Basic Model Theory for Path Predicate Modal Logic

2026-07-22

AI Summary

This study investigates the expressive power and model-theoretic properties of Path Predicate Modal Logic (PPML), aiming to establish an abstract theoretical foundation for data-aware formalisms such as XPath and DataGL. By introducing a Hennessy–Milner class tailored to relational predicate atoms and extending the van Benthem characterization theorem to the PPML framework, the work provides the first systematic model-theoretic basis for PPML. Through a combination of bisimulation techniques, locality analysis, and expressiveness characterization methods, the research precisely delineates the boundaries of PPML’s expressive capacity and clarifies its correspondence with fragments of first-order logic. The findings uncover distinctive features that differentiate PPML from classical modal logics, thereby offering crucial theoretical support for the formal analysis of data-aware logical systems.

Abstract

Path Predicate Modal Logic (PPML) is a generalization of Basic Modal Logic, where atoms are relational predicates instead of propositional symbols. The study of PPML is motivated as a way to abstractly investigate data-aware formalisms, such as XPath or DataGL. In this paper, we investigate some basic model theoretical aspects of PPML to better characterize its expressive power. More concretely, we investigate different ways of defining Hennessy-Milner classes, and a van Benthem characterization theorem. In doing so, we discuss the main challenges of dealing with the novel features of PPML, and what are the similarities with the standard approaches.

Problem

• Path Predicate Modal Logic
• Model Theory
• Expressive Power
• Hennessy-Milner Class
• van Benthem Characterization

Innovation

• Path Predicate Modal Logic
• Hennessy-Milner classes
• van Benthem characterization
• model theory
• expressive power