試論漢語的數學規範性質

On Formal Properties of Chinese

本文介紹自然語言的數學規範理論，並依據此理論初步探討漢語之數學現範性質。利用規範語言之封閉住（closure），本文先證明漢語包孕句的現象超出尋常語言（regular language）。接著本文更利用漢語反覆是非問句的現變，證明漢語的規範性質超過免用語境（context free）語言。此一結果對自然語言之規範理論相當重要。其意義不僅在於再次提供自然語言為超免用語境語言之實證，而且是第一個不藉同構轉換，直接以複寫形式（copying）證明的證明。

The study of mathematical properties of natural languages has both theoretical and applicational implications. In theoretical linguistics, a precise characterization of natural languages in terms of formal models, such as the Chomsky hierarchy, helps to capture the definition of possible natural languages and possible grammars for natural languages. Thus, the advantages and disadvantages of current grammatical theories can be compared and contrasted to motivate meaningful improvements. On the other hand, in natural language processing, knowledge of the formal properties of natural languages means the ability to chose and implement attested efficient parsing algorithms developed for corresponding formal languages. As a first study of the formal properties of Chinese, this article determines the position of this language in the Chomsky hierarchy. Formal proofs are given to show that Chinese is neither a (type 3) regular set nor a (type 2) context-free language. Thus it is concluded that Chinese is supra-context-free. These formal proofs base on the closure properties of a type N language under substitution and under intersection with regular sets.