The following axioms allow us to define precisely the space of mental situations. We use variables for blocks (x, y, z, w, ...), for situations (s, , ...), for actions (a, , ...), for mental situations (m, , ...), for mental actions ( , , ...), for formulas in the database (f, , ...), for subgoals -formulas in the goal stack- (g, , ...), for sequences of actions, (r, , ...), and for sequences of mental actions (l, , ...).
We assume uniqueness of names for every function symbol h, and every pair of distinct function symbols h and g. The symbols h and g are syntactical variables ranging over distinct function symbols; the symbols to are syntactical variables ranging over block constants. Axiom defines the expression , which means that mental situation can be reached from mental situation m by executing a nonempty sequence of appropriate mental actions ( is an abbreviation for ). We include domain closure axioms for blocks, mental situations, actions, and mental actions. Axiom of induction allows us to prove that a property holds for all mental situations that are reachable from a given mental situation.