The Problem of Learning the Semantics of Quantifiers

This paper is concerned with a possible mechanism for learning the meanings of quantifiers in natural language. The meaning of a natural language construction is identified with a procedure for recognizing its extension. Therefore, acquisition of natural language quantifiers is supposed to consist in collecting procedures for computing their denotations. A method for encoding classes of finite models corresponding to given quantifiers is shown. The class of finite models is represented by appropriate languages. Some facts describing dependencies between classes of quantifiers and classes of devices are presented. In the second part of the paper examples of syntax-learning models are shown. According to these models new results in quantifier learning are presented. Finally, the question of the adequacy of syntax-learning tools for describing the process of semantic learning is stated.