广义量词的单调性与其他语义性质之间的关系

Relations Between Monotonicity of Generalized Quantifiers and Other Semantic Properties

广义量词理论是一阶逻辑的扩展理论,它比一阶逻辑更有利于计算机进行知识表示和知识推理。广义量词的语义性质主要包括:同构闭包性、扩展性、驻留性、单调性、对称性。单调性是广义量词最为重要的语义性质。给出6个定理,主要论述广义量词的单调性与其他语义性质之间的关系,比如:具有单调性的广义量词首先得满足驻留性。

Generalized quantifier theory is an extension of first-order logic. It is more favorable than the first-order logic for knowledge representation and reasoning in computer science. Semantic properties of generalized quantifiers include the isomorphism closure,the extension,the conservativity,the monotonicity and the symmetry. And the monotonicity of generalized quantifiers is the most important semantic properties. Six theorems were given in this article and the relations between monotonicity and the other semantic properties were mainly illustrated. For example,the generalized quantifiers which are monotonic firstly must be conservative.