Probabilistic logic for reasoning about actions in time

Abstract

In this paper, we develop a probabilistic logic for reasoning about preconditions, postconditions and execution of actions in time. The language of our logic allows statements like “precondition of the action A will hold in the next moment” and uncertain information like “probability that the precondition of A will hold in the next moment is at least one half.” We axiomatize this logic, provide corresponding semantics built on branching-time temporal models, and prove that the axiomatization is sound and strongly complete.