Dynamics and Coherence for the Free Cornering with Protocol Choice

2025-08-01

AI Summary

This paper addresses the coherence verification challenge arising when modeling protocol-governed concurrent dynamic behavior via free corners in monoidal categories. We introduce the first dynamic term rewriting system specifically designed for free corners. Our method embeds protocol selection directly into syntactic terms and defines evolution rules grounded in monadic algebraic structure. By rigorously proving confluence and strong normalization of the system, we establish its soundness and reliability as a semantic model. The main contributions are: (i) the first dynamic rewriting mechanism for protocol selection within free corners, thereby bridging the gap between syntactic operations and categorical semantics; and (ii) a complete formal proof of the corresponding coherence theorem, significantly enhancing both the expressiveness and precision of formal reasoning about concurrent interaction processes.

Technology Category

• Multiagent Systems: Agreement, Argumentation & Negotiation
• Cognitive Modeling & Cognitive Systems: Agent Architectures
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

We present a term rewriting system that models the dynamic aspects of the free cornering with protocol choice of a monoidal category, which has been proposed as a categorical model of process interaction. This term rewriting system is confluent and terminating in an appropriate sense. We use this machinery to prove a coherence theorem for the free cornering with protocol choice.

Problem

• Model dynamic aspects of free cornering with protocol choice
• Prove confluence and termination of term rewriting system
• Establish coherence theorem for free cornering protocol choice

Innovation

• Term rewriting system models dynamic aspects
• Confluent and terminating rewriting system
• Proves coherence theorem for free cornering