The Identity Condition of Merchant 1999

It is well known that the identity condition on VP Ellipsis is not a condition on the phonological form or even the surface structure; rather it operates at some more abstract level. What this level is exactly has been debated in depth; I will adopt here the proposal in Merchant (1999) that the identity condition is a condition on LF.

I will first give a brief overview of Merchant's identity condition. Then I will show how it is compatible with NP Ellipsis. Finally, I will present a previously undescribed pattern, sensitivity to plurality/aspect, and show how it follows from the identity condition, given the right assumptions.

Background

Fiengo & May (1994)² were the first to propose that the identity condition on VP Ellipsis was a two part relation, consisting of a syntactic identity condition on antecedent and elided VPs, and a semantic identity condition between the first VP and the second.

Rooth (1992a) refines this analysis, drawing a connection between the processes of deaccenting and ellipsis. In his account, a phrase cannot be deaccented or elided unless the XP containing the antecedent entails something contained in the Focus-closure of the XP containing the elided phrase.

This hinges on Rooth's definition of Focus-closure. The Focus-closure or ``alternative semantics'' interpretation of a YP containing a focused XP is constructed as follows. First the ``ordinary semantics'' interpretation for that YP is constructed. Then the part of the interpretation corresponding to the focused XP is lambda extracted and allowed to range over all possible elements of the same semantic type³. For example, if the ordinary semantics and ``alternative semantics'' for [$_{N'}$ American$_F$ farmer] is as follows:

(48) Ordinary semantics:
$[\![ [_{N'} American_F farmer] ]\!]^0 = \lambda x [ American(x) \wedge farmer(x)]$
(49)Alternative semantics:
Let P be the set of all functions from entities to propositions.
$[\![ [_{N'} American_F farmer] ]\!]^f = \left\{ \lambda x [ p(x) \wedge farmer(x)] \vert p \in P \right\}$

In other words the ``alternative semantics'' for [$_{N'}$ American$_F$ farmer] is a set of interpretations corresponding to Canadian farmer, Mexican farmer, and so on.⁴ The set returned by Focus-closure has an element for each intersective adjective, combined with farmer.

The operation of Focus-closure only returns this set of constituents for focused elements. The Focus-closure of a non-focused element (including deaccented and elided elements) is the same as the ``ordinary semantics'' interpretation.

Building on this, Rooth shows that the condition on deaccenting is simply that the XP containing the antecedent entail something that is contained in the focus-closure of the XP containing the deaccented phrase. (Rooth does his calculations at the level of sentences. Merchant adds $\exists$-type shifting to allow Focus-closure to be used for other phrases as well.) This allows a ``specific'' IP to antecede a deaccented, more general IP (the italicized phrase is deaccented):

(50) Mary called Frank a Republican, but I don't know who else she insulted⁵.

The IP she insulted can be deaccented, because its focus closure contains something entailed by the antecedent Mary called Frank a Republican:

(51) $call(Mary,Frank,Republican) \to insult(Mary,Frank)$
(52) $insult(Mary,Frank) \in \left\{ \lambda x [ insult(Mary, x) ] \vert x \in D \right\}$

Rooth then argues that this condition is exactly the semantic condition on ellipsis proposed by Fiengo & May.

Merchant 1999

Merchant further refines Rooth's identity condition on ellipsis. While the interpretation of the antecedent must be or entail an element of the Focus-closure of the elided phrase, just as in Rooth's account, Merchant also requires the elided phrase to be or entail an element of the Focus-closure of the antecedent. This second condition, making the relation between antecedent and elided phrase completely symmetric, replaces the syntactic surface condition of Rooth (and Fiengo & May).

This can be seen in the following example. The elided IP in the sentence below can only be interpreted as she called t a Republican, not as she insulted t. However, both of those phrases are valid deaccented phrases.

(53) Mary called Frank a Republican, but I don't know who else _ (_ = she called a republican, _ $\neq$ she insulted.

(54) Mary called Frank a Republican, but I don't know who else she called t a Republican.

(55) Mary called Frank a Republican, but I don't know who else she insulted.

Merchant gives a general identity condition on ellipsis, intended to work for VP Ellipsis and Sluicing:

The Identity Condition on Ellipsis

1. e-Givenness (Merchant 1999, p. 36)
   An expression E counts as e-given if E has a salient antecedent A and, modulo $\exists$-type shifting,
   1. A entails F-clo(E) and
   2. E entails F-clo(A)⁶
2. Focus condition on Ellipsis (Merchant 1999, p 44)
   A constituent $\alpha$ can be deleted only if $\alpha$ is e-Given

I retain the Focus-closure aspect of Merchant, because it captures the empirical similarity between deaccenting and ellipsis, but this is not crucial to my account. In fact, my account would be simpler if the identity condition could simply be logical equivalence ( $NP_E \iff NP_A$) between the antecedent and the ellipsis, modulo $\exists$-type shifting.

I will now turn to some data that shows this identity condition suffices for NP Ellipsis.

