On the Role of Possibility in Action Execution and Knowledge in the Situation Calculus.

In the Situation Calculus the term do(a, s) denotes the successor situation to s, resulting from performing (i.e. executing) the action a. In other words, it is assumed that actions always succeed. If action a is not possible in situation s, then the action still succeeds but the resulting situation is not physically realizable. We will argue that consequences of this definition of do(a, s) puts some limitations on applicability of the Situation Calculus. In this paper, we view do(a, s) slightly differently which results in a more general form for successor state axioms. The new framework not only has all the benefits of the current version of the Situation Calculus but also offers several advantages. We suggest that it is more intuitive than the traditional account. As well, it leads to a more general solution to the projection problem. Last, it leads to a more general formalization of knowledge in the Situation Calculus.