Ask, Condition or Abstain: Reinforcement Learning for Missing-Premise Reasoning

• URL: http://arxiv.org/abs/2608.16554v2
• Date: Mon, 24 Aug 2026 04:59:14 GMT
• Title: Ask, Condition or Abstain: Reinforcement Learning for Missing-Premise Reasoning
• Abstract summary: We present emphAsk-Condition-Abstain Reinforcement Learning (ACA-RL), a data-augmented RL framework for this setting.<n>Its reasoning-graph-guided pipeline converts well-posed problems into missing-premise training instances with localized gap annotations.<n>We also introduce the emphMissing-Premise Benchmark (MPB), a 274-instance human-verified benchmark spanning mathematical, logical, and real-world word problems.
• Score: 44.87905259927536
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Answer-only reinforcement learning (RL) trains reasoning models to solve fully specified problems, but many realistic queries omit a premise needed for a unique answer. In this setting, the useful response is not always refusal: the model should ask for the missing premise, condition its answer on the unknown quantity, or abstain when no informative conditional response is available. We present \emph{Ask-Condition-Abstain Reinforcement Learning} (ACA-RL), a data-augmented RL framework for this setting. Its reasoning-graph-guided pipeline converts well-posed problems into missing-premise training instances with localized gap annotations; ACA-RL then trains on these instances with a structured reward over five observable response behaviors. We also introduce the \emph{Missing-Premise Benchmark} (MPB), a 274-instance human-verified benchmark spanning mathematical, logical, and real-world word problems. Across Qwen3 and Llama models, ACA-RL consistently improves on MPB while preserving competitive performance on well-posed reasoning tasks. Together with the released code, MPB, and training data, this work supports a new mission for NLP evaluation: measuring whether models can recognize when a task is underdetermined and handle uncertainty, not only whether they can answer fully specified questions.

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