  Extensive studies have been devoted to privatizing general-domain Large
Language Models (LLMs) as Domain-Specific LLMs via feeding specific-domain
data. However, these privatization efforts often ignored a critical aspect:
Dual Logic Ability, which is a core reasoning ability for LLMs. The dual logic
ability of LLMs ensures that they can maintain a consistent stance when
confronted with both positive and negative statements about the same fact. Our
study focuses on how the dual logic ability of LLMs is affected during the
privatization process in the medical domain. We conduct several experiments to
analyze the dual logic ability of LLMs by examining the consistency of the
stance in responses to paired questions about the same fact. In our
experiments, interestingly, we observed a significant decrease in the dual
logic ability of existing LLMs after privatization. Besides, our results
indicate that incorporating general domain dual logic data into LLMs not only
enhances LLMs' dual logic ability but also further improves their accuracy.
These findings underscore the importance of prioritizing LLMs' dual logic
ability during the privatization process. Our study establishes a benchmark for
future research aimed at exploring LLMs' dual logic ability during the
privatization process and offers valuable guidance for privatization efforts in
real-world applications.
