Distributive and Collective Readings

There are two entities associated with plural NPs--the set of entities referred to by the NP and the typical element of that set. In

The men ran.

each individual man must run by himself, so the predicate run applies to the typical element. This is the distributive reading. In

The men gathered.
The men were numerous.

the predicates gather and numerous apply to the set of men. This is the collective reading of the NP. The sentence

The men lifted the piano.

is ambiguous between the two readings. They could each have lifted it individually, the distributive reading, in which case the logical subject of lift would be the typical element of the set, or they could have lifted it together, the collective reading, in which case it would be the set, or the aggregate.

Typical elements can be thought of as reified universally quantified variables. Their principal property is that they are typical elements of a set, represented as typelt(x,s). The principal fact about typical elements is that their other properties are inherited by all the elements of the set. Functional dependencies among such elements are represented by independent predications discovered during interpretation. Difficulties involved in this approach are worked out in Hobbs (1983, 1995).

Compositional semantics in the approach taken here is strictly local, in the sense that composition rules acting at a level higher than an NP cannot reach inside the NP for information. The Syn predication associated with NPs only carries information about the entity referred to, and in the case of plural NPs, only about the typical element. The details of how the internal structure of NPs is analyzed will not be explicated here; it is in Hobbs (1998). Here we will only note that one of the properties made available by this analysis is the typical element property, typelt(x,s). Thus, to simplify the example, we will assume that the lexical axiom for the word ``men'' is

$man'(e,x) \& typelt(x,s) \, \supset \,Syn($``men'',x,n,-,-,-,-)

That is, if e is the eventuality of x being the typical element of a set s of men, then x can be described by the word ``men''. We will also assume there is an axiom that says that if x is the typical element of s, then s is a set.

$typelt(x,s) \, \supset \,set(s)$

In cases where the collective reading is the correct one, there must be a coercion from the typical element to the set. This can be effected by using the typical element relation, typelt(x,s), as the coercion relation. That is, distributive readings are taken as basic, and collective readings are taken as examples of metonymy.

Figure 8 illustrates the interpretation of ``Men gathered.'' The predicate gather requires a set for its argument. The explicit subject x of the verb phrase ``gathered'' is the typical element of the set of men, rather than the set itself. Thus, there is a coercion, in which the predication typelt'(x,s), relating x to s, is used as the instantiation of the coercion relation rel(s,x).

  

Figure 8: Parse of ``Men gathered.''

The opposite approach could have been followed, taking the basic referent of the NP to be the set and coercing it into the typical element when the distributive reading is required. This approach is perhaps more intuitively appealing since a plural NP by itself seems to describe a set. However, in the majority of cases the distributive reading is the correct one, so the approach taken here minimizes appeals to metonymy.