 One very general semantic framework for logics that can invalidate necessitation, inheritance, or other principles of normal modal logics is the neighborhood semantic  framework.[90]  , A neighborhood semantics works with a set of possible worlds (just like Kripke-semantics) but replaces the accessibility relation with a neighborhood function \(\rN\) that maps every world \(w\) onto a set of sets \(X, Y,\ldots\) of possible worlds \(\rN(w)\), often thought of as a set of propositions. On such a semantics, \(\OB p\) is true at a world \(w\) iff the set of all \(p\)-worlds is in the neighborhood of \(w\), i.e.