Probability for Trivalent Conditionals

This paper presents a unified theory of the truth conditions and probability of indicative conditionals and their compounds in a trivalent framework. The semantics validates a Reduction Theorem: any compound of conditionals is semantically equivalent to a simple conditional. We obtain Stalnaker’s Thesis in full generality and generalize Adams’s p-validity into a criterion for valid uncertain inference. Finally, we show that Bayesian updating on an indicative conditional is tantamount to updating on the corresponding material conditional.