Conditional Probabilistic Epistemic Logic Based on the General Frame
Abstract
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.
Fields of Study & Subjects
Logic
Reasoning
and Knowledge
Epistemology
Ethics
and Metaphysics
Bayesian Modeling and Causal Inference
Publication details
- Journal / source
- Philosophies
- Volume
- 11
- Issue
- 2
- Pages
- 30–30
- Publication date
- 5 March 2026
- Language
- EN