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 < 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.
@article{arxiv.2601.00880,
title = {Universal Conditional Logic: A Formal Language for Prompt Engineering},
author = {Anthony Mikinka},
journal= {arXiv preprint arXiv:2601.00880},
year = {2026}
}
Comments
25 pages, 15 figures, 5 tables. Includes appendices with variable reference, pattern library, and O_s calculation examples. Supplementary materials: V1-V4.1 prompt source code and 305 model responses available at GitHub repositories