We give sound and complete axiomatizations for XPath with data tests by
"equality" or "inequality", and containing the single "child" axis. This
data-aware logic predicts over data trees, which are tree-like structures whose
every node contains a label from a finite alphabet and a data value from an
infinite domain. The language allows us to compare data values of two nodes but
cannot access the data values themselves (i.e. there is no comparison by
constants). Our axioms are in the style of equational logic, extending the
axiomatization of data-oblivious XPath, by B. ten Cate, T. Litak and M. Marx.
We axiomatize the full logic with tests by "equality" and "inequality", and
also a simpler fragment with "equality" tests only. Our axiomatizations apply
both to node expressions and path expressions. The proof of completeness relies
on a novel normal form theorem for XPath with data tests
