Relation
Relation
The same as dyadic propositional function (q.v.). The distinction between relations in intension and relations in extension is the same as that for propositional functions. — Sometimes the word relation is used to mean a propositional function of two or more variables, and in this case one distinguishes binary (dyadic) relations, ternary (triadic) relations, etc.
If R denotes a (binary) relation, and X and Y denote arguments, the notation XRY may be used, instead of R(X, Y), to mean that the two arguments stand in the relation denoted by R The domain of a relation R is the class of things x for which there exists at least one y such that xRy holds. The converse domain of a relation R is the class of things y for which there exists at least one x such that xRy. The field of a relation is the logical sum of the domain and the converse domain.
See also Logic, formal, 8. — A.C.
Whitehead and Russell, Principia Mathematica, 2nd edn , vol 1, Cambridge, England, 1925.