Data-Aware Hybrid Tableaux

Labelled tableaux have been a traditional approach to define satisfiability checking procedures for Modal Logics. In many cases, they can also be used to obtain tight complexity bounds and lead to efficient implementations of reasoning tools. More recently, it has been shown that the expressive power provided by the operators characterizing Hybrid Logics (nominals and satisfiability modalities) can be used to \emph{internalize} labels, leading to well-behaved inference procedures for fairly expressive logics. The resulting procedures are attractive because they do not use external mechanisms outside the language of the logic at hand, and have good logical and computational properties. Many tableau systems based on Hybrid Logic have been investigated, with more recent efforts concentrating on Modal Logics that support data comparison operators. Here, we introduce an internalized tableau calculus for XPath, arguably one of the most prominent approaches for querying semistructured data. More precisely, we define data-aware tableaux for XPath featuring data comparison operators and enriched with nominals and the satisfiability modalities from Hybrid Logic. We prove that the calculus is sound, complete and terminating. Moreover, we show that tableaux can be explored in polynomial space, therefore establishing that the satisfiability problem for the logic is PSPACE-complete. Finally, we explore different extensions of the calculus, in particular how to handle data trees and other frame classes.