An Expressive Probabilistic Temporal Logic
This work addresses a foundational problem in AI and logic for researchers, but it is incremental as it builds on existing logical frameworks.
The paper tackles the need for a logic that integrates probabilities, time, and actions, resulting in an expressive probabilistic temporal logic that extends classical probability theory and is demonstrated through formalizing the Monty Hall problem.
This paper argues that a combined treatment of probabilities, time and actions is essential for an appropriate logical account of the notion of probability; and, based on this intuition, describes an expressive probabilistic temporal logic for reasoning about actions with uncertain outcomes. The logic is modal and higher-order: modalities annotated by actions are used to express possibility and necessity of propositions in the next states resulting from the actions, and a higher-order function is needed to express the probability operator. The proposed logic is shown to be an adequate extension of classical mathematical probability theory, and its expressiveness is illustrated through the formalization of the Monty Hall problem.