Formalizing MLTL Formula Progression in Isabelle/HOL

2024-10-04

arXiv.org

AI Summary

This paper addresses the lack of a trusted formal foundation for Mission-time Linear Temporal Logic (MLTL). We present the first complete higher-order logic formalization of MLTL’s syntax and semantics in Isabelle/HOL, systematically constructing a library of key properties and a formula progression algorithm. Our contributions are: (1) the first formal verification of MLTL’s progression algorithm correctness; (2) identification and correction of multiple definition flaws and proof gaps in the original theory; (3) design of reusable, domain-specific induction rules tailored to MLTL’s structure; and (4) implementation of a verified, executable MLTL toolchain leveraging Isabelle’s built-in code generator. The framework provides a rigorous formal basis for runtime verification and model checking, enabling both theoretical extensions of MLTL and development of trustworthy verification tools.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Machine Learning: Hardware-aware ML

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• 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
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Mission-time Linear Temporal Logic (MLTL) is rapidly increasing in popularity as a specification logic, e.g., for runtime verification and model checking, driving a need for a trustworthy tool base for analyzing MLTL. In this work, we formalize the syntax and semantics of MLTL and a library of key properties, including useful custom induction rules. We envision this library as being useful for future formalizations involving MLTL and as serving as a reference point for theoretical work using or developing MLTL. We then formalize the algorithm and correctness theorems for MLTL formula progression; along the way, we identify and fix several errors and gaps in the source material. A main motivation for our work is tool validation; we ensure the executability of our algorithms by using Isabelle's built-in code generator.

Problem

• Formalize MLTL syntax and semantics in Isabelle/HOL
• Develop MLTL formula progression algorithm and correctness proofs
• Validate tools by ensuring algorithm executability with Isabelle

Innovation

• Formalized MLTL syntax and semantics in Isabelle/HOL
• Developed MLTL formula progression algorithm
• Ensured algorithm executability with Isabelle code generator