# SymbolLKG: Towards Verifiable Logical Reasoning via Logical Knowledge Graph and Symbolic Solvers

arXiv: https://arxiv.org/abs/2608.26836 · HTML: https://mlsanity.com/paper/2608.26836/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 42 of its 52 references that are in the map.
- First posted on arXiv 27 Aug 2026.

## Placed in

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

## Builds on (most cited first, 30 of 42)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [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)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [REALM: Retrieval-Augmented Language Model Pre-Training](https://mlsanity.com/paper/2002.08909/) (2020)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [From Local to Global: A Graph RAG Approach to Query-Focused Summarization](https://mlsanity.com/paper/2404.16130/) (2024)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Unsupervised Dense Information Retrieval with Contrastive Learning](https://mlsanity.com/paper/2112.09118/) (2021)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks](https://mlsanity.com/paper/2211.12588/) (2022)
- [M3-Embedding: Multi-Linguality, Multi-Functionality, Multi-Granularity Text Embeddings Through Self-Knowledge Distillation](https://mlsanity.com/paper/2402.03216/) (2024)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [BloombergGPT: A Large Language Model for Finance](https://mlsanity.com/paper/2303.17564/) (2023)
- [Interleaving Retrieval with Chain-of-Thought Reasoning for Knowledge-Intensive Multi-Step Questions](https://mlsanity.com/paper/2212.10509/) (2022)
- [MuSiQue: Multihop Questions via Single-hop Question Composition](https://mlsanity.com/paper/2108.00573/) (2021)
- [Show Your Work: Scratchpads for Intermediate Computation with Language Models](https://mlsanity.com/paper/2112.00114/) (2021)
- [Unifying Large Language Models and Knowledge Graphs: A Roadmap](https://mlsanity.com/paper/2306.08302/) (2023)
- [PAL: Program-aided Language Models](https://mlsanity.com/paper/2211.10435/) (2022)
- [A Survey on Knowledge Graphs: Representation, Acquisition and Applications](https://mlsanity.com/paper/2002.00388/) (2020)
- [Knowledge Graphs](https://mlsanity.com/paper/2003.02320/) (2020)
- [RAPTOR: Recursive Abstractive Processing for Tree-Organized Retrieval](https://mlsanity.com/paper/2401.18059/) (2024)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [Large Dual Encoders Are Generalizable Retrievers](https://mlsanity.com/paper/2112.07899/) (2021)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [StructGPT: A General Framework for Large Language Model to Reason over Structured Data](https://mlsanity.com/paper/2305.09645/) (2023)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [Selection-Inference: Exploiting Large Language Models for Interpretable Logical Reasoning](https://mlsanity.com/paper/2205.09712/) (2022)

## Abstract (arXiv)

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.