arXiv:2509.10818v2 Announce Type: replace
Abstract: When consequential decisions depend on knowledge that exists nowhere in writing, LLMs hallucinate not from retrieval failure but from model absence. RAG and knowledge-graph methods share a structural ceiling. They cannot supply what has never been recorded. This paper reconceptualizes that failure as a model discovery problem. The proposed causal prompt engineering framework discovers and encodes a decision logic of a domain expert as an Expert Mental Model (EMM), providing it as principled input to LLM reasoning supplying what no retrieval method can. The framework is grounded in the theory of monotone Boolean and k-valued functions. A key technical contribution is the formalization of three LLM assisted prerequisite processes previously undeveloped for novel domains: factor formulation, factor monotonization, and monotonicity preserving hierarchical structuring. These enable a four step EMM construction algorithm that reduces elicitation from millions of combinations to a tractable, formally bounded set manageable by humans. The framework also enables, for the first time, formal measurement of LLM hallucination when expert knowledge is entirely tacit. Analysis shows conditional error rates on true positives can approach 100% for plausible LLM-expert mismatches invisible to prior evaluation methods. The approach is validated across grant proposal evaluation, cybersecurity design, and clinical diagnosis.
Abstract: When consequential decisions depend on knowledge that exists nowhere in writing, LLMs hallucinate not from retrieval failure but from model absence. RAG and knowledge-graph methods share a structural ceiling. They cannot supply what has never been recorded. This paper reconceptualizes that failure as a model discovery problem. The proposed causal prompt engineering framework discovers and encodes a decision logic of a domain expert as an Expert Mental Model (EMM), providing it as principled input to LLM reasoning supplying what no retrieval method can. The framework is grounded in the theory of monotone Boolean and k-valued functions. A key technical contribution is the formalization of three LLM assisted prerequisite processes previously undeveloped for novel domains: factor formulation, factor monotonization, and monotonicity preserving hierarchical structuring. These enable a four step EMM construction algorithm that reduces elicitation from millions of combinations to a tractable, formally bounded set manageable by humans. The framework also enables, for the first time, formal measurement of LLM hallucination when expert knowledge is entirely tacit. Analysis shows conditional error rates on true positives can approach 100% for plausible LLM-expert mismatches invisible to prior evaluation methods. The approach is validated across grant proposal evaluation, cybersecurity design, and clinical diagnosis.
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