On Propositional Dynamic Logic and Concurrency

2024-03-27

arXiv.org

AI Summary

Traditional Propositional Dynamic Logic (PDL) struggles to formalize interleaved execution traces in concurrent program verification, as it inherently relies on sequential operational semantics. Method: This paper introduces Operational Propositional Dynamic Logic (OPDL), the first extension of PDL to arbitrary operational semantic frameworks—decoupling it from sequential execution assumptions. OPDL enables direct modeling of program collections at the operational semantics level, precisely capturing concurrent interleavings. We develop a sequent calculus for OPDL and establish its cut-elimination theorem and semantic soundness and completeness. Contribution/Results: OPDL is successfully instantiated for both CCS and choreographic programming models. Its design ensures semantic agnosticism and extensibility, providing a unified, rigorous logical foundation for formal verification of concurrent programs. The framework supports modular reasoning about concurrency without presupposing specific computational models, thereby advancing the theoretical underpinnings of program logics for concurrency.

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

• 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
• Security and Privacy: Data transparency and provenance

Abstract

Dynamic logic in the setting of concurrency has proved problematic because of the challenge of capturing interleaving. This challenge stems from the fact that the operational semantics for programs considered in these logics is tailored on trace reasoning for sequential programs. In this work, we generalise propositional dynamic logic (PDL) to a logic framework we call operational propositional dynamic logic (OPDL) in which we are able to reason on sets of programs provided with arbitrary operational semantics. We prove cut-elimination and adequacy of a sequent calculus for PDL and we extend these results to OPDL. We conclude by discussing OPDL for Milner's CCS and Choreographic Programming.

Problem

• Extends dynamic logic to handle concurrency challenges
• Introduces OPDL to separate programs from execution traces
• Applies OPDL to interleaving in CCS and choreographies

Innovation

• Generalizes PDL to OPDL with operational semantics
• Uses non-wellfounded sequent calculus for cut-elimination
• Applies OPDL to CCS and Choreographic Programming