A Logic for Probabilities of Successive Events

Studies in Logic, Vol. 16, No. 6 (2023): 1–16              PII: 1674­3202(2023)­06­0001­16

Yanjun Li, Jiajie Zhao

Abstract. In the set language of probability theory, besides complement, intersection, and union, there is another important operation: product. The product of two basic events expresses that these events occur in succession. However, there is limited research about successive events in the literature on probability logic. In this paper, we propose a modal logic (called DML) to capture the reasoning about successive events in probability theory, and then we construct a probability logic (called ) based on DML. We compare DML with standard modal logic on Kripke semantics and show that DML is equivalent to the normal modal logic on deterministic models. We also give a deductive system of and show its completeness.