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.
Abstract
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.
SymDiag is proposed, a neuro-symbolic framework that reframes reasoning verification as structured failure diagnosis and incorporates a Self-Auditor that disentangles TranslationError from ReasoningError via dual symbolic encodings consistency checks, enabling robust diagnosis under partial observability.
Wenyao Cui, Huaping Zhang, Yongyi Huang et al.· Proceedings of the 32nd ACM...· 0 citations
Reason Popper-ly, a neurosymbolic framework that uses inductive logic programming (ILP) to learn relation composition rules from reasoning traces and deploys them as an online verifier for step-level correction, consistently improves terminal accuracy over standard CoT.
Results show that capability failures can manifest as distributed, task-dependent changes in the structure of visible reasoning, and that CoT dynamics agnostic to whether the verbalized trace reflects the model's internal computations can help diagnose and correct failures.
Shashwat Sourav, Aishwarya H. Balwani· 0 citations
SymboUQ is a symbolic uncertainty quantification framework that estimates final-answer reliability from reasoning traces by distinguishing symbolizability, whether a claim can be represented in the verifier's formal language, from semantic determinacy, whether its execution yields an entailed or contradicted verdict rather than an unknown or not-evaluable outcome.
Dahai Yu, Lin Jiang, Rongchao Xu et al.· 0 citations
LLMs generate fluent plans for robots but routinely violate the syntactic and se8mantic constraints they must satisfy to execute, and existing remedies trade formal guarantees against plan quality: soft methods (affordance scoring, grounded decoding) give no guarantee, while symbolic planners (LLM+P) discard the LM's commonsense. We propose \textbf{Meta-Ctrl}, a constrained-decoding framework that guarantees the encoded constraints while preserving the base LM's plan quality. Meta-Ctrl introduces \emph{meta-tokens}---a compact vocabulary of grounded actions---enforcing syntax at the token level and semantics (preconditions, goals, ordering) at the action level, an exact factorization that cuts the memory of constrained decoding from over 107TB to under 2GB. With it, a small open-weight LM becomes competitive where it otherwise sits at the bottom of the leaderboard: on WAH-NL under the LoTa-Bench protocol it reaches the highest reported subgoal success rate, exceeding GPT-4's, with consistent gains across the Embodied Agent Interface. We further demonstrate it on a real tabletop robot, where every generated plan satisfies its preconditions and goals by construction. Project website: https://metactrlg.github.io
Gwen Yidou-Weng, Edward Sun, Tianyi Ma et al.· 0 citations
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.
Hai-Zhao Fan, Yu-Chi Xiong, Jize Wang et al.· 0 citations
