In this paper, we propose a new data synthesis method called LogicPro, which leverages LeetCode-style algorithm Problems and their corresponding Program solutions to synthesize Complex Logical Reasoning data in text format. First, we synthesize complex reasoning problems through source algorithm problems and test cases. Then, standard answers and intermediate variable outputs are obtained for each problem based on standard python solutions and test cases. Finally, with the guidance of code intermediate variables, we synthesize the text reasoning process for each reasoning problems. Through this method, we can synthesize data that is difficult, scalable, effective, and comes with golden standard answers and high-quality reasoning processes. As a result, with our 540K synthesized dataset constructed solely from 2,360 algorithm problems, our approach achieves significant improvements in multiple models for the datasets BBH^27, LogicBench, DROP, AR-LSAT, and GSM8K, etc. outperforming a wide range of existing reasoning datasets.

Large Language Models (LLMs) have been shown to achieve breakthrough performances on complex logical reasoning tasks. Nevertheless, most existing research focuses on employing formal language to guide LLMs for deriving reliable reasoning paths, with systematic evaluations of these capabilities still being limited. In this paper, we aim to conduct a comprehensive evaluation of LLMs across various logical reasoning problems utilizing formal languages. From the perspective of three dimensions, i.e., spectrum of LLMs, taxonomy of tasks, and format of trajectories, our key findings are: 1) Thinking models significantly outperform Instruct models, especially when formal language is employed; 2). All LLMs exhibit limitations in inductive reasoning capability, irrespective of whether they use a formal language; 3). Data with PoT format achieves the best generalization performance across other languages. Additionally, we also curate the formal-relative training data to further enhance the small language models, and the experimental results indicate that a simple rejected fine-tuning method can better enable LLMs to generalize across formal languages and achieve the best overall performance.

Ensuring both interpretability and correctness is a great challenge in automated geometry problem solving (GPS), and the scarcity of labeled data hinders learning mathematical reasoning from samples. Therefore, we present GeoDRL, a self-learning geometry problem solving framework that integrates logic graph deduction and Deep Reinforcement Learning (DRL) to optimize geometry reasoning as a Markov Decision Process. GeoDRL employs a Graph Neural Network on a Geometry Logic Graph, updating the problem state using a symbolic system. Incorporating DRL into deductive reasoning enables GeoDRL to achieve unsupervised self-learning while maintaining correctness. GeoDRL, through unsupervised learning, exhibits enhanced accuracy in the Geometry3K dataset, improving by 11.1% over previous SOTA methods, and simultaneously boosts efficiency and interpretability.