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 that takes advantage of well-sorted unification between terms. We show that answering projection queries in our logical theories is sound and complete with respect to that of in Reiterâ€™s basic action theories. Moreover, we demonstrate that our regression operator based on order-sorted logic can provide significant computational advantages in comparison to Reiterâ€™s regression operator.