The Semantics of Determiners

T, the set of types, is the smallest set such that:

(i) e, t  T

(ii) if a, b  T, then < a, b >  T

An expression of type < a, b > is an expression whose denotation is a function from expressions of type a to expressions of type b.

8 This, of course, is not the only way to characterize the denotation of generalized quantifiers formally. Lambda expressions can be used instead, as in (i), where  is used to connect a natural language expression to its interpretation, using the notation from Heim and Kratzer (1998):

(i) a man  P.x:man(x) P(x)

the man  P. !x:man(x) P(x)
every man  P.x:man(x) P(x)
John  P.P(j)

9 These sentences are fine with a plural pronoun (see, for instance, Karttunen 1976, Roberts 1989, Poesio and Zucchi 1992 among many others). But note that intra-sententially, every can bind singular pronouns and therefore the fact that this cannot happen inter-sententially remains problematic:

(i) Every politician thought that he was safe.

Note also that under special conditions such inter-sentential binding becomes possible:

(ii) Every soldier approached the platform. He shook hands with the President and got

his medal.

10 We disregard here specificational sentences such as The student that solved the problem was John/him.

11There are various ways of bringing together Montagovian and dynamic semantic approaches. See Muskens (1996) and, most recently, Brasoveanu (2007).

12 Embedding functions are partial functions from discourse referents to D. A function f’ extends a function f iff f’ and f agree on values for the discourse referents for which f is defined.

13 For a discussion that covers much of the same territory but in significantly greater detail and from a different perspective, see Heim (1991).

14 Whether bare plurals used in generic sentences such as (i) in English should count as definite or indefinite is a matter of debate. We will deal with this particular issue here but see Farkas and de Swart (2007a) for discussion.

(i) Bears are intelligent/widespread.

15 We have assumed here, following the literature, that the definite/indefinite distinction is a dichotomy, so that one side of the distinction is sensitive to some property P and the other to its complement. It is, however, possible that this assumption is in fact unwarranted. Unexplored in the literature as well as here is the view that the definite article marks some sort of uniqueness, while the indefinite article marks novelty. This observation was made by Carla Umbach, p.c.

16 There is no definite article on the noun perete ‘wall’ here because of a general rule that forbids definite articles on unmodified nominals that are objects of prepositions. The only exception is nominals that are objects of the preposition cu ‘with’.

17 Further relevant distinctions might have to be drawn to account for the details of the distribution of non-unique definites. Adrian Brasoveanu (p.c.) notes that even if a house has four walls and four windows, (i) is more natural than (ii):

(i) Maria a văzut o pată pe perete