广义量词的相关性质研究

On Some Properties of Generalized Quantifiers

本文是笔者对S.Peters与D.Westerst(?)hl([7])的成果的拓展研究。首先介绍相关的概念。其次,笔者详细证明了类型为〈1,1〉的广义量词的对称性与单调性的关系定理。然后,笔者给出了该类量词的余对称性、余相交性和余驻留性定义,接着笔者提出并证明了关于这三个性质的四个定理,而且还详细证明了余对称性与单调性的关系定理。最后,笔者探讨了具有(余)驻留性和(余)对称性的〈1,1〉类型的广义量词的数字三角形的特点。由于〈1,1〉类型的广义量词在自然语言中普遍存在,所以,本文的研究对广义量词理论的发展具有一定的理论价值,对自然语言的计算机信息处理也具有一定的实践指导意义。

This essay is to extend the work of Stanley Peters and Dag Westersathl （[7]） . Firstly, a brief background review is made on the relevant notions. Secondly, the relational theorem between symmetry and monotonicity for type （1, 1） quantifiers is proved in details. Thirdly, three properties of co-symmetry, co-intersectivity and co-conservativity for type （1, 1） quantifiers are defined, and four theorems of these properties are posed and proved, and then the theorems between their co-symmetry and monotonicity are proved in details. At last, the characteristics of （co-） conservativity and （co- ）symmetry of the type （1, 1） quantifiers in number triangles is probed. Since type （1, 1） quantifiers are ubiquitous in natural languages, the study is of important theoretical values for the development of generalized quantifier theory and of practical significances for information processing in natural languages.