  Even in modal logic, one may wish to restrict the range of possible worlds which are relevant in determining whether \(\Box A\) is true at a given world. For example, I might say that it is necessary for me to pay my bills, even though I know full well that there is a possible world where I fail to pay them. In ordinary speech, the claim that \(A\) is necessary does not require the truth of \(A\) in all possible worlds, but rather only in a certain class of worlds which I have in mind (for example, worlds where I avoid penalties for failure to pay). In order to provide a generic treatment of necessity, we must say that \(\Box A\) is true in \(w\) iff \(A\) is true in all worlds that are related to \(w\) in the right way. So for an operator \(\Box\) interpreted as necessity, we introduce a corresponding relation \(R\) on the set of possible worlds \(W\), traditionally called the accessibility relation. The accessibility relation \(R\) holds between worlds \(w\) and \(w'\) iff \(w'\) is possible given the facts of \(w\). Under this reading for \(R\), it should be clear that frames for modal logic should be reflexive. It follows that modal logics should be founded on \(M\), the system that results from adding \((M)\) to \(\bK\). Depending on exactly how the accessibility relation is understood, symmetry and transitivity may also be desired.