From Indeterminacy to Determinacy: Augmenting Logical Reasoning
  Capabilities with Large Language Models
Hongda Sun Weikai Xu Wei Liu Jian Luan Bin Wang Shuo Shang Ji-Rong Wen Rui Yan
Recent advances in LLMs have revolutionized the landscape of reasoning tasks.
To enhance the capabilities of LLMs to emulate human reasoning, prior works
focus on modeling reasoning steps using specific thought structures like
chains, trees, or graphs. However, LLM-based reasoning continues to encounter
three challenges: 1) Selecting appropriate reasoning structures for various
tasks; 2) Exploiting known conditions sufficiently and efficiently to deduce
new insights; 3) Considering the impact of historical reasoning experience. To
address these challenges, we propose DetermLR, a novel reasoning framework that
formulates the reasoning process as a transformational journey from
indeterminate premises to determinate ones. This process is marked by the
incremental accumulation of determinate premises, making the conclusion
progressively closer to clarity. DetermLR includes three essential components:
1) Premise identification: We categorize premises into two distinct types:
determinate and indeterminate. This empowers LLMs to customize reasoning
structures to match the specific task complexities. 2) Premise prioritization
and exploration: We leverage quantitative measurements to assess the relevance
of each premise to the target, prioritizing more relevant premises for
exploring new insights. 3) Iterative process with reasoning memory: We
introduce a reasoning memory module to automate storage and extraction of
available premises and reasoning paths, preserving historical reasoning details
for more accurate premise prioritization. Comprehensive experimental results
show that DetermLR outperforms all baselines on four challenging logical
reasoning tasks: LogiQA, ProofWriter, FOLIO, and LogicalDeduction. DetermLR can
achieve better reasoning performance while requiring fewer visited states,
highlighting its superior efficiency and effectiveness in tackling logical
reasoning tasks.