MCP-Logic

MCP-Logic

An MCP server providing automated reasoning capabilities using Prover9/Mace4 for AI systems. This server enables logical theorem proving and logical model verification through a clean MCP interface.

Design Philosophy

MCP-Logic bridges the gap between AI systems and formal logic by providing a robust interface to Prover9/Mace4. What makes it special:

• AI-First Design: Built specifically for AI systems to perform automated reasoning
• Knowledge Validation: Enables formal verification of knowledge representations and logical implications
• Clean Integration: Seamless integration with the Model Context Protocol (MCP) ecosystem
• Deep Reasoning: Support for complex logical proofs with nested quantifiers and multiple premises
• Real-World Applications: Particularly useful for validating AI knowledge models and reasoning chains

Features

• Seamless integration with Prover9 for automated theorem proving
• Support for complex logical formulas and proofs
• Built-in syntax validation
• Clean MCP server interface
• Extensive error handling and logging
• Support for knowledge representation and reasoning about AI systems

Quick Example

# Prove that understanding + context leads to application
result = await prove(
    premises=[
        "all x all y (understands(x,y) -> can_explain(x,y))",
        "all x all y (can_explain(x,y) -> knows(x,y))",
        "all x all y (knows(x,y) -> believes(x,y))",
        "all x all y (believes(x,y) -> can_reason_about(x,y))",
        "all x all y (can_reason_about(x,y) & knows_context(x,y) -> can_apply(x,y))",
        "understands(system,domain)",
        "knows_context(system,domain)"
    ],
    conclusion="can_apply(system,domain)"
)
# Returns successful proof!

Installation

Prerequisites

• Python 3.12+
• UV package manager
• Download Prover9/Mace4 with the given fixes for your platform (from https://www.cs.unm.edu/~mccune/prover9/gui/v05.html)

Setup

1. Install Prover9/Mace4 to a known location (e.g., F:/Prover9-Mace4/)
2. Clone this repository
3. Install dependencies:

uv venv
uv pip install -e .

Configuration

Add to your MCP environment configuration:

{
  "mcpServers": {
    "mcp-logic": {
      "command": "uv",
      "args": [
        "--directory",
        "path/to/mcp-logic/src/mcp_logic",
        "run",
        "mcp_logic",
        "--prover-path",
        "path/to/Prover9-Mace4/bin-win32"
      ]
    }
  }
}

Available Tools

prove

Run logical proofs using Prover9:

{
  "tool": "prove",
  "arguments": {
    "premises": [
      "all x (man(x) -> mortal(x))",
      "man(socrates)"
    ],
    "conclusion": "mortal(socrates)"
  }
}

check-well-formed

Validate logical statement syntax:

{
  "tool": "check-well-formed",
  "arguments": {
    "statements": [
      "all x (man(x) -> mortal(x))",
      "man(socrates)"
    ]
  }
}

Documentation

See the Documents folder for detailed analysis and examples:

• Knowledge to Application: A formal logical analysis of understanding and practical application in AI systems

Project Structure

mcp-logic/
├── src/
│   └── mcp_logic/
│       └── server.py    # Main MCP server implementation
├── tests/
│   ├── test_proofs.py   # Core functionality tests
│   └── test_debug.py    # Debug utilities
├── Documents/           # Analysis and documentation
├── pyproject.toml      # Python package config
└── README.md          # This file

Development

Run tests:

uv pip install pytest
uv run pytest

License

MIT