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Euclid-MCP: A Model Context Protocol Server for Det... | AI Research

Key Takeaways

  • Euclid-MCP: A Model Context Protocol Server for Deterministic Logical Reasoning via Prolog Large Language Models (LLMs) are highly effective at generating te...
  • Large Language Models (LLMs) excel at natural language understanding and generation but remain unreliable for multi-step logical reasoning, especially in safety-critical or compliance-sensitive domains.
  • Recent neuro-symbolic approaches address this gap by coupling neural models with external symbolic engines, yet most integrations are bespoke and lack a standardized interface for tool-augmented agents.
  • This paper presents Euclid-MCP, an open-source MCP server that provides deterministic logical reasoning via SWI-Prolog.
  • Euclid-MCP introduces Euclid-IR, an engine-agnostic intermediate representation for Horn-clause logic that is human-readable, easy for LLMs to generate, and straightforward to compile into Prolog or alternative backends.
Paper AbstractExpand

Large Language Models (LLMs) excel at natural language understanding and generation but remain unreliable for multi-step logical reasoning, especially in safety-critical or compliance-sensitive domains. Recent neuro-symbolic approaches address this gap by coupling neural models with external symbolic engines, yet most integrations are bespoke and lack a standardized interface for tool-augmented agents. This paper presents Euclid-MCP, an open-source MCP server that provides deterministic logical reasoning via SWI-Prolog. Euclid-MCP introduces Euclid-IR, an engine-agnostic intermediate representation for Horn-clause logic that is human-readable, easy for LLMs to generate, and straightforward to compile into Prolog or alternative backends. The server exposes a compact tool interface that supports a translate-run-inspect-repair loop, enabling LLM clients to delegate inference while retaining full access to proof traces and derivation logs. We evaluate Euclid-MCP on a realistic IT security and compliance use case. Results show that while LLMs alone are sufficient on small knowledge bases, they hallucinate systematically on larger problems, whereas Euclid-MCP delivers exact answers with lower latency and more compact outputs. We argue that semantic RAG is fundamentally unsuited for rule enforcement, and that Euclid-MCP can serve as a stable, shared reasoning substrate for both RAG-based assistants and agentic systems.

Euclid-MCP: A Model Context Protocol Server for Deterministic Logical Reasoning via Prolog
Large Language Models (LLMs) are highly effective at generating text but often struggle with complex, multi-step logical reasoning, particularly in fields like IT security and regulatory compliance where accuracy and auditability are mandatory. Euclid-MCP addresses this by acting as a bridge between LLMs and a deterministic symbolic reasoning engine. Instead of forcing the LLM to perform logical deductions internally—which can lead to hallucinations—Euclid-MCP allows the LLM to translate problems into a formal language, which is then solved by a reliable Prolog engine.

A New Language for Logical Reasoning

The core of the system is Euclid-IR, an engine-agnostic intermediate representation designed to be easily generated by LLMs and understood by humans. It uses a simple, declarative syntax to define facts, rules, and queries. By focusing on the essentials of Horn-clause logic, Euclid-IR ensures that the reasoning process remains deterministic and traceable. This language acts as a stable foundation that can be compiled into Prolog or other future backends without requiring changes to the user-facing interface.

The Translate-Run-Inspect-Repair Loop

Euclid-MCP provides a standardized tool interface through the Model Context Protocol (MCP), enabling LLMs to interact with the reasoning engine through a structured workflow. The system supports four primary operations:

  • Reason: Performs the actual deduction and returns solutions along with proof trees.

  • Diagnose: Explains why a specific query succeeded or failed, helping the LLM understand the logic behind the result.

  • What-If: Allows for scenario analysis by applying hypothetical changes to the knowledge base to see how they impact outcomes.

  • Check-KB: Validates the knowledge base for syntax errors or logical inconsistencies before execution.
    This cycle allows the LLM to act as an intelligent agent that can refine its own inputs based on feedback from the symbolic engine, ensuring that the final output is both logically sound and verifiable.

Performance and Reliability

Evaluations in IT security and compliance settings demonstrate that while LLMs can handle small knowledge bases, they tend to hallucinate on larger, more complex problems. Euclid-MCP overcomes this by delegating the heavy lifting of deduction to a deterministic engine. This approach not only results in exact answers but also provides lower latency and more compact, auditable outputs. By separating the "thinking" (symbolic deduction) from the "talking" (natural language generation), the system provides a robust substrate for agentic systems that require strict adherence to formal rules.

Considerations for Implementation

Euclid-MCP is designed to be safe and transparent. The translation layer from Euclid-IR to Prolog includes built-in sanitization to prevent the execution of unauthorized commands, and the system enforces limits on input size and execution time. While the current prototype uses SWI-Prolog, the architecture is intentionally decoupled, meaning the system can adapt to other solvers in the future. The project highlights that for rule-centric tasks, traditional semantic search—often used in standard RAG pipelines—is fundamentally mismatched, and that symbolic reasoning is a necessary component for reliable, rule-based AI.

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