A neuro-symbolic framework that cleanly decouples reasoning into two formal dimensions: Symbolic Validity and Semantic Groundedness is proposed, which significantly improves reasoning reliability without the sprawling heuristics of prior frameworks.
Abstract
While tool-augmented Large Language Models have significantly improved multi-step reasoning in quantitative STEM tasks, a critical residual failure mode remains: intermediate reasoning steps that are syntactically well-formed, mathematically executable, and unit-consistent, yet contextually ungrounded. Current approaches either rely on formal verifiers that cannot assess semantic intent, or burden Process Reward Models (PRMs) with the dual task of checking both arithmetic and logic. In this paper, we propose a neuro-symbolic framework that cleanly decouples reasoning into two formal dimensions: Symbolic Validity ($V$) and Semantic Groundedness ($G$). We guarantee $V$ by construction using a deterministic symbolic verifier acting as a hard filter. To assess $G$, we train a PRM conditionally on the verifier-accepted manifold. To train this PRM efficiently, we introduce Counterfactual Symbolic Perturbation (CSP), a novel data synthesis strategy that algorithmically generates constraint-preserving hard negatives (steps that perfectly pass the verifier but are logically flawed). At inference, we deploy a verifier-first constrained search that guarantees execution consistency for verifier-covered operations while relying on the PRM solely to rank semantic grounding. By targeting the exact residual error class of strong tool-using LLMs, our method significantly improves reasoning reliability without the sprawling heuristics of prior frameworks.
Large language models (LLMs) increasingly serve as data-driven reasoners, yet their chains-of-thought (CoT) can be unfaithful even when final answers are correct. Most existing ''verification'' signals are not diagnostic: answer matching observes only the outcome, LLM-as-judge provides subjective and non-verifiable critiques, and scalar rewards (e.g., PRMs/RMs) offer little insight into where a multi-step derivation fails.We propose SymDiag, a neuro-symbolic framework that reframes reasoning verification as structured failure diagnosis. SymDiag translates natural-language CoT into symbolic constraints and performs step-level satisfiability/entailment checks to (i) localize failing steps and (ii) produce verifiable diagnostic evidence, including counterexamples, inconsistency witnesses, and missing-premise indicators. A central challenge is that apparent ''logic violations'' can be caused either by genuine reasoning defects or by neural-to-symbolic translation noise. SymDiag therefore incorporates a Self-Auditor that disentangles TranslationError from ReasoningError via dual symbolic encodings consistency checks, enabling robust diagnosis under partial observability. Across diverse mathematical, logical, scientific, and general reasoning benchmarks, SymDiag improves detection of unfaithful reasoning and provides substantially more effective feedback for multi-round reasoning repair than outcome-only verification and LLM-based judging, offering a principled foundation for trustworthy and scalable reasoning diagnosis.
Wenyao Cui, Huaping Zhang, Yongyi Huang et al.· Proceedings of the 32nd ACM...· 0 citations
A Neuro-Symbolic architecture that integrates a Logical Knowledge Graph (LKG) with dynamic solver routing, and introduces an ontology-based LKG that treats logical rules and constraints as first-class topological nodes, enabling explicit modeling of dependencies extracted from text.
Hai-Zhao Fan, Yu-Chi Xiong, Jize Wang et al.· 0 citations
This research proposes an Agentic Neuro-Symbolic Framework that decouples semantic interpretation from geometric verification and establishes a scalable foundation for autonomous compliance, demonstrating that AI reliability in engineering significantly improves when probabilistic models orchestrate deterministic tools rather than predicting physical realities.
N. Mirhosseini, D. Shojaei, Soheil Sabri· Buildings· 0 citations
Large language models (LLMs) and retrieval-augmented generation (RAG) are increasingly used in legal decision support, but retrieved evidence and fluent explanations do not guarantee valid normative inference. This paper proposes a proof-carrying neuro-symbolic method for non-monotonic legal reasoning. The LLM component is restricted to source-linked extraction of facts, defeasible rules, defeaters, priorities, citations, and operational confidence scores, while a deterministic symbolic engine computes the conclusion. Evidence is represented as a finite defeasible normative theory and compiled into a Dung-style argumentation framework; accepted conclusions are obtained from the grounded extension and returned with proof graphs showing support, attacks, and priority-based defeats. Under gold formalization, the symbolic engine achieved 99.3% accuracy on a 600-case controlled benchmark. In a 240-scenario LLM-to-logic experiment, the GPT-4o extractor followed by symbolic reasoning achieved 86.7% downstream accuracy versus 75.8% for a direct LLM over the same retrieved evidence; the paired difference was supported by an exact McNemar test after Holm correction (adjusted p = 0.016). Differences from the PDL and simpler symbolic baselines were not statistically established. Validation-triggered repair yielded 90.4% observed accuracy. Public-contract, Russian-law, stress-test, scalability, and lawyer-verification experiments further delimit the feasibility and current limitations of proof-carrying legal decision support.
Maxim Ulizko, Tatiana Polevaya, I. Tomilov et al.· Big Data and Cognitive Compu...· 0 citations
: The design and specification of experiments in Model-Based Systems Engineering is challenging: state-of-the-art tools are deemed either precise, but too cumbersome or too imprecise due to natural-language descriptions that lack formal semantics. This is compounded by the high complexity of systems, especially in safety-critical domains. Large Language Models (LLMs) offer a promising avenue for automating the elicitation step, but their probabilistic nature precludes unmediated use: hallucinations cannot be allowed to propagate into formal artifacts. We propose a neuro-symbolic framework combining LLM-driven elicitation constrained by a rule-based reasoner fed by an ontology-compliant knowledge graph. A deterministic orchestrator drives an elicitation loop where the symbolic engine poses context-sensitive questions, the LLM proposes candidate answers, and every candidate is validated against formal domain constraints before acceptance. We present a proof-of-concept implementing the proposed framework and an empirical evaluation across three case studies using four state-of-the-art LLMs. Results indicate that the framework reliably prevents hallucinations from propagating into formal specifications.
Diego Ferreira, Rakshit Mittal, Lucas Lima et al.· International Conference on...· 0 citations
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.
