More on bounding introspection in modal nonmonotonic logics

By L, we denote the set of all propositional formulas. Let C be the set of all clauses. Define C-0=C boolean OR {-L eta : eta is an element of }. In S ec. 2 of this paper, we prove that for normal modal logics S; the notions o f (S, C-0)-expansions and S-expansions coincide. In Sec. 3, we prove that i f I consists of default clauses then the notions of S-expansions for I and (S, C)-expansions for I coincide. To this end, we first show, in Sec. 3, th at the notion of S- expansions for I is the same as that of (S, L)-expansio ns for I.