A Probabilistic Logic Between LPP1 and LPP2

Abstract

An extension of the propositional probability logic LPP2 given in Ognjanović et al. (Probability Logics. Probability-Based Formalization of Uncertain Reasoning, Theoretical Springer, Cham, Switzerland, 2016) that allows mixing of propositional formulas and probabilistic formulas is introduced. We describe the corresponding class of models, and we show that the problem of deciding satisfiability is in NP. We provide infinitary axiomatization for the logic and we prove that the axiomatization is sound and strongly complete.