From Language to Logic: A Bi-Level Framework for Structured Reasoning

Abstract

Structured reasoning over natural language inputs remains a core challenge in artificial intelligence, as it requires bridging the gap between unstructured linguistic expressions and formal logical representations. In this paper, we propose a novel \textbf{bi-level framework} that maps language to logic through a two-stage process: high-level task abstraction and low-level logic generation. At the upper level, a large language model (LLM) parses natural language queries into intermediate structured representations specifying the problem type, objectives, decision variables, and symbolic constraints. At the lower level, the LLM uses these representations to generate symbolic workflows or executable reasoning programs for accurate and interpretable decision making. The framework supports modular reasoning, enforces explicit constraints, and generalizes across domains such as mathematical problem solving, question answering, and logical inference. We further optimize the framework with an end-to-end {bi-level} optimization approach that jointly refines both the high-level abstraction and low-level logic generation stages. Experiments on multiple realistic reasoning benchmarks demonstrate that our approach significantly outperforms existing baselines in accuracy, with accuracy gains reaching as high as 40\%. Moreover, the bi-level design enhances transparency and error traceability, offering a promising step toward trustworthy and systematic reasoning with LLMs.