It might be worth using standard vocabulary. For example:

> Reciprocal relations are their own inverse.

The usual word for this is "symmetric".

> Recursive relations can be chained to themselves infinitely. For example, "my ancestor's ancestor is also my ancestor."

The usual word for this is "transitive".

A reflexive, symmetric, transitive relation is called an "equivalence relation", and it can be used much like equality. It'd be nice if your language had support for this, though I don't immediately see how to add it.