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In this paper we introduce sound and strongly complete axiomatizations forXPath with data constraints extended with hybrid operators. First, we presentHXPath=, a multi-modal version of XPath with data, extended with nominals andthe hybrid operator @. Then, we introduce an axiomatic system for HXPath=, andwe prove it is strongly complete with respect to the class of abstract datamodels, i.e., data models in which data values are abstracted as equivalencerelations. We prove a general completeness result similar to the one presentedin, e.g., [BtC06], that ensures that certain extensions of the axiomatic systemwe introduce are also complete. The axiomatic systems that can be obtained inthis way cover a large family of hybrid XPath languages over different classesof frames, for which we present concrete examples. In addition, we investigateaxiomatizations over the class of tree models, structures widely used inpractice. We show that a strongly complete, finitary, first-orderaxiomatization of hybrid XPath over trees does not exist, and we propose twoalternatives to deal with this issue. We finally introduce filtrations toinvestigate the status of decidability of the satisfiability problem for theselanguages.

Axiomatizing Hybrid XPath with Data