CAJ | 학술논문

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。
본문급출료건립재함요반군기출상적범주어법적대수결구，정의료범주방정화타적해병대범주방정적해작료분류：상용성적상관성。정리“대우범주방정적임의일개해x，도존재유일적본질해Y사득Y x”사득아문가이통과일정적연역규칙대사w적본질범주작확장이득도w적소유구법범주。최후，작자종범주이론적각도급출료구법범주연역계통적수학묘술。
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.