Carlos Areces ; Raul Fervari - Axiomatizing Hybrid XPath with Data

lmcs:6259 - Logical Methods in Computer Science, July 20, 2021, Volume 17, Issue 3 - https://doi.org/10.46298/lmcs-17(3:5)2021
Axiomatizing Hybrid XPath with Data

Authors: Carlos Areces ; Raul Fervari

In this paper we introduce sound and strongly complete axiomatizations for XPath with data constraints extended with hybrid operators. First, we present HXPath=, a multi-modal version of XPath with data, extended with nominals and the hybrid operator @. Then, we introduce an axiomatic system for HXPath=, and we prove it is strongly complete with respect to the class of abstract data models, i.e., data models in which data values are abstracted as equivalence relations. We prove a general completeness result similar to the one presented in, e.g., [BtC06], that ensures that certain extensions of the axiomatic system we introduce are also complete. The axiomatic systems that can be obtained in this way cover a large family of hybrid XPath languages over different classes of frames, for which we present concrete examples. In addition, we investigate axiomatizations over the class of tree models, structures widely used in practice. We show that a strongly complete, finitary, first-order axiomatization of hybrid XPath over trees does not exist, and we propose two alternatives to deal with this issue. We finally introduce filtrations to investigate the status of decidability of the satisfiability problem for these languages.


Volume: Volume 17, Issue 3
Published on: July 20, 2021
Accepted on: June 19, 2021
Submitted on: April 2, 2020
Keywords: Computer Science - Logic in Computer Science,03B70,F.4.1


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