Logical Reasoning in Large Language Models: A Survey (2502.09100v1)

Abstract: With the emergence of advanced reasoning models like OpenAI o3 and DeepSeek-R1, LLMs have demonstrated remarkable reasoning capabilities. However, their ability to perform rigorous logical reasoning remains an open question. This survey synthesizes recent advancements in logical reasoning within LLMs, a critical area of AI research. It outlines the scope of logical reasoning in LLMs, its theoretical foundations, and the benchmarks used to evaluate reasoning proficiency. We analyze existing capabilities across different reasoning paradigms - deductive, inductive, abductive, and analogical - and assess strategies to enhance reasoning performance, including data-centric tuning, reinforcement learning, decoding strategies, and neuro-symbolic approaches. The review concludes with future directions, emphasizing the need for further exploration to strengthen logical reasoning in AI systems.

The paper provides an extensive survey on the incorporation of formal logical reasoning within LLMs, meticulously distinguishing structured, symbolic inference from heuristic reasoning strategies such as chain-of-thought. The work reviews the evolution of logic in artificial intelligence, starting from classical formal logic foundations and extending to modern neuro-symbolic methods. It systematically categorizes logical reasoning into four primary paradigms: deductive, inductive, abductive, and analogical reasoning.

Scope and Taxonomy

The survey rigorously defines logical reasoning in AI as the process of deriving conclusions from structured premises, contrasting it with general-purpose reasoning that relies on statistical correlations. It offers a taxonomy that separates:

• Deductive Reasoning: Deriving specific, guaranteed conclusions from general rules.
• Inductive Reasoning: Generalizing from specific instances to broader abstractions, albeit without absolute certainty.
• Abductive Reasoning: Inferring the most plausible explanations for an observed set of facts under uncertainty.
• Analogical Reasoning: Transferring knowledge across domains by leveraging similarities between different concepts.

Datasets and Benchmarks

A significant portion of the survey is dedicated to the landscape of datasets and benchmark suites designed for evaluating logical reasoning in LLMs. The paper categorizes these datasets into:

• Rule-Based Datasets: Automatically synthesized through formal logical rules, these support large-scale evaluation but may suffer from repetitive patterns.
• Expert-Designed Datasets: Manually crafted, typically with a focus on rigor and precision, albeit at smaller scale.
• Exam-Based Datasets: Derived from standardized tests (e.g., civil service exams, LSAT, GRE), offering naturally complex and real-world challenges.

Key tasks include Natural Language Inference (NLI) and Machine Reading Comprehension (MRC), with datasets such as LogiQA, ReClor, AR-LSAT, CLUTRR, GSM, and LINGOLY. Additionally, benchmark suites like GLoRE, LogiGLUE, and LogiTorch are highlighted for their role in standardizing evaluation protocols, emphasizing metrics beyond mere accuracy.

Evaluation Metrics and Analysis

The survey stresses that traditional evaluation metrics (accuracy, F1-score) are insufficient for capturing the nuances of logical reasoning. It proposes more sophisticated metrics such as:

• Consistency: Invariance to logically equivalent reformulations.
• Generalization: Performance on out-of-distribution examples.
• Explainability: The clarity and verifiability of reasoning chains.

For instance, the work discusses the use of metrics like BERTScore combined with logical fidelity measures to better correlate model outputs with human judgments. The paper underscores the need to assess logical soundness explicitly, such as adherence to transitivity, contraposition, and other formal inference rules.

Enhancement Methods

Enhancing logical reasoning in LLMs is explored along several dimensions:

• Data-Centric Approaches:
  • $D$ represents the training dataset,
  • $M_D$ is the model trained on $D$, and
  • $R$ is a reasoning performance evaluator.

Three types of datasets are considered: - Expert-Curated Datasets: Highly precise, such as those with first-order logic (FOL) annotations. - Synthetic Datasets: Generated via rules to cover large-scale logical phenomena. - LLM-Distilled Datasets: Leveraging advanced models to generate intermediate reasoning chains.

• Model-Centric Approaches:
  • $\theta$ denotes the model parameters,
  • $S$ represents the decoding strategy (e.g., chain-of-thought prompting), and
  • $R$ evaluates reasoning performance.

Subcategories include: - Instruction Fine-Tuning (IFT): Models are fine-tuned on multi-grained instructions designed to mimic formal deduction processes. - Reinforcement Learning (RL): Techniques such as reverse curriculum learning and Monte Carlo Tree Search (MCTS) are used to iteratively refine reasoning pathways. For example, a method is highlighted where minimal long-chain-CoT data is used as a cold start, followed by reinforcement learning to generate structured reasoning data. - Inference-Time Decoding: Encompassing methods that improve reasoning without parameter updates—such as Maieutic Prompting, Logic-of-Thoughts, and constrained decoding—to ensure outputs adhere to formal logical constraints.

• External Knowledge Utilization:

The integration of external knowledge bases and retrieval-augmented systems is formalized as: $(M^*, K^*) = \arg\max_{M, K} R(M,K)$ where $K$ represents the knowledge integration strategy. This approach is particularly useful in reducing model hallucinations and improving factual accuracy in complex reasoning tasks.

• Neuro-Symbolic Approaches:

These hybrid methods seek to reconcile the scalability of neural networks with the precision of symbolic solvers. The general framework involves mapping natural language $x$ to a symbolic representation $z$ via: $z = M(x), \quad z \in \mathcal{L},$ then applying a symbolic solver $P$ to obtain the final output: $y = P(z).$ The joint optimization of $M$ and $P$ allows the system to leverage the strengths of both paradigms. Recent advances include approaches where the entire reasoning pipeline—from translation to verification—is performed within the LLM architecture.

Discussion and Future Directions

The survey identifies unresolved tensions in the field:

• Robustness vs. Generalization: Despite strong performance on curated datasets like those with FOL annotations, LLMs remain vulnerable to adversarial perturbations and syntactic variations, indicating a heavy reliance on surface-level correlations.
• Interpretability vs. Performance: While neuro-symbolic methods provide clearer reasoning chains, they come with scalability challenges and increased computational overhead.
• Evaluation Rigor: Current benchmarks often conflate pattern recognition with genuine logical reasoning, highlighting a need for gold standards that isolate core logical inference abilities.

Future research directions proposed include the development of:

• Hybrid architectures that dynamically integrate neural and symbolic components.
• More robust and interpretable evaluation frameworks with perturbation-based testing (e.g., negated premises, swapped quantifiers) to decouple memorization from reasoning.
• Multimodal reasoning systems that combine text, images, and code to mimic more holistic human reasoning.

Conclusion

The survey methodically synthesizes the landscape of logical reasoning in LLMs, critiquing current capabilities and proposing a roadmap toward enhancing formal logical inference in AI systems. It emphasizes that while state-of-the-art LLMs exhibit impressive performance on many heuristics-based tasks, significant challenges remain in achieving consistent, interpretable, and scalable logical reasoning. The work calls for a concerted effort in developing rigorous benchmarks, hybrid modeling strategies, and advanced evaluation metrics to bridge the gap between neural statistical patterns and formal logical rigor.

This deep technical analysis is of particular interest to researchers seeking to improve the logical consistency and robustness of LLMs, with strong implications for domains that demand high-stakes reasoning such as legal analysis, scientific discovery, and complex problem-solving.