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The question is a region: A neurosymbolic retrofit for categorical question answering over rule engines

By Liana Hadarean, Tancrède Lepoint, Martin Schäf, Willem Visser
2026
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Many consequential decisions, from tax liability and travel reimbursement to benefit eligibility and building-code compliance, are governed by rule engines that map a fully specified set of typed input variables to a finite set of output categories. To retrofit these engines for agentic or chatbot settings, we must relax the requirement of a complete input: users rarely ask about one fully specified case. They ask about regions of the input space, leaving variables under-specified that they do not yet know or do not consider relevant. Neither a language model nor a symbolic enumeration answers regional questions completely on its own. A language model gives no completeness guarantee, and the gap widens as the decision space grows. A symbolic enumeration finds every path, but a large partition cannot be summarized faithfully. Our method resolves both: we enumerate the paths symbolically, and when the partition is too large to state faithfully, we ask the one follow-up question that removes the most cases. We prove the partition complete by reconstructing the engine's own path constraints in an SMT solver, so completeness is a checked theorem rather than a claim about the path enumerator, and the budget keeps the presented answer small and its verification cheap. The result is a natural conversational interface: instead of an overwhelming partition, the user gets a meaningful follow-up that drives the dialog to a complete answer. We demonstrate the approach by retrofitting Catala, a domain-specific language for computational law. Catala provides a concolic execution engine, CUTECat, which we drive to enumerate the paths, wrapped in an LLM agent that lifts the question to a region and verbalizes the cited answer. We evaluate on open-source encodings of French and United States legal texts. The system returns complete, cited partitions where a one-shot language model given the same rules does not; every verdict comes from the unmodified engine. Completeness is a checked theorem for the region the lift produces, and o
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