Euclid-MCP: A Model Context Protocol Server for Deterministic Logical Reasoning via Prolog

Frontier reasoning-tuned language models still fail on deductive tasks at depth, and the cost of improved performance through extended internal reasoning scales poorly. Symbolic delegation offers a complementary route: a language model translates the problem, while a solver performs the inference. However, current autoformalization pipelines for logic programming are typically bespoke integrations tied to particular tasks or agents. We introduce PrologMCP, a task-agnostic, open-source server that exposes Prolog as a stateful tool through the Model Context Protocol (MCP). Its compact tool interface, structured error reporting, and per-session isolation make the translate-run-inspect-repair loop a reusable primitive for MCP-capable agents. We evaluate a formalizer agent enhanced with PrologMCP against standard and reasoning LLMs (Claude Sonnet 4.6, GPT-4.1, and o4-mini) on two subsets of PARARULE-Plus: a general-purpose sample and a more challenging one targeting a specific failure mode of natural-language reasoning. On the general sample, the formalizer matches or exceeds reasoning LLMs (accuracy 1.00 vs.\ 1.00 / 0.998), with the largest gains over standard models (0.762 for GPT-4.1). On the challenging subset, the formalizer remains near-perfect (1.00 / 0.99) while reasoning LLMs drop to 0.95 / 0.94. These results suggest that delegating inference to Prolog via MCP is a robust and inspectable alternative to extended natural-language reasoning.

We independently reproduce two recent methods for making large language model (LLM) reasoning more reliable, and stress-test them across domains and models (RPC across four new task domains with Qwen3-8B, LCF across four 7-8B models). The first, RPC, aggregates token probabilities and self-consistency at inference; the second, LCF, trains projectors that split hidden states into "content" and "logic" and edits the logic part toward a valid region. Validating such reliability claims matters because the original evaluations are run by each method's own authors and were never independently reproduced or stress-tested across models and domains, and LCF shipped no public code. We re-run RPC's published-path aggregation and re-implement LCF's projector, contrastive, and intervention pipeline, then extend both to text-to-SQL, legal extraction, fallacy identification, and precedent grading, and probe LCF's representation directly. RPC reproduces the original grid exactly on the authors' released reasoning paths; on four new domains its edge over self-consistency is never significant (ties or small mixed differences, paired p >= 0.28), and on BIRD, the one domain where we vary the budget, the edge grows with K as predicted but its largest gap (+2.5 accuracy at K=32, p=0.16) reverses to -0.25 when we enlarge the sample to n=200. LCF's logic-validity direction is real but weak (0.82 separability at the single best sub-layer versus 0.95 for a semantic-attribute control); its one positive effect (Qwen3 $Δ$Prob) is not significant (p=0.56), while it significantly reduces $Δ$Prob on two of the other three models.

Despite recent advances in large language models (LLMs), performing logically consistent deductive reasoning over extended interactions remains challenging. Tasks that require integrating evidence across multiple reasoning steps, maintaining consistency with prior inferences, and updating beliefs under new constraints can surface limitations in current models while providing a useful testbed for evaluating reasoning enhancements. In this paper, we implement a text-based, multi-agent version of the classic board game Clue as an environment to evaluate multi-step, agentic deductive reasoning. In this setting, agents must infer hidden information from a sequence of observations, maintain consistency across turns, and reason over an evolving set of logical constraints. We instantiate six LLM-based agents (GPT-4o-mini and Gemini-2.5-Flash) as players that engage in turn-based gameplay; using three agents per model family, we establish baseline performance across repeated games. We then introduce a tool-augmented approach in which a structured possibility matrix converts implicit game state from generated reasoning logs into an explicit representation of remaining possibilities. The possibility matrix encodes extended-turn memory and deductive constraints, offloading these tasks from the agent. We compare this approach against the baseline to evaluate how tool augmentation supports reasoning quality and task success for autonomous agents in a strategic reasoning environment.