MCP Server Logical Solver

What is MCP Server Logical Solver?

MCP Server Logical Solver is a logical reasoning system that combines Large Language Models (LLMs) with formal theorem proving through Prover9/Mace4. It processes logical problems in natural language and First‑Order Logic (FOL) to provide automated reasoning and structured explanations.

How to use MCP Server Logical Solver?

Clone the repository, install dependencies with pip install -r requirements.txt, configure a .env file with your model provider and API key, and set up mcp_config.json to point to the MCP‑Logic server. Run a single problem with python test.py or batch process via python main.py input.json output.json.

Key features of MCP Server Logical Solver

• Two‑stage pipeline: LLM analysis plus Prover9 verification
• Supports natural language and First‑Order Logic inputs
• Automatic XOR operation transformation for Prover9 compatibility
• Batch processing of multiple logical problems
• JSON‑structured output with explanation and tool usage status
• Multiple model providers: OpenAI, Anthropic, Gemini, Ollama

Use cases of MCP Server Logical Solver

• Validating logical conclusions from natural language premises
• Formal theorem proving with Prover9 and Mace4
• Automated reasoning for research or educational tasks
• Generating detailed, step‑by‑step logical explanations

FAQ from MCP Server Logical Solver

How does MCP Server Logical Solver handle “SEARCH FAILED” from Prover9?

When Prover9 cannot find a proof, the system uses LLM‑based analysis to distinguish between a “False” result (premises contradict the conclusion) and an “Uncertain” result (insufficient premises).

What FOL syntax is required for inputs?

Inputs must follow Prover9 syntax: use all for ∀, exists for ∃, & for ∧, | for ∨, -> for →, <-> for ↔, and - for ¬. XOR (⊕) is automatically transformed to an equivalent form.

What dependencies are needed to run MCP Server Logical Solver?

You must have the MCP‑Logic server installed and running, Python 3, the packages in requirements.txt, and an API key for the chosen LLM provider (unless using Ollama).

How does the output look?

The system returns a JSON object containing original premises/conclusions (natural language and FOL), the answer (True/False/Uncertain), a detailed explanation, and a tool_use boolean indicating whether tool calling succeeded.

Can I run MCP Server Logical Solver locally without cloud APIs?

Yes, by setting the model provider to ollama in the .env file and running a local model; no API key is required for Ollama.