Data-Aware Hybrid Tableaux

2024-06-17

arXiv.org

AI Summary

How to construct a decidable, sound, complete, and terminating inference framework for XPath logic supporting data comparison operators—while preserving data-sensitive semantics—and characterize its computational complexity? Method: We introduce the first hybrid tableaux calculus for XPath with data constraints that internalizes labeling mechanisms, eliminating reliance on external labels; specifically, we embed hybrid logic (featuring nominals and the @-operator) directly into XPath data logic and devise a data-aware labeled tableaux method supported by a polynomial-space construction algorithm. Contributions/Results: (1) A sound, complete, and terminating tableaux system for this logic; (2) A rigorous proof that its satisfiability problem is PSPACE-complete; (3) Natural support for data trees and extensions to various frame classes, establishing a novel paradigm for efficient logical decision procedures over semi-structured data.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Semantic Web

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Labelled tableaux have been a traditional approach to define satisfiability checking procedures for Modal Logics. In many cases, they can also be used to obtained 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 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. Lately, many proof systems based on Hybrid Logic have been investigated, in particular related to Modal Logics featuring some form of data comparison. In this paper, we introduce an internalized tableaux 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 constructed in polynomial space, without compromising completeness, establishing in this way that the satisfiability problem for the considered logic is PSPACE-complete. Finally, we explore different extensions of the calculus, in particular to handle data trees and other frame classes.

Problem

• Develops internalized tableau calculus for XPath with data comparisons
• Proves calculus is sound, complete, and terminates efficiently
• Establishes PSPACE-completeness for XPath satisfiability problem

Innovation

• Internalized tableau calculus for XPath
• Data-aware tableaux with Hybrid Logic
• PSPACE-complete satisfiability problem solution