AI 中文总结
针对自然语言能否完全取代形式语言的争议，引入基于“任务特异性”的形式框架并证明“特异性交叉定理”，通过跨模态案例分析表明二者各有优势，是互补工具，倡导开发混合系统。
AI 中文摘要
大语言模型的进展及广泛应用引发自然语言可完全取代形式语言（如软件设计编程语言）的说法。本文认为此观点忽视自然语言基本属性，其在开放式语境中针对欠规范进行优化。引入以“任务特异性”为核心的形式框架，定义为给定用户特定要求时输出空间（如所有可能图像）中不确定性的信息论减少。证明“特异性交叉定理”，表明存在阈值，超过该阈值将形式要求表达为自然语言的成本超过直接形式规范的成本。通过跨模态案例分析表明，自然语言在低特异性任务中表现出色，形式语言在要求更严格的任务中更具优势。结论是自然语言和形式语言是互补工具，提倡开发允许用户在特异性范围内转换的混合系统。
英文摘要
Recent advances in large language models and their widespread adoption have prompted claims that natural language could entirely replace formal languages, such as programming languages for software design. In this position paper, we argue that this perspective overlooks fundamental linguistic properties of natural language, specifically that it is optimized for underspecification in open-ended contexts. We introduce a formal framework centered on *task specificity*, defining it as the information-theoretic reduction of uncertainty in an output space -- such as all possible images -- given a user's specific requirements. We prove a *specificity crossover theorem*, showing the existence of a threshold beyond which the cost to express formal requirements into natural language exceeds the cost of direct formal specification. By analyzing case studies across modalities, such as image generation, code synthesis, and audio production, we demonstrate that natural language excels at low specificity tasks, while formal languages are advantageous on tasks with stricter requirements. We conclude that natural and formal languages are complementary tools and advocate the development of hybrid systems that allow users to move across the specificity spectrum.
CommentsTo be published in ICML 2026 (position track)
