Terminology for relations with certain properties

Question

Are there terms describing relations with the following properties?

• transitive and not reflexive. In other words, is there term for a relation that is transitive and (irreflexive or nonreflexive)? I am aware that a strict partial order is transitive and irreflexive (and asymmetric, by consequence of the first two), but I am looking for a term referring to such a relation that could also be nonreflexive. If not, is there a term for a relation that is transitive and nonreflexive?
• not transitive and not reflexive. In other words, is there term for a relation that is (intrasitive or nontranstive) and (irreflexive or nonreflexive)?

Thanks!

Answer 1

I think the answer to both questions is "no". It's best to just say what you mean in standard terminology, not invent new terms for concepts which are rarely needed.