Conditional Probabilistic Epistemic Logic Based on the General Frame

With conditional probability as a primitive notion rather than a ratio of classical probability, we extend the language of epistemic logic by introducing conditional probability operators. We propose a conditional probabilistic epistemic logic (CPEL) based on the general frame, which enables the assignment of conditional probabilities to any formula in the language defined in this paper. Furthermore, we discuss the relationship between knowledge and conditional probability in CPEL, as well as the connection between indicative conditionals and conditional probability. Finally, we present a sound and weakly complete axiomatization for our framework and demonstrate its application in analyzing the lottery paradox.