AS-NMRer: Improving Autoformalization for Non-monotonic Reasoning via Abstraction, Search, and Fine-tuning

ACL ARR 2026 January Submission7317 Authors

Keywords: Neuro-symbolic framework, Non-monotonic Reasoning, Autoformalization

Abstract: LLMs often struggle with complex logical reasoning, particularly in non-monotonic reasoning (NMR), where conclusions may be withdrawn in light of new evidence. While autoformalization-based neuro-symbolic frameworks offer a promising solution by translating text into logic programs, they often fail to handle ambiguity and noise present in realistic linguistic contexts. To address these challenges, we propose AS-NMRer, a framework that enhances autoformalization through abstraction, search, and fine-tuning. First, we introduce an abstraction module to extract atomic facts and rules from noisy contexts. Next, a step-wise Best-of-N search algorithm incrementally maps these facts and rules into logic programs with dual verification ensuring both syntactic correctness and semantic fidelity. Finally, we design an expert iteration loop that leverages solver-verified examples to fine-tune the model, enabling iterative self-improvement. Extensive experiments on four NMR benchmarks show that AS-NMRer significantly outperforms competitive baselines. AS-NMRer with gemma3-27B improves the F1 score by 7\% over the prompt-based DeepSeek-V3.2-671B on the challenging LogicBench.

Paper Type: Long

Research Area: Mathematical, Symbolic, Neurosymbolic, and Logical Reasoning

Research Area Keywords: neurosymbolic reasoning, logical reasoning

Contribution Types: Approaches to low-resource settings

Languages Studied: English

Submission Number: 7317