 In 1965, Saul Kripke introduced a special kind of world, the non-normal worlds, in order to provide semantics for non-normal modal logics. Let us introduce some simple semantic machinery for propositional modal logic. Take a non-normal interpretation of a propositional modal language, \(\langle W, N, R, v\rangle\), where \(W\) is a set of worlds; \(N\) is a proper subset of \(W\), the set of normal worlds; \(R\) is a binary accessibility relation between worlds; and \(v\) is a valuation function assigning truth values to formulas at worlds: “\(v_w(A)\)” denotes the truth value of \(A\) at world \(w\). Worlds in \(W - N\) are the non-normal worlds. The truth conditions for the extensional logical vocabulary (negation, conjunction, disjunction, the material conditional) are given the usual way. The same holds for the modal operators of necessity \(\Box\) and possibility \(\Diamond\), but only at normal worlds. If \(w\) is non-normal, the truth conditions for the modalizers go as follows: