Logical reasoning with large language models (LLMs) is a critical capability, as it reflects a system's ability to correctly deduce hypotheses from a given context using faithful deductive processes. However, LLM reasoning has often been shown to be sensitive to small surface-level variations in problem formulation, raising questions about whether models truly follow the underlying logical structure. Studying this behavior is challenging because the symbolic components of logical problems, such as operators and predicates, are difficult to systematically manipulate in natural language. We introduce a tool-driven framework for generating controlled, label-preserving edits to logical reasoning problems. Our method operates on symbolic representations of first-order logic and constraint satisfaction problem tasks, enabling targeted modifications to logical operators and other structural components before translating them back into natural language. Using this framework, we evaluate various LLMs under cumulative and individual operator edits and analyze their behavior in response to these changes. Our quantitative and qualitative analyses show that LLM reasoning behavior under controlled operator edits is inconsistent, regardless of model size or family: models sometimes adapt correctly to structural changes but often fail to track their logical consequences. The results from this automated stress test enable an evaluation of language models across different dimensions and help measure the reliability of their reasoning.
Large Language Models (LLMs) have demonstrated remarkable proficiency in natural language understanding, yet they struggle with strict multi-step reasoning, frequently suffering from hallucinations and inconsistency. Existing solutions like Chain-of-Thought (CoT) lack rigorous verification mechanisms, while standard Retrieval-Augmented Generation (RAG) often misses the complex, structural dependencies inherent in logical tasks. To bridge this gap, we propose a Neuro-Symbolic architecture that integrates a Logical Knowledge Graph (LKG) with dynamic solver routing. Specifically, we introduce an ontology-based LKG that treats logical rules and constraints as first-class topological nodes, enabling explicit modeling of dependencies extracted from text. We further design a Logic Router to dynamically dispatch tasks to the optimal symbolic engine, which is supported by a topology-aware hybrid retrieval mechanism. Experimental results on logical reasoning benchmarks demonstrate that our framework significantly outperforms state-of-the-art prompting and RAG baselines, delivering higher accuracy and verifiable reasoning paths.
Chain-of-thought (CoT) prompting can fail severely on constraint-dense logical reasoning tasks, where unverified errors accumulate silently across steps. We introduce SymStep: an LLM makes one atomic claim at a time (DEDUCE: Alice, pet, Cat), then a lightweight constraint propagator checks the claim for consistency with prior accepted deductions, rejects contradictions, and cascades implied facts automatically. SymStep+G additionally provides MRV guidance after each accepted step, directing the LLM toward the most constrained unresolved variable. On a 35-puzzle retained subset of ZebraLogicBench, a benchmark of 1,000 Einstein-style logic puzzles, Direct and CoT both achieve 0%, while SymStep+G reaches 97%. On AR-LSAT analytical reasoning problems, SymStep achieves 100% vs. CoT's 87%. On LGP-14, SymStep+G achieves 100% vs. 0% for CoT and Logic-LM, the strongest prior symbolic+LLM baseline we compare against. Ablation studies reveal that MRV guidance is a key mechanism for reducing directionless cycling, while consistency checking provides a safety net against explicit contradictions. Across six benchmarks spanning five task domains, SymStep variants match or exceed every baseline on constraint-dense and arithmetic tasks. Experiments on AQUA-RAT algebra confirm the advantage is constraint-density-specific.
Large language models (LLMs) have become powerful tools for language understanding and logical reasoning. However, they still make mistakes when a problem requires both understanding meaning and following logic. A key reason is that natural-language statements often carry implicit semantic relations before any formal reasoning begins. If these hidden meanings are not properly organized, the model may reach incorrect conclusions even when the subsequent reasoning process appears logically valid. Existing methods improve reasoning through decomposition, symbolic translation, external solvers, or self-verification, but pay comparatively less attention to the semantic structure on which reasoning depends. In this paper, we further investigate how semantic organization influences logical reasoning in LLMs. To this end, we propose HexLogicAgent, a framework that first organizes the meaning of natural-language statements and then guides logical reasoning through structured verification. In our investigation, we also make two observations. First, incomplete semantic representations, rather than deductive inference itself, are a major source of logical reasoning failures in LLMs. Second, explicitly modeling the complete structure of semantic opposition substantially delays the degradation of reasoning performance as logical complexity increases. Experiments on challenging logical reasoning benchmarks demonstrate that HexLogicAgent consistently improves reasoning reliability across multiple LLMs. The core idea is supported by a logical hexagon theory, which explains why a complete structure of opposing meanings is necessary for reliable reasoning.
