 Specifically, if "M" is a model on the frame, then

where

is the "truth set" of "A".Neighborhood semantics is used for the classical modal logics that are strictly weaker than the normal modal logic K.

To every relational model M = (W,R,V) there corresponds an equivalent (in the sense of having point-wise equivalent modal theories) neighborhood model M' = (W,N,V) defined by

The fact that the converse fails gives a precise sense to the remark that neighborhood models are a generalization of relational ones.Another (perhaps more natural) generalization of relational structures are general relational structures.