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Elements of Formal Semantics Published online by Cambridge University Press: 11 August 2018
This chapter addresses noun phrases (NPs) that involve counting and other statements about quantity. We compositionally analyze complex NP structures by letting them denote (et)t functions, or generalized quantifiers. Quantificational elements within the noun phrase are analyzed as denoting (et)((et)t) functions, or determiner relations. This analysis accounts for many entailments with quantified NPs: monotonicity-based entailments, entailments with various coordinations, and a possibly universal entailment pattern in natural language, known as conservativity.When studying NP coordinations, we reveal new facts about the behavior of proper names. To deal with these facts, we reanalyze proper names using generalized quantifiers, so that they end up being treated similarly to quantified NPs.
Many expressions intuitively involve processes of counting ormeasuring. Consider for instance the italicized expressions in the following sentences:
1) John rarely/usually eats meat.
2) We are close to/far from Beijing.
3) There is little/a lot of work to do today.
4) Many/few people admire Richard Wagner.
We refer to such items as quantificational expressions. Intuitively, in sentence (4.1) the adverbs refer to the frequency of John's carnivorousness; in (4.2) the prepositional phrases estimate the distance to Beijing; in (4.3) the mass term expressions evaluate an amount of work. Similarly, in (4.4) the quantificational expressions many and few evaluate the number ofWagner's admirers.
In general, words like many and few combine with count nouns, such as tables or people in (4.4). In the previous chapter, we have described the denotations of such nouns using sets of entities from the domain E. The members of the E domain are assumed to be distinct, separated objects, without any smooth variation from one to the other. For instance, in our entity domain, we have no entity that “lies between”, say, different entity denotations for Tina and Mary. This is unlike the situation in sets of real numbers, geometrical shapes etc., where there are endless variations between any two different entities. Because the E domain has this property, we refer to it as being discrete.
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