Logic and Data Bases
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This paper examines quantification in relation to a typed three-valued logical system which was developed to serve as the internal query language for virtual data bases accepting natural language (NL) consultation. Such a system is capable, among, other things, of reflecting certain NL presuppositions, handling relations among sets and coping with certain NL ambiguities, within a simple though natural and fairly vast NL subset. In our approach, quantification is dealt with through a single mechanism by which all NL quantifiers introduce the formula "those(x,p)", denoting the set of all those x's in x's associated domain which satisfy statement p. The meaning of each particular NL quantifier--including any presuppositions it may induce-- is rendered through particular constraints upon the set (e.g., cardinality constraints).