句法范畴的代数结构与演绎系统

本文给出了建立在含幺半群基础上的范畴语法的代数结构,定义了范畴方程和它的解并对范畴方程的解作了分类:相容性的相关性。定理“对于范畴方程的任意一个解X ,都存在唯一的本质解Y使得Y?X”使得我们可以通过一定的演绎规则对词w的本质范畴作扩张以得到w的所有句法范畴。最后,作者从范畴理论的角度给出了句法范畴演绎系统的数学描述。

The Algebraic Structure and Deductive System of Syntactic Categories

In this article, we showed the algebraic structure of syntactic categories based on monoid and defined categorial equation whose solutions are described by consistency and correlation . The result “If X is a solution of a categorial equation, then there exists an unique essential solution Y such thatY X”makes it possible that the essential catgories of a word could generate all possible syntactic categories by some deductive rules. Finally, the author described the deductive system of syntactic categories from the viewpoint of Category Theory in mathematics.