Neighborhood semantics

Summary

Neighborhood semantics, also known as Scott–Montague semantics, is a formal semantics for modal logics. It is a generalization, developed independently by Dana Scott and Richard Montague, of the more widely known relational semantics for modal logic. Whereas a relational frame $\langle W,R\rangle$ 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 $\langle W,N\rangle$ still has a set W of worlds, but has instead of an accessibility relation a neighborhood function