aiqbench analysis
This research addresses a critical bottleneck in LLMs by introducing DREAM, a self-adaptive framework that improves multi-step first-order logic theorem proving through strategy diversification and error feedback. By leveraging an axiom-driven approach and sub-proposition correction mechanisms, the method significantly enhances accuracy on complex mathematical deductions where current models often fail early. The work also contributes a curated dataset of 447 Lean 4 formatted theorems to standardize future evaluation in formal reasoning tasks.
Towards Advanced Mathematical Reasoning for LLMs via First-Order Logic Theorem Proving
arXiv:2506.17104v2 Announce Type: replace-cross Abstract: Large language models (LLMs) have shown promising first-order logic (FOL) reasoning capabilities with applications in various areas. However, their effectiveness in complex mathematical reasoning involving multi-step FOL deductions is still under-researched. While LLMs perform competitively on established mathematical reasoning benchmarks, they struggle with multi-step FOL tasks, as demonstrated by Deepseek-Prover-V2-7B's low accuracy (4.2%) on our proposed theorem proving dataset. This issue arises from the limited exploration of diverse proof strategies and the potential for early reasoning mistakes to undermine entire proofs. To address these issues, we propose DREAM, a self-adaptive solution that enhances the Diversity and REAsonability of LLMs' generation strategies. DREAM incorporates an Axiom-Driven Strategy Diversification mechanism to promote varied strategic outcomes and a Sub-Proposition Error Feedback to help LLMs reflect on and correct their proofs. Our contributions include pioneering advancements in LLMs' mathematical reasoning through FOL theorem proving, introducing a novel inference stage solution that improves performance by 0.6% to 6.4%, and providing a curated dataset of 447 mathematical theorems in Lean 4 format for evaluation.
Abstract:Large language models (LLMs) have shown promising first-order logic (FOL) reasoning capabilities with applications in various areas. However, their effectiveness in complex mathematical reasoning involving multi-step FOL deductions is still under-researched. While LLMs perform competitively on established mathematical reasoning benchmarks, they struggle with multi-step FOL tasks, as demonstrated by Deepseek-Prover-V2-7B's low accuracy (4.2%) on our proposed theorem proving dataset. This issue arises from the limited exploration of diverse proof strategies and the potential for early reasoning mistakes to undermine entire proofs. To address these issues, we propose DREAM, a self-adaptive solution that enhances the Diversity and REAsonability of LLMs' generation strategies. DREAM incorporates an Axiom-Driven Strategy Diversification mechanism to promote varied strategic outcomes and a Sub-Proposition Error Feedback to help LLMs reflect on and correct their proofs. Our contributions include pioneering advancements in LLMs' mathematical reasoning through FOL theorem proving, introducing a novel inference stage solution that improves performance by 0.6% to 6.4%, and providing a curated dataset of 447 mathematical theorems in Lean 4 format for evaluation.
Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Logic in Computer Science (cs.LO)
arXiv:2506.17104 [cs.AI]
(or arXiv:2506.17104v2 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2506.17104 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 269 words