Axiomatizations for Downward XPath

SERGIO ABRIOLA; SANTIAGO FIGUEIRA; RAUL FERVARI; MARÍA EMILIA DESCOTTE

Reykjavik

Workshop; Women in Logic (WiL) Workshop; 2017

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 overdata trees, which are tree-like structures whose every node contains a label from a nitealphabet and a data value from an innite domain. The language allows us to comparedata values of two nodes but cannot access the data values themselves (i.e. there is nocomparison by constants). Our axioms are in the style of equational logic, extendingthe 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 simplerfragment with `equality' tests only. Our axiomatizations apply both to node expressionsand path expressions. The proof of completeness relies on a novel normal form theoremfor XPath with data tests.