reasoning and synthesis

Large language models (LLMs) suffer from poor interpretability and opaque reasoning processes when performing complex logical inference under multiple constraints and rules. Method: This paper proposes a non-iterative Symbol-Augmented Chain-of-Thought (CoT) approach, integrating lightweight first-order logic symbols into few-shot prompts to explicitly structure reasoning steps—enabling traceable, analyzable inference paths without iterative optimization. The method is general and scalable across LLMs of varying sizes. Contribution/Results: Evaluated on four logical reasoning benchmarks—ProofWriter, FOLIO, ProntoQA, and LogicalDeduction—it achieves significant improvements over standard CoT on three datasets, substantially enhancing both accuracy and transparency. Its core innovation lies in the first seamless integration of symbolic logical representation into a non-iterative CoT framework, enabling structured, interpretable, and efficient reasoning.

This work addresses the insufficient logical rigor and frequent premise-conclusion disconnections in natural language proof generation by large language models (LLMs), particularly within chain-of-thought (CoT) reasoning. To this end, we propose a subgoal-decomposition and contrastive stepwise decoding framework. Our key contribution is the first integration of negative reasoning paths into stepwise decoding, coupled with fine-grained, subgoal-driven proof planning. We further enhance the framework via lightweight model fine-tuning, multi-step entailment modeling (leveraging EntailmentBank), and contrastive learning to strengthen logical coherence and structural integrity. Experimental results on the EntailmentBank benchmark demonstrate substantial improvements over strong CoT baselines: our method achieves significant gains in Proof Accuracy and Step Consistency—key metrics reflecting both global correctness and local logical soundness—thereby advancing the reliability and fidelity of LLM-generated formal proofs.

This study systematically investigates the task boundaries of chain-of-thought (CoT) prompting for enhancing large language model (LLM) performance. Through a quantitative meta-analysis and controlled experiments across 14 models and 20 datasets, we find CoT gains are highly concentrated in mathematical and symbolic reasoning tasks (+12.3% average improvement), yet negligible in commonsense reasoning and language understanding (+0.8%). We propose that CoT’s core mechanism is augmenting symbolic execution—not general-purpose reasoning—and demonstrate that its efficacy is strongly predicted by symbol-triggered behaviors (e.g., equality signs). A planning-execution decoupling analysis further reveals inherent computational paradigm limitations. Consequently, we advocate selective CoT activation to balance performance gains against inference cost, and call for novel intermediate computation architectures integrating explicit symbolic solvers—empirically shown to substantially outperform CoT.

Large language models (LLMs) frequently exhibit inconsistencies between reasoning chains and final conclusions, as well as incomplete extraction of logical information in complex logical reasoning tasks. To address these issues, we propose Logic-of-Thought (LoT), a novel prompting framework that introduces propositionally grounded, expanded logical descriptions as context to ensure logical completeness—constituting the first such integration of formal logic into prompting. LoT is orthogonal to existing paradigms and seamlessly integrates with Chain-of-Thought (CoT), Self-Consistency, and Tree-of-Thoughts (ToT). Its methodology comprises three core components: formal logical modeling, automated expansion of logical expressions, and multi-strategy orchestration. Evaluated on five rigorous benchmarks—including ReClor, RuleTaker, and ProofWriter—LoT achieves consistent gains: +4.35% accuracy over CoT on ReClor and +8.0% over ToT on ProofWriter.

Chain-of-thought (CoT) reasoning in mathematical problem solving suffers from excessive token consumption, high KV cache overhead, and low inference efficiency due to long dependency chains. Method: We propose Markovian Chain-of-Thought (MCoT), modeling each reasoning step as a text state augmented with executable Python code; an integrated code interpreter enables automatic verification and dynamic history compression, reducing redundant intermediate steps to equivalent problem representations. MCoT formally recasts multi-step CoT as a Markov process, eliminating reliance on full-history KV caching. We construct the MCoTInstruct dataset—grounded in symbolic reasoning, code execution, and instruction tuning—and adapt it to mainstream LLM inference pipelines. Results: Experiments show MCoT matches baseline accuracy on mathematical reasoning while significantly reducing latency (−38% on average) and KV cache memory usage (−62%), validating a novel paradigm for efficient long-horizon reasoning.

This work addresses the challenge of diagnosing errors in chain-of-thought (CoT) reasoning generated by large language models, which are often verbose and prone to logical or factual inaccuracies. To this end, the authors propose the first step-level error detection method that integrates external fact-checking with symbolic logical verification. They further develop ReasonDiag, an interactive visualization system that combines arc diagrams and hierarchical node-link graphs to reveal the reasoning flow and trace error propagation paths. Through technical evaluation, two case studies, and user interviews with 16 participants, the study demonstrates that ReasonDiag effectively supports users in comprehending complex reasoning processes, accurately identifying erroneous steps, and tracing underlying root causes.

This work addresses the inefficiency and logical fragmentation often observed in traditional Chain-of-Thought (CoT) prompting during complex multi-step reasoning, which frequently arises from redundant intermediate steps. To overcome these limitations, the authors propose Hierarchical Chain-of-Thought (Hi-CoT), a novel approach that introduces a structured, hierarchical reasoning paradigm. Hi-CoT alternates between high-level directive planning and low-level step-by-step execution, thereby decomposing intricate tasks into logically coherent sub-steps. Empirical evaluations demonstrate that this method substantially enhances both accuracy and efficiency in long-horizon reasoning for large language models. Across multiple mainstream models and mathematical reasoning benchmarks, Hi-CoT achieves an average accuracy improvement of 6.2%—reaching up to 61.4% in certain cases—while simultaneously reducing reasoning trajectory length by 13.9%, underscoring the critical role of a strict hierarchical structure in boosting performance.

This work addresses the significant yet poorly understood performance variations of Chain-of-Thought (CoT) reasoning across different tasks by providing the first theoretical framework for its step-by-step inference process. The authors model CoT as a Markov chain and propose that its effectiveness hinges on the consistency of the transition kernels between reasoning steps, while also quantifying how noise in intermediate steps degrades performance. Through rigorous theoretical analysis, they prove that consistent transition kernels substantially reduce sample complexity. To validate these predictions, they construct synthetic benchmark experiments that align with their theoretical findings and offer a principled explanation for the observed disparities in CoT’s empirical success across real-world tasks. This study thus establishes a novel theoretical lens and analytical framework for understanding and improving CoT reasoning.

This work addresses systematic deficiencies in large language models (LLMs) regarding structured logical reasoning—such as conflation of hypotheses with verification and unconstrained propagation of weak inference steps—by proposing a symbolic reasoning framework that integrates Peircean triadic inference (abduction, deduction, and induction). Central to this approach is the Gamma Quintet algebraic invariant system, particularly its “Weakest Link bound,” which mitigates inconsistency accumulation across multi-step reasoning from a possibilistic logic perspective, thereby providing the first formal logical guarantees for LLMs. Leveraging attribute-based testing and fuzz testing, we validate all invariants across over 10⁵ generated cases, releasing an open-source, reproducible implementation that establishes a new benchmark for structured reasoning.