with finite domain. The conditionals in L ∗ serve as a means for the construction and manipulation of probability distributions respecting the Principle of Maximum Entropy and of Minimum Relative Entropy. This principle allows a sound inference even in the presence of uncertain evidence. The inference is directed, it respects a probabilistic version of Modus Ponens—not of Modus Tollens—, it permits transitive chaining and supports a cautious monotony. Conjunctive, conditional and material deduction are manageable in this probabilistic logic, too. The concept is not merely theoretical, but enables large-scale applications in the expert system-shell SPIRIT.