Guarded Fragments Meet Dynamic Logic: The Story of Regular Guards (Extended Version)

2025-09-11

AI Summary

This paper investigates the Regularly Guarded Fragment (RGF), a novel logic integrating the Guarded Fragment (GF) with Propositional Dynamic Logic extended with intersection and converse (ICPDL). Addressing the satisfiability and query entailment problems, the authors employ a combined approach of tree unravelling and automata-theoretic techniques, introducing regular guards into the GF framework for the first time. Their main contributions are: (1) establishing 2EXPTIME-completeness of RGF satisfiability, thereby settling its tight complexity bound; (2) proving undecidability of query entailment in RGF; and (3) identifying the largest EXPSPACE-complete decidable subfragment of RGF. By incorporating regular expressions into guarded quantification while preserving decidability, this work substantially extends the expressive power of guarded logics, achieving an optimal balance between expressivity and computational tractability.

Technology Category

• Knowledge Representation and Reasoning: Description Logics
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• 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

Abstract

We study the Guarded Fragment with Regular Guards (RGF), which combines the expressive power of the Guarded Fragment (GF) with Propositional Dynamic Logic with Intersection and Converse (ICPDL). Our logic generalizes, in a uniform way, many previously-studied extensions of GF, including (conjunctions of) transitive or equivalence guards, transitive or equivalence closure and more. We prove 2EXPTIME-completeness of the satisfiability problem for RGF, showing that RGF is not harder than ICPDL or GF. Shifting to the query entailment problem, we provide undecidability results that significantly strengthen and solidify earlier results along those lines. We conclude by identifying, in a natural sense, the maximal EXPSPACE-complete fragment of RGF.

Problem

• Combines Guarded Fragment with Propositional Dynamic Logic
• Proves 2EXPTIME-completeness for satisfiability problem
• Provides undecidability results for query entailment

Innovation

• Regular Guards combining GF and ICPDL
• Proving 2EXPTIME-completeness for satisfiability
• Identifying maximal EXPSPACE-complete fragment