State Constraints Revisited 1

We pursue the perspective of Reiter that in the situation calculus one can formalize primitive, determinate actions with axioms which, among others, include two disjoint sets: a set of successor state axioms and a set of action precondition axioms. We posed ourselves the problem of automatically generating successor state axioms, given only a set of e ect axioms and a set of state constraints. This is a special version of what has been traditionally called the rami cation problem. To our surprise, we found that there are state constraints whose role is not to yield indirect e ects of actions. Rather, they are implicit axioms about action preconditions. As such, they are intimately related to the classical quali cation problem. We also discovered that other kinds of state constraints arise; these are related to the formalization of strategic or control information. This paper is devoted to describing our results along these lines, focusing on rami cation and quali cation state constraints. More speci cally, we propose a two step procedure for determining an axiomatization which monotonically solves our versions of the rami cation and quali cation problems. We justify the rst step semantically by appealing to a suitable minimization policy. Step two we justify by simple Clark predicate completion.