LogiNumSynth: Synthesizing Joint Logical-Numerical Reasoning Problems for Language Models

• URL: http://arxiv.org/abs/2510.11031v1
• Date: Mon, 13 Oct 2025 06:01:02 GMT
• Title: LogiNumSynth: Synthesizing Joint Logical-Numerical Reasoning Problems for Language Models
• Authors: Yiwei Liu, Yucheng Li, Xiao Li, Gong Cheng,
• Abstract summary: LogiNum Synth is a natural language problem synthesizer that synthesizes tasks requiring proficiency in joint logical reasoning.<n>It supports fine-grained control over reasoning world richness, logical reasoning depth, and the complexity of numerical computations.<n>It can serve as both a diagnostic tool and a source of targeted supervision for advancing integrated reasoning skills.
• Score: 14.833385574931855
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Joint logical-numerical reasoning remains a major challenge for language models, yet existing datasets rely on fixed rule sets and offer limited control over task complexity, constraining their generalizability for evaluation and training. We present LogiNumSynth, a flexible natural language problem synthesizer that synthesizes tasks requiring proficiency in joint logical reasoning (e.g., rule-based reasoning) and numerical reasoning (e.g., arithmetic computation). LogiNumSynth supports fine-grained control over reasoning world richness, logical reasoning depth, and the complexity of numerical computations, enabling flexible data synthesis across difficulty levels. We demonstrate three key contributions: (1) Synthesizer -- synthesizing fully controllable joint reasoning tasks over natural language; (2) Evaluation & Process Analysis -- evaluating both process accuracy and answer accuracy; (3) Targeted Training -- using synthesized data to enhance LLMs' reasoning performance. Experiments with multiple LLMs highlight persistent weaknesses in logical-numerical reasoning, showing that LogiNumSynth can serve as both a diagnostic tool and a source of targeted supervision for advancing integrated reasoning skills.

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