TAILIEUCHUNG - Báo cáo khoa học: "ABSTRACT CONTROL STRUCTURES AND THE SEMANTICS OF QUANTIFIERS"

Intuitively, a Ruantifier 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 ver~ few, wherever, whoever, whoever there is, and also, it can be argued, 0nly (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. | ABSTRACT CONTROL STRUCTURES AND THE SEMANTICS OF QUANTIFIERS Steven Cushing Computer. Science Department St. Anselm College Manchester New Hampshire 03102 USA ABSTRACT 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 argued 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 and 3 but most of what we say will generalize to the other meanings of this class. In Section 1 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 functions 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. I MODELS AND SATISFACTION Given a semantic representation language L containing predicate constants and individual constants and variables an Interpretation I of L is a triple I JI _f where D is a set of individuals the domain of R is a function the Interpretation function of I_ that assigns members of 1 to Individual constants in L and sets of lists of members of to predicates In L the length of a list being equal to the number of arguments In the predicate to which it corresponds and _f Is a set of functions the .

• Báo cáo khoa học
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• THE SEMANTICS OF QUANTIFIERS
• Steven Cushing
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