Universal Conditional Logic: A Formal Language for Prompt Engineering
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909980171436032 |
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| author | Mikinka, Anthony |
| author_facet | Mikinka, Anthony |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_00880 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Conditional Logic: A Formal Language for Prompt Engineering Mikinka, Anthony Artificial Intelligence Computation and Language Machine Learning Programming Languages Software Engineering 68T50, 68Q42 I.2.7; F.4.2; D.3.2 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. |
| title | Universal Conditional Logic: A Formal Language for Prompt Engineering |
| topic | Artificial Intelligence Computation and Language Machine Learning Programming Languages Software Engineering 68T50, 68Q42 I.2.7; F.4.2; D.3.2 |
| url | https://arxiv.org/abs/2601.00880 |