Recent advancements in large language models have showcased their remarkable generalizability across various domains. However, their reasoning abilities still have significant room for improvement, especially when confronted with scenarios requiring multi-step reasoning. Although large language models possess extensive knowledge, their reasoning often fails to effectively utilize this knowledge to establish a coherent thinking paradigm. These models sometimes show hallucinations as their reasoning procedures are unconstrained by logical principles. Aiming at improving the zero-shot chain-of-thought reasoning ability of large language models, we propose LoT (Logical Thoughts), a self-improvement prompting framework that leverages principles rooted in symbolic logic, particularly Reductio ad Absurdum, to systematically verify and rectify the reasoning processes step by step. Experimental evaluations conducted on language tasks in diverse domains, including arithmetic, commonsense, symbolic, causal inference, and social problems, demonstrate the efficacy of enhanced reasoning by logic. The implementation code for LoT can be accessed at: https://github.com/xf-zhao/LoT.