Large language models (LLMs) have transformed the landscape of language processing, yet struggle with significant challenges in terms of security, privacy, and the generation of seemingly coherent but factually inaccurate outputs, commonly referred to as hallucinations. Among these challenges, one particularly pressing issue is Fact-Conflicting Hallucination (FCH), where LLMs generate content that directly contradicts established facts. Tackling FCH poses a formidable task due to two primary obstacles: Firstly, automating the construction and updating of benchmark datasets is challenging, as current methods rely on static benchmarks that don't cover the diverse range of FCH scenarios. Secondly, validating LLM outputs' reasoning process is inherently complex, especially with intricate logical relations involved. In addressing these obstacles, we propose an innovative approach leveraging logic programming to enhance metamorphic testing for detecting Fact-Conflicting Hallucinations (FCH). Our method gathers data from sources like Wikipedia, expands it with logical reasoning to create diverse test cases, assesses LLMs through structured prompts, and validates their coherence using semantic-aware assessment mechanisms. Our method generates test cases and detects hallucinations across six different LLMs spanning nine domains, revealing hallucination rates ranging from 24.7% to 59.8%. Key observations indicate that LLMs encounter challenges, particularly with temporal concepts, handling out-of-distribution knowledge, and exhibiting deficiencies in logical reasoning capabilities. The outcomes underscore the efficacy of logic-based test cases generated by our tool in both triggering and identifying hallucinations. These findings underscore the imperative for ongoing collaborative endeavors within the community to detect and address LLM hallucinations.