# Leveraging LLMs for Hypothetical Deduction in Logical Inference: A Neuro-Symbolic Approach

arXiv: https://arxiv.org/abs/2410.21779 · HTML: https://mlsanity.com/paper/2410.21779/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 33 of its 44 references that are in the map.
- First posted on arXiv 29 Oct 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 33)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Least-to-Most Prompting Enables Complex Reasoning in Large Language Models](https://mlsanity.com/paper/2205.10625/) (2022)
- [PaLM 2 Technical Report](https://mlsanity.com/paper/2305.10403/) (2023)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Graph of Thoughts: Solving Elaborate Problems with Large Language Models](https://mlsanity.com/paper/2308.09687/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [ProofWriter: Generating Implications, Proofs, and Abductive Statements over Natural Language](https://mlsanity.com/paper/2012.13048/) (2020)
- [Faithful Chain-of-Thought Reasoning](https://mlsanity.com/paper/2301.13379/) (2023)
- [Transformers as Soft Reasoners over Language](https://mlsanity.com/paper/2002.05867/) (2020)
- [To CoT or not to CoT? Chain-of-thought helps mainly on math and symbolic reasoning](https://mlsanity.com/paper/2409.12183/) (2024)
- [Reasoning with Language Model Prompting: A Survey](https://mlsanity.com/paper/2212.09597/) (2022)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [ReClor: A Reading Comprehension Dataset Requiring Logical Reasoning](https://mlsanity.com/paper/2002.04326/) (2020)
- [Retrieve, Program, Repeat: Complex Knowledge Base Question Answering via Alternate Meta-learning](https://mlsanity.com/paper/2010.15875/) (2020)
- [Evaluating the Logical Reasoning Ability of ChatGPT and GPT-4](https://mlsanity.com/paper/2304.03439/) (2023)
- [LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers](https://mlsanity.com/paper/2310.15164/) (2023)
- [Cumulative Reasoning with Large Language Models](https://mlsanity.com/paper/2308.04371/) (2023)
- [Beyond Accuracy: Evaluating the Reasoning Behavior of Large Language Models -- A Survey](https://mlsanity.com/paper/2404.01869/) (2024)
- [Premise Order Matters in Reasoning with Large Language Models](https://mlsanity.com/paper/2402.08939/) (2024)
- [LAMBADA: Backward Chaining for Automated Reasoning in Natural Language](https://mlsanity.com/paper/2212.13894/) (2022)
- [Logic-Driven Context Extension and Data Augmentation for Logical Reasoning of Text](https://mlsanity.com/paper/2105.03659/) (2021)
- [GPT-4 Can't Reason](https://mlsanity.com/paper/2308.03762/) (2023)
- [An Examination on the Effectiveness of Divide-and-Conquer Prompting in Large Language Models](https://mlsanity.com/paper/2402.05359/) (2024)
- [Abstract Meaning Representation-Based Logic-Driven Data Augmentation for Logical Reasoning](https://mlsanity.com/paper/2305.12599/) (2023)

## Built on by (most cited first, 6 of 6)

- [Empowering LLMs with Logical Reasoning: A Comprehensive Survey](https://mlsanity.com/paper/2502.15652/) (2025)
- [How does Chain of Thought Think? Mechanistic Interpretability of Chain-of-Thought Reasoning with Sparse Autoencoding](https://mlsanity.com/paper/2507.22928/) (2025)
- [Are LLMs Stable Formal Logic Translators in Logical Reasoning Across Linguistically Diversified Texts?](https://mlsanity.com/paper/2506.04575/) (2025)
- [Integrating Expert Knowledge into Logical Programs via LLMs](https://mlsanity.com/paper/2502.12275/) (2025)
- [Adaptive Selection of Symbolic Languages for Improving LLM Logical Reasoning](https://mlsanity.com/paper/2510.10703/) (2025)
- [Know Your Limits : On the Faithfulness of LLMs as Solvers and Autoformalizers in Legal Reasoning](https://mlsanity.com/paper/2606.16118/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have exhibited remarkable potential across a wide array of reasoning tasks, including logical reasoning. Although massive efforts have been made to empower the logical reasoning ability of LLMs via external logical symbolic solvers, crucial challenges of the poor generalization ability to questions with different features and inevitable question information loss of symbolic solver-driven approaches remain unresolved. To mitigate these issues, we introduce LINA, a LLM-driven neuro-symbolic approach for faithful logical reasoning. By enabling an LLM to autonomously perform the transition from propositional logic extraction to sophisticated logical reasoning, LINA not only bolsters the resilience of the reasoning process but also eliminates the dependency on external solvers. Additionally, through its adoption of a hypothetical-deductive reasoning paradigm, LINA effectively circumvents the expansive search space challenge that plagues traditional forward reasoning methods. Empirical evaluations demonstrate that LINA substantially outperforms both established propositional logic frameworks and conventional prompting techniques across a spectrum of five logical reasoning tasks. Specifically, LINA achieves an improvement of 24.34% over LINC on the FOLIO dataset, while also surpassing prompting strategies like CoT and CoT-SC by up to 24.02%. Our code is available at https://github.com/wufeiwuwoshihua/nshy.