Position: Natural Language Should Not Fully Replace Formal Languages

立场：自然语言不应完全取代形式语言

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. 大型语言模型的最新进展及其广泛应用引发了一种观点，即自然语言可以完全取代形式语言（例如用于软件设计的编程语言）。

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. 在这篇立场论文中，我们认为这种观点忽视了自然语言的基本语言学特性，即它在开放式语境下针对“欠规范性”（underspecification）进行了优化。

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. 我们引入了一个以“任务特异性”（task specificity）为核心的形式化框架，将其定义为在给定用户特定需求的情况下，输出空间（例如所有可能的图像）中不确定性的信息论缩减。

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. 我们证明了一个“特异性交叉定理”（specificity crossover theorem），表明存在一个阈值，一旦超过该阈值，将形式化需求转化为自然语言的成本就会超过直接进行形式化规范的成本。

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. 通过分析图像生成、代码合成和音频制作等不同模态的案例研究，我们证明了自然语言在低特异性任务中表现出色，而形式语言在具有更严格要求的任务中更具优势。

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. 我们得出结论：自然语言和形式语言是互补的工具，并主张开发混合系统，使用户能够在特异性谱系中灵活切换。