What do we call the state of being proper? The set $\\{1, 2\\}$ is a proper subset of $\\{1, 2, 3\\}$. But $\\{1, 2, 3\\}$ itself is not. More generally, we might want to define a notion of "proper-ness" that derives from this basic notion of proper super- and subsets. For example, I might want to talk about a sequence $(f_i)_{i = 1}^n$ of surjective functions, and call it "proper" if not one of the $f_i$s is a bijection. Then I might have some way of manipulating such sequences, and I might want to write that "... is not in general preserved under [such a manipulation]", where ... is the name of the state of being proper. What do we call the property of being proper? Do we call it "propriety", perhaps, or something else?

The paper "Completeness and properness of refinement operators in inductive logic programming" uses _properness_ , though the authors may not be English first-language speakers.

Wiktionary also has this meaning as the third offered for _properness_

_-ness_ and _-less_ are productive in English (for example as in _memorylessness_ ) so I see nothing wrong with _properness_.