An Expressive Probabilistic Temporal Logic
Abstract
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 higherorder: modalities annotated by actions are used to express possibility and necessity of propositions in the next states resulting from the actions, and a higherorder 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2016
 arXiv:
 arXiv:1603.07453
 Bibcode:
 2016arXiv160307453W
 Keywords:

 Computer Science  Logic in Computer Science;
 Computer Science  Artificial Intelligence