Relations as Characteristic Functions
Let R(x, y) be a binary relation between two finite (co)domains or data types X and Y.
R is defined assymetrically as a multivalued function or mapping (MVM) y = R(x) from Domain X to Range or CoDomain Y.
R is defined symmetrically by its Characteristic Function, CFR: XxY --> {TRUE, FALSE}. CFR(x,y) is a Boolean expression which defines the exact subset of XxY for which R is TRUE.
The rules defining the CFR are usually extensible at run-time: they supply a recognition rule or criterion for recognizing membership in R.