PrefRAG: Correcting Semantic Errors in Auto-Formalization for Logical Reasoning with Program Preference RAG

ACL ARR 2026 January Submission7352 Authors

Keywords: Logical reasoning, LLMs, Neurosymbolic Reasoning, Auto-formalization, Retrieval-Augmented Generation

Abstract:

Recent advances in large language models (LLMs) have spurred interest in neuro‑symbolic methods for logical reasoning based on auto‑formalization, where LLMs first formalize problems into symbolic programs, then symbolic solvers perform reasoning over these programs.
However, existing auto-formalization methods remain prone to both syntactic and semantic errors.
Specifically, the absence of a program‑level semantic verification mechanism leaves semantic errors largely unaddressed.
In this paper, we propose a novel approach to semantic error correction via program preference RAG.
First, we conduct an in-depth analysis of semantic error patterns, and then automatically synthesize $\textbf{SemanticPref}$, a program preference dataset to model these patterns. Utilizing the dataset as knowledge base, we introduce $\textbf{PrefRAG}$, a general retrieval‑augmented generation framework for refinement in auto-formalization, which enables LLMs to detect and repair both syntactic and semantic errors.
Extensive evaluations across both in‑distribution (AR‑LSAT and FOLIO) and out‑of‑distribution benchmarks show that PrefRAG consistently outperforms strong baselines, achieving an average improvement of 2.39\% on ID and 6.23\% on OOD datasets.

Paper Type: Long

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

Research Area Keywords: neurosymbolic reasoning, logical reasoning

Contribution Types: NLP engineering experiment, Publicly available software and/or pre-trained models, Data resources

Languages Studied: English

Submission Number: 7352