  Language serves as a vehicle for conveying thought, enabling communication
among individuals. The ability to distinguish between diverse concepts,
identify fairness and injustice, and comprehend a range of legal notions
fundamentally relies on logical reasoning. Large Language Models (LLMs) attempt
to emulate human language understanding and generation, but their competency in
logical reasoning remains limited. This paper seeks to address the
philosophical question: How can we effectively teach logical reasoning to LLMs
while maintaining a deep understanding of the intricate relationship between
language and logic? By focusing on bolstering LLMs' capabilities in logical
reasoning, we aim to expand their applicability in law and other
logic-intensive disciplines. To this end, we propose a Reinforcement Learning
from Logical Feedback (RLLF) approach, which serves as a potential framework
for refining LLMs' reasoning capacities. Through RLLF and a revised evaluation
methodology, we explore new avenues for research in this domain and contribute
to the development of LLMs capable of handling complex legal reasoning tasks
while acknowledging the fundamental connection between language and logic.
