To me it looks that it is:
- irreflexivity: NaN < NaN == false
- transitivity: if a < b and b < c then a < c (the antecedent is never true for NaNs)
- asymmetry: if a < b then not b < a (again, the antecedent is never true for NaNs)
However, it cannot be extended to non-strict partial ordering <= because there's no (reflexive) equality for doubles (NaN != NaN).