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Intuitively, a quantifier is any word or phrase that expresses a meaning that answers one of the questions "How many?" or "How much?" Typical English examples include all, no, many, few, some but not many, all but at most a very few, wherever, whoever, whoever there is, and also, it can be arguesd, only (Keenan, 1971), also (Cushing, 1978b), and the (Chomsky, 1977), In this paper we review an empirically motivated analysis of such meanings (Cushing, 1976; 1982a) and draw out its computational significance. For purposes of illustration, we focus our attention on the meanings expressed by the English words whatever and some, commonly represented, respectively, by the symbols "V" and "3", but most of what we say will generalize to the other meanings of this class.In Section I, we review the notion of satisfaction in a model, through which logical formulas are customarily imbued implicitly with meaning. In Section 2, we discuss quantifier relativization, a notion that becomes important for meanings other than V and 3. In Section 3, we use these two notions to characterize quantifier meanings as structured function of a certain sort. In Section 4, we discuss the computational significance of that analysis. In Section 5, we elaborate on this significance by outlining a notion of abstract control structure that the analysis instantiates.

Abstract control structures and the semantics of quantifiers