Discovering a Shared Logical Subspace: Steering LLM Logical Reasoning via Alignment of Natural-Language and Symbolic Views

• URL: http://arxiv.org/abs/2604.19716v1
• Date: Tue, 21 Apr 2026 17:42:54 GMT
• Title: Discovering a Shared Logical Subspace: Steering LLM Logical Reasoning via Alignment of Natural-Language and Symbolic Views
• Abstract summary: Large Language Models (LLMs) still struggle with multi-step logical reasoning.<n>We ask whether LLMs contain a shared internal logical subspace that simultaneously aligns natural-language and symbolic-language views.
• Score: 16.869958532486258
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Large Language Models (LLMs) still struggle with multi-step logical reasoning. Existing approaches either purely refine the reasoning chain in natural language form or attach a symbolic solver as an external module. In this work, we instead ask whether LLMs contain a shared internal logical subspace that simultaneously aligns natural-language and symbolic-language views of the reasoning process. Our hypothesis is that this logical subspace captures logical reasoning capabilities in LLMs that are shared across views while remaining independent of surface forms. To verify this, we employ Canonical Correlation Analysis on the paired residual activations from natural-language and symbolic-language reasoning chains, learning a low-dimensional subspace with maximum cross-view correlation. Furthermore, we design a training-free approach that steers LLMs reasoning chain along this logical subspace, thereby leveraging the complementary reasoning signals from both views. Experiments on four logical reasoning benchmarks demonstrate the effectiveness of our approach, improving accuracy by up to 11 percentage points and generalizing well on out-of-domain problems.

Related papers

• SALA: Semantic-Aware Logical Alignment for Complex Reasoning in In-Context Learning [61.13104919370034]
  We propose SALA, a Semantic-Aware Logical Alignment framework.<n>Instead of relying on a fixed inventory, SALA automatically learns task-specific reasoning operations.<n>It then embeds these operations into a continuous semantic space and uses dynamic time warping to align the reasoning sequences.
  arXiv  Detail & Related papers  (2026-09-02T09:12:03Z)
• A Balanced Neuro-Symbolic Approach for Commonsense Abductive Logic [21.003276503456632]
  We propose a novel method to augment a logic problem with commonsense relations provided by the Large Language Models.<n>This involves a search procedure through potential commonsense assumptions to maximize the chance of finding useful facts.
  arXiv  Detail & Related papers  (2026-01-26T15:40:26Z)
• Leveraging LLMs for Hypothetical Deduction in Logical Inference: A Neuro-Symbolic Approach [11.400815134634016]
  We introduce LINA, a 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 bolsters the resilience of the reasoning process. Empirical evaluations demonstrate that LINA substantially outperforms both established propositional logic frameworks and conventional prompting techniques.
  arXiv  Detail & Related papers  (2024-10-29T06:38:46Z)
• Disentangling Logic: The Role of Context in Large Language Model Reasoning Capabilities [31.728976421529577]
  We investigate the contrast across abstract and contextualized logical problems from a comprehensive set of domains. We focus on standard propositional logic, specifically propositional deductive and abductive logic reasoning. Our experiments aim to provide insights into disentangling context in logical reasoning and the true reasoning capabilities of LLMs.
  arXiv  Detail & Related papers  (2024-06-04T21:25:06Z)
• LogicBench: Towards Systematic Evaluation of Logical Reasoning Ability of Large Language Models [52.03659714625452]
  Recently developed large language models (LLMs) have been shown to perform remarkably well on a wide range of language understanding tasks. But, can they really "reason" over the natural language? This question has been receiving significant research attention and many reasoning skills such as commonsense, numerical, and qualitative have been studied.
  arXiv  Detail & Related papers  (2024-04-23T21:08:49Z)
• Language Models can be Logical Solvers [99.40649402395725]
  We introduce LoGiPT, a novel language model that directly emulates the reasoning processes of logical solvers. LoGiPT is fine-tuned on a newly constructed instruction-tuning dataset derived from revealing and refining the invisible reasoning process of deductive solvers.
  arXiv  Detail & Related papers  (2023-11-10T16:23:50Z)
• Towards LogiGLUE: A Brief Survey and A Benchmark for Analyzing Logical Reasoning Capabilities of Language Models [56.34029644009297]
  Large language models (LLMs) have demonstrated the ability to overcome various limitations of formal Knowledge Representation (KR) systems. LLMs excel most in abductive reasoning, followed by deductive reasoning, while they are least effective at inductive reasoning. We study single-task training, multi-task training, and "chain-of-thought" knowledge distillation fine-tuning technique to assess the performance of model.
  arXiv  Detail & Related papers  (2023-10-02T01:00:50Z)
• Modeling Hierarchical Reasoning Chains by Linking Discourse Units and Key Phrases for Reading Comprehension [80.99865844249106]
  We propose a holistic graph network (HGN) which deals with context at both discourse level and word level, as the basis for logical reasoning. Specifically, node-level and type-level relations, which can be interpreted as bridges in the reasoning process, are modeled by a hierarchical interaction mechanism.
  arXiv  Detail & Related papers  (2023-06-21T07:34:27Z)
• Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning [101.26814728062065]
  Large Language Models (LLMs) have shown human-like reasoning abilities but still struggle with complex logical problems. This paper introduces a novel framework, Logic-LM, which integrates LLMs with symbolic solvers to improve logical problem-solving.
  arXiv  Detail & Related papers  (2023-05-20T22:25:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.