The first approach is to treat equality as no different than any other binary relation.

In the semantic web, a property is a binary relation.

The second is the level of binary relations or relational mappings.

Some important types of binary relations over a set X are:

That is, they are the binary relations describing how subsets meet.

Given a binary relation it is then possible to put all the elements of the set in a certain order.

In set theory, the transitive closure of a binary relation.

Strict weak ordering is a binary relation on a set.

The formal approach requires that we start with a study of binary relations.

This is closely related to the notion of reflexivity for binary relations.