In this paper, we introduce a probabilistic justification logic PJ, a logic in which we can reason about the probability of justification statements. We present its syntax and semantics, and establish a strong completeness theorem. Moreover, we investigate the relationship between PJ and the logic of uncertain justifications.

Probabilistic justification logic is a modal logic with two kind of modalities: probability measures and explicit justification terms. We present a tableau procedure that can be used to decide the satisfiability problem for this logic in polynomial space. We show that this upper complexity bound is tight.

The logic PJ is a probabilistic logic over the basic justification logic J. In this paper we establish upper and lower bounds for the complexity of PJ. The main result of the paper is that the complexity of the logic PJ remains the same as the complexity of the logic J.

Let L be some extension of classical propositional logic. The noniterated probabilistic logic over L, is the logic PL that is defined by adding non-nested probabilistic operators in the language of L. For example in PL we can express a statement like “the probability of truthfulness of A is at 0.3” where A is a formula of L. The iterated probabilistic logic… (More)