On the role of possibility in action execution and knowledge in the Situation Calculus

Formalization of knowledge is an important aspect of reasoning about change. We review how knowledge is formalized in the Situation Calculus (a logical formalism for reasoning about action and change) and discuss the problems that occur when unexecutable actions (those actions whose preconditions are not met at the time of execution) are involved. We then provide a generalized framework that addresses these problems by tracing back source of the problem to the answer provided to the Frame Problem in the Situation Calculus. We develop a more generalized form for Successor Sate Axioms based on the new account of the solution to the Frame Problem and show how this solves the problems related to involvement of unexecutable actions.