Aspects of the Cardinality of Numeral Quantifiers

Abstract

This study primarily starts from a survey, but it's not just a survey. By raising a couple of topic-based issues about the cardinality of numeral quantifiers, this paper tries to offer a body of ideas about some procedural aspects of the mathematical complexity of denotational assignments. What is meant by the notion 'cardinality' is that, as advanced by a couple of van Benthem's (1985, 1986a, 1986b) works, quantifiers are characterized by the automata that control the acceptance of strings describing the algebraic properties of a domain of discourse. First, it is reviewed how A-quantifiers are compatible with D-quantifiers. Then, concentrating on the data of polarity-sensitive numeral quantifiers, we characterize the cardinal properties of numeral quantifiers in terms of Semantic Automata and Number Tree. In this perspective, this study leans towards the formulation of the procedural vies as regards the cardinality of numeral quantifiers.