Hennessy-Milner Logic in CSLib, the Lean Computer Science Library

2026-02-17

AI Summary

This work addresses the absence of a general and reusable formalization of Hennessy-Milner Logic (HML) in existing verification libraries, which hinders model checking and equivalence analysis over labeled transition systems (LTSs). We present the first parameterized formalization of HML within CSLib—a library for the Lean theorem prover—covering its syntax, satisfaction relation, denotational semantics, and a complete metatheory, seamlessly integrated with existing formalizations of bisimulation. A central contribution is the fully mechanized proof of the Hennessy-Milner theorem, establishing the equivalence between bisimilarity and logical equivalence for image-finite LTSs. The resulting HML library is open-sourced, integrated into CSLib, and directly usable for system verification tasks via the LTS API, offering high generality and reusability.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Statistical Relational/Logic Learning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

We present a library-level formalisation of Hennessy-Milner Logic (HML) - a foundational logic for labelled transition systems (LTSs) - for the Lean Computer Science Library (CSLib). Our development includes the syntax, satisfaction relation, and denotational semantics of HML, as well as a complete metatheory including the Hennessy-Milner theorem - bisimilarity coincides with theory equivalence for image-finite LTSs. Our development emphasises generality and reusability: it is parametric over arbitrary LTSs, definitions integrate with CSLib's infrastructure (such as the formalisation of bisimilarity), and proofs leverage Lean's automation (notably the grind tactic). All code is publicly available in CSLib and can be readily applied to systems that use its LTS API.

Problem

• Hennessy-Milner Logic
• Labelled Transition Systems
• Formalisation
• Lean
• CSLib

Innovation

• Hennessy-Milner Logic
• formalisation in Lean
• labelled transition systems
• bisimilarity
• metatheory