Sequent Calculi for Data-Aware Modal Logics

2025-05-22

AI Summary

The data-aware modal logic HXPathD lacks a structured proof system. Method: This paper introduces the first Gentzen-style sequent calculus for HXPathD, rigorously grounded in its modal semantics and data-sensitive path semantics, and fully supporting variable binding, data equivalence, and path navigation. Contribution/Results: We establish soundness, strong completeness, invertibility of all inference rules, and full cut elimination for the calculus; as a consequence, HXPathD is shown to be decidable. This work bridges a foundational gap in formal reasoning for data-aware modal logics and provides a new deductive framework that balances expressive power with proof-theoretic tractability—particularly applicable to data-sensitive systems such as XML/JSON validation and database query logics.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Data Mining & Knowledge Management: Representing, Reasoning, and Using Provenance, Trust

Application Category

• Semantics and Knowledge: Provenance, trust, security and privacy, and ethical issues in managing semantic data
• Security and Privacy: Data transparency and provenance
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

This document serves as a companion to the paper of the same title, wherein we introduce a Gentzen-style sequent calculus for HXPathD. It provides full technical details and proofs from the main paper. As such, it is intended as a reference for readers seeking a deeper understanding of the formal results, including soundness, completeness, invertibility, and cut elimination for the calculus.

Problem

• Introducing sequent calculus for HXPathD logic
• Proving soundness and completeness of the calculus
• Establishing invertibility and cut elimination properties

Innovation

• Gentzen-style sequent calculus
• HXPathD logic framework
• soundness completeness proofs