Large Language Models (LLMs) excel at natural language understanding, yet they struggle with strict multi‑step reasoning, often producing hallucinations and inconsistencies. Conventional Chain‑of‑Thought (CoT) lacks rigorous verification, and standard Retrieval‑Augmented Generation (RAG) usually overlooks the structural dependencies inherent in logical tasks. To address this gap, we introduce a neuro‑symbolic architecture called SymbolLKG, which consists of a Logical Knowledge Graph (LKG) and a dynamic Logic Router.
Logical Knowledge Graph is ontology‑driven: logical rules and constraints are treated as first‑class topological nodes. Each node stores predicates, premises, conclusions, and other attributes, while edges capture dependency or constraint propagation between rules. This yields a queryable, structured semantic network extracted directly from text.
Logic Router dynamically dispatches reasoning requests to the most suitable symbolic engine (e.g., SAT solver, SMT solver, or a custom logical calculus). The routing relies on a topology‑aware hybrid retrieval mechanism: relevant sub‑graphs are first located in the LKG, then vector‑based retrieval fetches matching rule instances, and finally a scheduling instruction is sent to the chosen symbolic solver.
We evaluate SymbolLKG on several logical reasoning benchmarks such as LogicalDeduction and ProofWriter. The framework outperforms state‑of‑the‑art CoT prompting and vanilla RAG baselines by 8%‑12% in accuracy and, importantly, produces complete, verifiable reasoning traces for auditability.
Blogger's Review: By making logical structure explicit and coupling it with symbolic solvers, this work achieves both interpretability and verifiability for LLM reasoning. It offers a practical blueprint for future neuro‑symbolic systems and is definitely worth following.