The Typed Situation Calculus

We propose a theory for reasoning about actions based on order-sorted predicate logic where one can consider an elaborate taxonomy of objects. We are interested in the projection problem: whether a statement is true after executing a sequence of actions. To solve it we design a regression operator takes advantage of well-sorted unification between terms. We show that answering projection queries in our logical theories is sound and complete wrt answering similar queries in Reiter’s basic action theories. This proves correctness of our approach. Moreover, we demonstrate that our regression operator based on order-sorted logic can provide significant computational advantages in comparison to Reiter’s regression operator.