How Does Natural Language Quantify?

HOW DOES NATURAL LANGUAGE QUANTIFY? Michael Hess University of Zurich, Seminar of General Linguistics, Plattenstrasse 54, CH-8032 Zurich, Switzerland ABSTRACT It has traditionally been assumed that Natural Language uses explicit quantifier expressions (such as "all" and "most", "the" and "a") for the purpose of quantification. We argue that expressi- ons of the first type are comparatively rare in real world Natural Language sentences, and that the latter (articles) cannot be considered stra- ightforward quantlfiers in the first place. How- ever, practically all applications of Natural Language Processfng require sentences to be quantified unambiguously. We llst a few possible ( syntactical, semantical, and "pragmatical") sour- ces of "implicit" quantiflcatlonal information in Natural Language; they combine in sometimes intricate ways to give a sentence a (more or less) unambiguous quantification. i. THE LACK OF EXPLICIT QUANTIFICATION IN NATURAL LANGUAGE - " I. i INTRODUCTION The subject of the present paper is not strictly one of Computational LinEuistics. Neither does it outline a working computer program, nor investi- gate a linguistic problem with the help of compu- tational methods. A/though the subject may be purely linguistic in character it is particularly relevant to Computational Linguistics. Moreover it seems to have been ignored by most non-computa- tional linguists. Computational as well as non-computational linguists agree that we have to represent Natural Language sentences as quantified logical senten- ces, either in a graphical variant of logic such as semantic networks, or in some other form of logic. However, non-computational linguists do not very often use real-world examples in their investigations; they create their own example sen- tences to make a certain point. Everything which is not in the prhnary focus of their interest is made so explicit as to become largely self-expla- natory. They tend, for instance, to create only sentences where quantification is explicit. Com- putational linguists, on the other hand, have to use real world texts. They have to face certain nasty facts of life which they, too, would prefer to ignore. One of them concerns the way in which Natural Language quantifies. 1.2 THE TRADITIONAL POINT OF VIEW: QUANTIFIERS ARE EXPLICIT Traditionally it has almost always been assumed that quantification is expressed in Natural Langu- age by explicit means. The most traditional view had it that simple surface words correspond one- to-one to the two classical quantifiers: "every" and "all" stand for the universal quantifier, "some" for the existential quantifier: every man is mortal some gods are mortal However, it has long been known that the over- whelmlng majority of real world sentences simply don't contain any of those explicit simple quanti- fier words.* For this reason (among others) Bar- wise and Cooper (1981) suggested that the con- cept of simple quantiflers should be extended to the concept of- gemern]|~ed quant/fiers. They should take care of simple cases such as most men as well as of very complicated ones such as more than half of John's arrows. A generalised quanti- fer consists, in English, of a determiner (such as . 11 . …

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