测试大模型在逻辑查询下的一致性，发现其易出错且可改进。

In recent years, large language models (LLMs) have demonstrated significant success in performing varied natural language tasks such as language translation, question-answering, summarizing, fact-checking, etc. Despite LLMs' impressive ability to generate human-like texts, LLMs are infamous for their inconsistent responses - a meaning-preserving change in the input query results in an inconsistent response and attributes to vulnerabilities of LLMs such as hallucination. Consequently, existing research focuses on simple paraphrasing-based consistency assessment of LLMs, and ignores complex queries that necessitate an even better understanding of logical reasoning by an LLM. Our work therefore addresses the logical inconsistency of LLMs under complex logical queries with primitive logical operators, e.g., negation, conjunction, and disjunction. As a test bed, we consider retrieval-augmented LLMs on a fact-checking task involving propositional logic queries from knowledge graphs (KGs). Our contributions are threefold. Benchmark: We introduce three logical fact-checking datasets over KGs for community development towards logically consistent LLMs. Assessment: We propose consistency measures of LLMs on propositional logic queries and demonstrate that existing LLMs lack logical consistency, especially on complex queries. Improvement: We employ supervised fine-tuning to improve the logical consistency of LLMs on the complex fact-checking task with KG contexts. We have made our source code and benchmarks available.