In the context of large language models (LLMs), current advanced reasoning methods have made impressive strides in various reasoning tasks. However, when it comes to logical reasoning tasks, significant challenges remain in both efficacy and efficiency. This is rooted in the fact that these systems fail to fully leverage the inherent structure of logical tasks throughout the reasoning processes, including decomposition, search, and resolution. To address this, this paper proposes a logic-complete reasoning framework, Aristotle. The framework consists of three key components: Logical Decomposer, Logical Search Router, and Logical Resolver, in which symbolic expressions and logical rules are comprehensively integrated into the entire reasoning process, significantly alleviating the bottlenecks of logical reasoning, i.e., reducing sub-task complexity, minimizing search errors, and resolving logical contradictions. Experimental results demonstrate that Aristotle consistently outperforms state-of-the-art reasoning frameworks in both accuracy and efficiency, particularly excelling in complex logical reasoning scenarios.

While the recent Chain-of-Thought (CoT) technique enhances the reasoning ability of large language models (LLMs) with the theory of mind, it might still struggle in handling logical reasoning that relies much on symbolic expressions and rigid deducing rules. To strengthen the logical reasoning capability of LLMs, we propose a novel Symbolic Chain-of-Thought, namely SymbCoT, a fully LLM-based framework that integrates symbolic expressions and logic rules with CoT prompting. Technically, building upon an LLM, SymbCoT 1) first translates the natural language context into the symbolic format, and then 2) derives a step-by-step plan to solve the problem with symbolic logical rules, 3) followed by a verifier to check the translation and reasoning chain. Via thorough evaluations on 5 standard datasets with both First-Order Logic and Constraint Optimization symbolic expressions, SymbCoT shows striking improvements over the CoT method consistently, meanwhile refreshing the current state-of-the-art performances. We further demonstrate that our system advances in more faithful, flexible, and explainable logical reasoning. To our knowledge, this is the first attempt at combining symbolic expressions and rules into CoT for logical reasoning with LLMs. Code is open at https://github.com/Aiden0526/SymbCoT.