 Whereas a relational frame formula_1 consists of a set "W" of worlds (or states) and an accessibility relation "R" intended to indicate which worlds are alternatives to (or, accessible from) others, a neighborhood frame formula_2 still has a set "W" of worlds, but has instead of an accessibility relation a "neighborhood function"

that assigns to each element of "W" a set of subsets of "W".Intuitively, each family of subsets assigned to a world are the propositions necessary at that world, where 'proposition' is defined as a subset of "W" (i.e.the set of worlds at which the proposition is true).