{"ID":2823631,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2601.00880","arxiv_id":"2601.00880","title":"Universal Conditional Logic: A Formal Language for Prompt Engineering","abstract":"We present Universal Conditional Logic (UCL), a mathematical framework for prompt optimization that transforms prompt engineering from heuristic practice into systematic optimization. Through systematic evaluation (N=305, 11 models, 4 iterations), we demonstrate significant token reduction (29.8%, t(10)=6.36, p \u003c 0.001, Cohen's d = 2.01) with corresponding cost savings. UCL's structural overhead function O_s(A) explains version-specific performance differences through the Over-Specification Paradox: beyond threshold S* = 0.509, additional specification degrades performance quadratically. Core mechanisms -- indicator functions (I_i in {0,1}), structural overhead (O_s = gamma * sum(ln C_k)), early binding -- are validated. Notably, optimal UCL configuration varies by model architecture -- certain models (e.g., Llama 4 Scout) require version-specific adaptations (V4.1). This work establishes UCL as a calibratable framework for efficient LLM interaction, with model-family-specific optimization as a key research direction.","short_abstract":"We present Universal Conditional Logic (UCL), a mathematical framework for prompt optimization that transforms prompt engineering from heuristic practice into systematic optimization. Through systematic evaluation (N=305, 11 models, 4 iterations), we demonstrate significant token reduction (29.8%, t(10)=6.36, p \u003c 0.001...","url_abs":"https://arxiv.org/abs/2601.00880","url_pdf":"https://arxiv.org/pdf/2601.00880v1","authors":"[\"Anthony Mikinka\"]","published":"2025-12-31T05:27:00Z","proceeding":"cs.AI","tasks":"[\"cs.AI\",\"cs.CL\",\"cs.LG\",\"cs.PL\",\"cs.SE\"]","methods":"[\"Large Language Model\"]","has_code":false}