LogicSR: A Unified Benchmark for Logical Discovery from Data

Discovering underlying logical expressions from data is a critical task for interpretable AI and scientific discovery, yet it remains poorly served by existing research infrastructure. The field of Symbolic Regression (SR) primarily focuses on continuous mathematical functions, while Logic Synthesis (LS) is designed for exact, noise-free specifications, not for learning from incomplete or noisy data. This leaves a crucial gap for evaluating algorithms that can learn generalizable logical rules in realistic scenarios. To address this, we introduce LogicSR, a large-scale and comprehensive benchmark for logical symbolic regression. LogicSR is built from two sources: real-world problems from digital circuits and biological networks, and a novel synthetic data generator capable of producing a diverse set of complex logical formulas at scale. We use LogicSR to conduct a rigorous evaluation of 17 algorithms, spanning classical logic solvers, modern machine learning models, and Large Language Models (LLMs). Our findings reveal that the logical modeling capabilities and generalization robustness of these algorithms significantly depend on task scale and logical complexity, with current cutting-edge LLMs showing limited complex logical reasoning ability. LogicSR provides a robust foundation to benchmark progress, unify evaluation across disparate fields, and steer the future development of powerful neuro-symbolic systems.