relsrels

Relsrels is a term found in niche discussions of relational theory and higher-order logic. It does not denote a single established concept, but rather a family of ideas about relations between other relations. The term appeared in online discussions in the 2020s and has no widely accepted definition.

A relsrel is a higher-order relation that takes two base relations on the same domain and yields a new relation or a truth value reflecting how those relations relate. In practice, it captures meta-properties such as containment, compatibility, or the result of composing R and S.

Formally, if R and S are binary relations on a set X, a relsrel P assigns truth to the pair (R,S) when a specified criterion holds (for example, R is contained in S, or the composition R ∘ S has a given property). No canonical definition exists, and various proposals describe different permissible criteria.

Proposed variants include directional relsrels (order matters), symmetric relsrels (invariance under reversal), and partial relsrels (defined for limited families of relations). These distinctions reflect how strictly the meta-relations treat the inputs and whether they apply universally or only in restricted contexts.

In a knowledge-graph setting, a relsrel could express when two relations jointly imply a third; for instance, if R connects A to B and S connects B to C, the relsrel may specify conditions under which a path from A to C holds. Such meta-relations are discussed as tools for reasoning about relational structure rather than as established formal elements.

The concept remains largely theoretical, with potential roles in ontology design, meta-relational reasoning, and linguistic semantics. It has limited formal adoption and is not part of standard textbooks. See also relation algebra, higher-order logic, and meta-relations.