MCP-Logic

Overview

MCP‑Logic is a Model Context Protocol server that exposes the powerful theorem prover Prover9 and its model finder Mace4 as a first‑class resource for AI assistants. By wrapping these formal logic engines behind a clean MCP interface, the server allows conversational agents to ask for automated reasoning on arbitrary first‑order formulas, receive proofs or counter‑models, and integrate the results back into their knowledge base. This solves a long‑standing gap between natural language reasoning systems and formal verification tools: developers can now validate the logical consistency of knowledge graphs, policy rules, or inference chains directly from within an AI workflow.

What the Server Does

When a client sends a prove request, MCP‑Logic translates the premises and conclusion into the syntax expected by Prover9, invokes the prover, and streams back a concise proof object. If Prover9 cannot find a proof within the allotted time, it falls back to Mace4 to search for a counter‑model, giving the assistant concrete evidence of logical failure. The server also performs syntax validation before dispatching to Prover9, ensuring that malformed formulas are caught early. All interactions occur over standard MCP messages, so any agent built to speak the protocol—Claude Desktop, ChatGPT‑plus, or a custom integration—can leverage automated reasoning without bespoke code.

Key Features

• AI‑First Design – The API is intentionally minimal, exposing only the prove tool and a simple JSON payload. This keeps the surface area small for agents while still offering full access to Prover9’s advanced options via optional arguments.
• Formal Knowledge Validation – Developers can verify that their knowledge representations (e.g., ontology rules, business logic) are logically sound or discover hidden contradictions.
• Deep Reasoning Support – Prover9’s ability to handle nested quantifiers, equality, and complex term structures means that even sophisticated inference chains can be checked.
• Built‑in Syntax Checking – Errors are caught before the prover is invoked, reducing latency and providing clearer feedback to users.
• Extensive Logging – Every proof attempt is logged with timestamps, parameters, and outcome, facilitating audit trails in regulated environments.

Use Cases

1. AI Knowledge Graph Integrity – A system that continuously ingests new facts can automatically prove that the updated graph remains consistent with existing rules.
2. Policy Compliance Checking – Business rules expressed in first‑order logic can be proven against regulatory constraints, ensuring that automated decisions never violate compliance.
3. Debugging Inference Chains – When an assistant produces unexpected conclusions, developers can ask MCP‑Logic to prove the implication chain, revealing whether a missing premise or incorrect rule is at fault.
4. Educational Tools – Students learning formal logic can experiment with proof requests in a conversational interface, receiving instant feedback from Prover9.

Integration into AI Workflows

Because MCP‑Logic follows the same message format as other MCP servers, it plugs into any existing agent pipeline with a single configuration entry. In Claude Desktop, for example, the server is launched via a simple JSON block that specifies the command and prover path. Once running, an assistant can invoke the prove tool by sending a JSON payload; the server returns a structured proof object that can be displayed, stored, or fed back into further reasoning steps. This tight coupling means developers can build end‑to‑end systems where natural language prompts trigger formal verification, and the results are seamlessly incorporated into subsequent AI actions.

Unique Advantages

MCP‑Logic stands out because it bridges two historically separate worlds: conversational AI and formal logic engines. Its AI‑first design eliminates the need for custom wrappers or language bindings, while its focus on clean MCP integration ensures that developers can add automated reasoning to any agent with minimal friction. By providing both proof search and counter‑model generation in a single, well‑documented server, it gives developers the confidence that their knowledge bases are not only expressive but also logically sound.