Formal Semantics for Agentic Tool Protocols: A Process Calculus Approach

arXiv cs.AI / 3/27/2026

💬 OpinionSignals & Early TrendsIdeas & Deep AnalysisModels & Research

共有:

Key Points

The paper addresses the need for formally verified protocols for LLM agents that invoke external tools, focusing on the relationship between Schema-Guided Dialogue (SGD) and the Model Context Protocol (MCP).
It provides the first process-calculus formalization of SGD and MCP and shows they are structurally bisimilar via a mapping Phi, establishing a rigorous equivalence result.
The authors also show that the reverse mapping (Phi^{-1}) is partial and lossy, demonstrating gaps in MCP expressivity relative to SGD.
They derive five necessary-and-sufficient principles (e.g., semantic completeness and explicit action boundaries) for full behavioral equivalence and encode these as type-system extensions in MCP+.
The work claims MCP+ is isomorphic to SGD, framing schema quality as a provable safety property and laying groundwork for verified agent systems.

Abstract

The emergence of large language model agents capable of invoking external tools has created urgent need for formal verification of agent protocols. Two paradigms dominate this space: Schema-Guided Dialogue (SGD), a research framework for zero-shot API generalization, and the Model Context Protocol (MCP), an industry standard for agent-tool integration. While both enable dynamic service discovery through schema descriptions, their formal relationship remains unexplored. Building on prior work establishing the conceptual convergence of these paradigms, we present the first process calculus formalization of SGD and MCP, proving they are structurally bisimilar under a well-defined mapping Phi. However, we demonstrate that the reverse mapping Phi^{-1} is partial and lossy, revealing critical gaps in MCP's expressivity. Through bidirectional analysis, we identify five principles -- semantic completeness, explicit action boundaries, failure mode documentation, progressive disclosure compatibility, and inter-tool relationship declaration -- as necessary and sufficient conditions for full behavioral equivalence. We formalize these principles as type-system extensions MCP+, proving MCP+ is isomorphic to SGD. Our work provides the first formal foundation for verified agent systems and establishes schema quality as a provable safety property.