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.
Abdullah Shaikh, Zain Naqi, Taha Zahid +2cs.CL cs.AI
While Large Language Models (LLMs) excel in many general NLP tasks, their formal reasoning capabilities are often compromised by content effects, demonstrating a measurable bias towards real-world plausibility. In this paper, we present our system for SemEval-2026 Task 11, which evaluates the ability of models to disentangle formal logic from content across 12 languages with and without distractor premises. We address this challenge using mDeBERTa-v3 networks fine-tuned on a synthetic, rule-based dataset of syllogistic schemes to avoid the semantic noise of LLM-augmented data. To explicitly decouple plausibility from logical structure, our training pipeline employs a multi-objective loss function combining Adaptive Group Distributionally Robust Optimization (DRO), a scheduled differentiable bias penalty, and KL-Divergence consistency regularization. Our system achieved #1 ranks and perfect Ranking Scores (100.0) with 0.00% bias and 100.0% accuracy on Subtask 1 (English), Subtask 2 (Noisy English), and Subtask 3 (Multilingual). On the highly complex Subtask 4 (Noisy Multilingual), the system achieved the 6th rank with 89.06% Accuracy and F1-score, alongside a limited 2.89% Bias and a 37.78 Ranking Score. Our dataset generation engine and codebase are publicly available to facilitate future work on robust logical reasoning.
Logical reasoning is essential for reliable AI, yet existing benchmarks are largely first-order-logic-centric, focusing on object-level deduction over fixed predicates. This misses many realistic scenarios where models must reason over rules, predicates, functions, constraints, and decision procedures themselves. We introduce HOLMES (Higher-Order Logic Meets real-world Explainable Symbolic reasoning), the first real-world benchmark for higher-order symbolic reasoning in LLMs, containing 1379 instances. Built on higher-order logic, HOLMES pairs natural-language problems with HOL formalizations, ground-truth answers, verifiable reasoning traces, and fine-grained controllable reasoning factors across law and finance. Experiments show that current LLMs still struggle on HOLMES, with an average accuracy of only 50.64% and the best model reaching 59.54%. Our analyses further reveal that high final-answer accuracy can mask shortcut reasoning in conflict-resolution settings, while performance drops sharply under scope-conditioned and compositional reasoning. These findings identify higher-order symbolic reasoning as a key bottleneck for building reliable and verifiable LLMs. The project code and dataset are publicly available at https://github.com/wuyucheng2002/HOLMES.
Hanna Abi Akl, Fabien Gandon, Catherine Faron +1cs.CL cs.AI
This paper revisits our pipeline called Syllogistic Evaluation Framework-Common Logic Grammar Construction (SEF-CLGC). We combine formal logical notations with Small Language Models (SLMs) to evaluate reasoning performance on the SemEval-2026 Task 11 Subtask 1: Disentangling Content and Formal Reasoning in Large Language Models. Our experiments show that by relying solely on SLMs, trained on a combination of natural and symbolic languages, our best model achieves a content score of 27.80% on the task while significantly lowering the content bias in reasoning.
Process reward models (PRMs) rely on high-quality process supervision data, yet existing construction methods often provide limited control over error location, error type, and trajectory consistency. We propose a controllable and verifiable framework for synthesizing process supervision data for PRMs. Our framework first constructs a correct symbolic reasoning chain, injects a template-aware error into an intermediate step, recomputes subsequent steps under the corrupted state, and verifies that the injected step is not derivable from its prefix. The resulting paired trajectories are prefix-invalid at the first error while remaining trajectory-consistent after symbolic recomputation, and are translated into aligned natural-language processes for PRM training and evaluation. Experiments show that the synthesized data improve Best-of-8 reranking on logical reasoning benchmarks and transfer to mathematical reasoning. Step-level evaluation further shows that first-error localization remains substantially more challenging than overall step classification, highlighting the need for fine-grained and verifiable process supervision.