Reciprocul

Reciprocul is a term used to describe a reciprocal relation in abstract structures, often appearing in discussions of mathematics, logic, and theoretical linguistics. It is a neologism built from the Latin root common to words meaning returning or mutual exchange, and is used to emphasize bidirectional reciprocity in a formal or semantic sense.

In formal use, a binary relation R on a set X is described as reciprocal (reciprocul) when it is equal to its inverse, that is, R = R^{-1}. Equivalently, for all a,b in X, if aRb then bRa. In many contexts this condition is called symmetry, but proponents of the term reciprocul stress the mutual, bidirectional aspect rather than mere invariance under reversal. In extended frameworks with multiple relations, reciprocul may denote a subset of relations that are closed under taking inverses and under certain compositions.

Examples: In a social network modeled by a graph, a reciprocal relation corresponds to undirected edges where friendship is mutual. In a database of interactions, a reciprocul link ensures that if an interaction from A to B is recorded, the reverse interaction from B to A is also present.

Applications: Reciprocally defined structures appear in network theory, game theory when modeling reciprocal strategies, and formal semantics where reciprocal predicates relate entities in both directions.

See also: reciprocity, symmetry, inverse relation, mutualism, bidirectional.