  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.
