On the Semantics of Hindi-Urdu Multiple Correlatives

Dayal (1995, 1996) argues that Hindi-Urdu (HU) correlatives are internally headed free relatives left-adjoined to a clause that contains a demonstrative matching the head of the relative in number. Following Jacobson’s (1995) analysis of free relatives, Dayal argues that the correlatives are interpreted as definite descriptions. In the case of correlatives, the definite does not occupy an argument position but, from its adjoined position, binds a variable introduced by its matching demonstrative.

(1)

When the internal head is singular, the correlative is interpreted as a singular definite description. When the internal head is plural, the correlative is interpreted as a plural definite, receiving either a distributive reading (2a) or a collective one (2b).

(2)

a.

b.

In addition to these simple cases, HU allows the typologically rare multiple correlative. A multiple correlative contains more than one relative operator, each of which must be matched by an agreeing demonstrative element in the clause to which the correlative is adjoined. Consider the multiple correlative in (3).

(3)

Interestingly, though both heads are singular, the correlative need not refer to a single girl-boy pair, but may instead quantify universally over multiple girl-boy pairs. So, multiple correlatives have universal force (UF). There are two restrictions, however, on when such universal quantification over girl-boy pairs can take place felicitously. The first, the Exhaustion Requirement (ER), is that there must be a pair in the set for every member of the thematically/hierarchically higher head. In this case, for example, every girl must have played a boy. The second, the Uniqueness Requirement (UR), is that there can be no more than one pair for each member of the higher head. So, in this case, no girl can have played more than one boy. The three components of the meaning of (3) are summarized in (4).

(4) (ER) Every girl played a boy.

  (UR) No girl played more than one boy.

  (UF) Every girl beat the boy she played.

The purpose of this squib is to examine Dayal’s (1996) influential account of the semantics of multiple correlatives and demonstrate that it can be simplified. Dayal stipulates the ER, the UR, and UF in the lexical entry of the complementizer of multiple correlatives. I suggest that each of these can be derived from independent principles of grammar.

1 Dayal’s Analysis of Multiple Correlatives

As stated above, Dayal (1995, 1996) analyzes correlatives as free relatives and follows Jacobson (1995) in assigning correlatives the semantics of definite descriptions. Unlike Jacobson, Dayal suggests that the definite determiner is contributed by the complementizer of the free relative.¹

(5)

a.

b. [[C_corr]] = λX.λ Y.λZ. Z[σx(X(x) & Y(x))]

To handle the case of multiple correlatives, Dayal suggests a generation of the definite determiner denoted by the correlative complementizer to take multiple heads.

(6) λX.λY.λZλR. ∃f′[f = ιf[dom f = Y & ∀y[Z(f(y))] & ∀z ∈ Y X(z)(f)]] & ∀x ∈ Y R(x,f′(x))]

(7) Dayal’s logical form for (3)

 

(8) [[t₁ played t¹₂]]= λx λf. x played f(x)

UF follows from the last conjunct of (6). The ER follows from setting the domain of f to Y. The UR follows from the uniqueness of f: if X related a member of Y to two members of Z, f would not be unique. I contend that none of this stipulation is necessary—that these aspects of the meaning can be derived with a more Jacobsonian analysis of free relatives along with natural principles of type-shifting and presupposition projection.

2 Jacobson 1995

Jacobson suggests that free relatives become individual-denoting expressions in two steps. As is standard, relativization produces a predicate of individuals. In the first step of Jacobson’s analysis, the predicate is maximalized owing to the semantics of the relative operator; see (10). That is, the relative operator maps a predicate to a predicate that is true of exactly one individual. In the second step, this predicate may or may not be shifted from this singleton set to its member (Partee’s (1987...