Axiomatizations for downward XPath on Data Trees

TL;DR

This paper develops sound and complete axiomatizations for a data-aware XPath logic on data trees, enabling formal reasoning about data value comparisons with a novel normal form theorem.

Contribution

It introduces the first complete axiomatizations for XPath with data tests and the child axis, extending previous data-oblivious axiomatizations.

Findings

Axiomatizations are sound and complete for XPath with data tests.

The logic predicts over data trees with data value comparisons.

A novel normal form theorem underpins the completeness proof.

Abstract

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.