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In such cases, the useful response may involve asking for the missing premise, conditioning the answer on the unknown quantity, or abstaining when no informative conditional response exists. The work introduces Ask-Condition-Abstain Reinforcement Learning (ACA-RL), a data-augmented framework that builds missing-premise training instances via a reasoning-graph-guided pipeline and learns with structured reward across five response behaviors. It also presents the Missing-Premise Benchmark (MPB).",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/ask-condition-or-abstain-reinforcement-learning-for-missing-premise-reasoning/273479/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/ask-condition-or-abstain-reinforcement-learning-for-missing-premise-reasoning/273479.png","ImageObject",300,407,{"name":92,"@type":93},"Emma Wilson","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",16,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What problem does missing-premise reasoning address?","Question",{"text":113,"@type":114},"It addresses queries that resemble standard reasoning tasks but omit information needed to determine a unique answer. In these cases, a model should ask for missing premises, condition its answer, or abstain rather than guess.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does ACA-RL create training data for missing-premise reasoning?",{"text":118,"@type":114},"ACA-RL uses a reasoning-graph-guided pipeline to decompose well-posed problems, perturb critical premises, and generate missing-premise training instances with localized gap annotations.",{"name":120,"@type":111,"acceptedAnswer":121},"What is the Missing-Premise Benchmark (MPB)?",{"text":122,"@type":114},"MPB is a 274-instance human-verified benchmark covering mathematical, logical, and real-world word problems. It evaluates responses using a five-category taxonomy and an averaged Behavior Score aligned to behaviors such as asking, conditioning, and abstaining.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},273479,1789471628,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145,"preview_page_count":4},3848291630094,"https://eur-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","arXiv : 2608 . 16554v2 [cs .CL] 24 Aug 2026  \nAugust 25, 2026  \nAsk, Condition or Abstain: Reinforcement Learning for Missing-Premise Reasoning  \nYongqi Tong1* Zhenyu Zhang1* Zimi Liu4 Kewei Fu1 Mingli Song2 Haofei Zhang2 Junshao Zhang3 Hong Zhu3 Jiang-Ming Yang1 Xin Zhang1 Jianshe Li1  \n1Ant International 2Zhejiang University 3Dingtalk, Alibaba Group 4Ant Group  \nCorrespondence: [tongyongqi.yq@ant-intl.com](tongyongqi.yq@ant-intl.com)  \n Benchmark  \nAbstract  \nAnswer-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 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 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.  \nKeywords: reinforcement learning, missing-premise reasoning, abstention, uncertainty, evaluation  \n1 Introduction  \nModern reasoning models are increasingly optimized by reinforcement learning on problems with verifiable final answers. This setting is productive because the reward is clear: solve the problem and match the expected answer. It is also incomplete. A user can omit a rate, leave a relation ambiguous, narrow a definition outside its usable domain, or ask for a value that cannot be identified from the stated premises. In those cases, a model rewarded primarily for definite answers may still produce a confident solution even when the question no longer determines one [Kalai et al., 2025, Ouyang, 2025, Sun et al., 2024] .  \nThe failure mode isnot solved by replacing every uncertain response with “I don’t know.” Abstention is safer than hallucination, but it is often less helpful than explaining the missing variable, giving a conditional expression, or asking the user for the needed premise. We study this response space as a missing-premise reasoning problem: given a query that looks like a standard reasoning problem but lacks information required for a unique answer, the model should decide whether to ask, condition, or abstain instead  \nof fabricating a value.  \nThis framing separates our goal from retrieval and inference-time screening. Retrieval can supply external facts but does not teach the base model to notice underdetermined prompts; screen-then-answer prompting can flag missing premises but depends on an extra inference-time step. We instead learn the missing-premise response policy within the model itself. Our comparison with LM Introspection shows that prompting alone is insufficient for making a model reliably ask, condition, or abstain under missing premises.  \nWe propose Ask-Condition-Abstain Reinforcement Learning (ACA-RL), a data-augmented RL framework for learning missing-premise response policies. ACA-RL first uses our reasoning-graph-guided pipeline to decompose well-posed problems, perturb critical premises, and create 120K natural missing-premise training instances with localized gap annotations. It then optimizes a structured reward over five behaviors: silent h","cbCaibPCml063Xpz","https://ap.wps.com/l/cbCaibPCml063Xpz","pdf",3430824,15,"English","# Abstract\n# 1 Introduction\n## Missing-premise reasoning motivation\n## ACA-RL framework\n## Missing-Premise Benchmark (MPB)\n## Experiments and results","[{\"question\":\"What problem does missing-premise reasoning address?\",\"answer\":\"It addresses queries that resemble standard reasoning tasks but omit information needed to determine a unique answer. In these cases, a model should ask for missing premises, condition its answer, or abstain rather than guess.\"},{\"question\":\"How does ACA-RL create training data for missing-premise reasoning?\",\"answer\":\"ACA-RL uses a reasoning-graph-guided pipeline to decompose well-posed problems, perturb critical premises, and generate missing-premise training instances with localized gap annotations.\"},{\"question\":\"What is the Missing-Premise Benchmark (MPB)?\",\"answer\":\"MPB is a 274-instance human-verified benchmark covering mathematical, logical, and real-world word problems. It evaluates responses using a five-category taxonomy and an averaged Behavior Score aligned to behaviors such as asking, conditioning, and abstaining.\"}]","Ask, Condition or Abstain - Reinforcement Learning for Missing-Premise Reasoning | PDF",38]