  Large Language Models (LLMs) have achieved remarkable performance across a
wide variety of natural language tasks. However, they have been shown to suffer
from a critical limitation pertinent to 'hallucination' in their output. Recent
research has focused on investigating and addressing this problem for a variety
of tasks such as biography generation, question answering, abstractive
summarization, and dialogue generation. However, the crucial aspect pertaining
to 'negation' has remained considerably underexplored. Negation is important
because it adds depth and nuance to the understanding of language and is also
crucial for logical reasoning and inference. In this work, we address the above
limitation and particularly focus on studying the impact of negation in LLM
hallucinations. Specifically, we study four tasks with negation: 'false premise
completion', 'constrained fact generation', 'multiple choice question
answering', and 'fact generation'. We show that open-source state-of-the-art
LLMs such as LLaMA-2-chat, Vicuna, and Orca-2 hallucinate considerably on all
these tasks involving negation which underlines a critical shortcoming of these
models. Addressing this problem, we further study numerous strategies to
mitigate these hallucinations and demonstrate their impact.
