RMath: A Logic Reasoning-Focused Datasets Toward Mathematical Multistep Reasoning Tasks

Mathematical reasoning ability objectively reflects a language model's understanding of implicit knowledge in contexts, with logic being a prerequisite for exploring, articulating and establishing effective reasoning. Large language models (LLMs) have shown great potential in complex reasoning tasks represented by mathematical reasoning. However, existing mathematical datasets either focus on commonsense reasoning, assessing the model's knowledge application ability, or arithmetic problems with fixed calculation rules, evaluating the model's rapid learning capability. There is a lack of datasets that require solving problems solely through logical reasoning. As a result, the performance of LLMs in accurately understanding the implicit logical relationships in problems and deriving conclusions based solely on given conditions is hindered. To address this challenge, we construct a dataset specifically for multiple step reasoning tasks: Reasoning-Math (RMath). This dataset focuses on evaluating logical reasoning abilities with mathematical reasoning problems, covering typical problem types, including direct reasoning problems, hypothetical reasoning problems, and nested reasoning problems. Additionally, we design a standardized annotation scheme that transforms natural language descriptions of conditions into formal propositions. Other annotation contents include problem categories, proposition truth values, and proposition relationship types. This not only reduces biases caused by semantic misunderstandings during problem-solving, but also facilitates the incorporation of theoretically grounded logical reasoning methods to enhance reasoning abilities. Furthermore, we propose a normalization problem-solving framework based on propositional logic for RMath and design the problem-solving process for prompt tuning to guide LLMs to absorb mathematical logical theories and improving reasoning abilities. Finally, we evaluate RMath on several popular LLMs and present the corresponding results.