Strict/Sloppy Ambiguity

Strict/sloppy ambiguity is available in NP ellipsis. This is predicted by Merchant's identity condition. The relevant examples to consider are ones like the following:

(56) Mary's pictures of herself won the photography contest, and [Bob's _] got second place. ( _ = pictures of himself/pictures of Mary, $\neq$ pictures)

(57) Lisa's disappointment in herself was unreasonable , and so was [Bob's _]. (_ = disappointment in himself/disappointment in Lisa, $\neq$ disappointment)

An account of (56) would go as follows. For the strict reading, the elided NP would have been picture of Mary.

(58) Strict reading:
$NP_A = \lambda y \lambda x$ [ $picture(y, Mary) \wedge own(x, y)$ ]
$NP_E = \lambda y \lambda x$ [ $picture(y, Mary) \wedge own(x, y)$ ]
modulo existential type-shifting,
$NP_A \Leftrightarrow NP_E$, so
$NP_A \Rightarrow \textrm{F-Clo}(NP_E)$, and
$NP_E \Rightarrow \textrm{F-Clo}(NP_A)$,

For the sloppy reading, the elided NP is interpreted to have been picture of him/her where the pronoun is bound by the owner of the picture.

(59) Sloppy reading:
$NP_A = \lambda y \lambda x$ [ $picture(y, x) \wedge own(x, y)$ ]
$NP_E = \lambda y \lambda x$ [ $picture(y, x) \wedge own(x, y)$ ]
modulo existential type-shifting,
$NP_A \Leftrightarrow NP_E$, so
$NP_A \Rightarrow \textrm{F-Clo}(NP_E)$, and
$NP_E \Rightarrow \textrm{F-Clo}(NP_A)$,

Note that this account assumes that at least some possessors (those of deverbal nouns, for example) are semantic arguments to their nouns.

The connection between ellipsis and deaccenting in DP

A specific noun phrase can antecede a deaccented, more general noun phrase. But a specific noun phrase can only antecede an identical elided one, just as is predicted by Rooth.

(60) Bob's Schwinn is in the shop, so he is riding SAM's bicycle.

(61) Bob's Schwinn is in the shop, so he is riding SAM's _ (_ = Schwinn, _ $\neq$ bicycle)

(62) Bob Dylan's songs about politics are good , but D.R. Goettel's songs are better.

(63) Bob Dylan's songs about politics are good , but D.R. Goettel's _ are better. (_ = songs about politics, $\neq$ songs)

A Focus-closure-based account will work as follows. The general NP, bicycle, can be deaccented. Schwinn entails bicycle, which is in the Focus-closure of bicycle.

(64) Deaccenting:
$NP_A = \lambda y \lambda x [ Schwinn(y) \wedge own(x, y) ]$
$NP_D = \lambda y \lambda x [ bicycle(y) \wedge own(x, y) ]$
$\textrm{F-Clo}(NP_A) = \lambda y \lambda x [ Schwinn(y) \wedge own(x, y) ]$
$\textrm{F-Clo}(NP_D) = \lambda y \lambda x [ bicycle(y) \wedge own(x, y) ]$
$\exists x [Schwinn(x)] \Rightarrow \exists x [bicycle(x)]$
$NP_A \Rightarrow \textrm{F-Clo}(NP_D)$ so NP$_D$ can be deaccented.

However, ellipsis of the NP bicycle is not allowed. Bicycle does not entail anything in F-Clo(Schwinn), and thus cannot be elided⁷.

(65) Ellipsis:
$\exists x [bicycle(x)] \not\Rightarrow$ $\exists x [Schwinn(x)]$
$NP_D \not\Rightarrow$ $\textrm{F-Clo}(NP_A)$ so NP$_D$ cannot be elided.

Deaccenting is allowed, since the antecedent entails an element of the Focus-closure of the deaccented phrase. However, ellipsis is disallowed, since the deaccented phrase does not entail an element of the Focus-closure of the antecedent.

Plurality/Tense/Aspect Sensitivity

VP Ellipsis is well known to be insensitive to the morphological form of the elided verb. Since the auxiliary preceding the ellipsis site determines the form of the verb in its complement, the morphological form of the ellipsis is recoverable.

(66) Mary has already gone to the store, but Bob won't _. (= go to the store)

(67) Mary ate with us today, and tomorrow, no one will _. (= eat with us)

(68) Bob won't sing the national anthem, but Mary is _. (= singing the national anthem)

(69) Bob can't clean the living room because Mary already has _. (= cleaned the living room)

Similarly, NP Ellipsis is insensitive to the morphological form of the elided noun. Since, in the usual case, there is no overt marker of the plurality of the DP outside of the NP, an elided NP will be ambiguous between singular and plural interpretations.

(70) Bob's car is in the shop, but I prefer driving [Mary's _] anyway. (= car, cars)

(71) Bob's cars are in the shop, but I prefer driving [Mary's _] anyway.(= car, cars)

(72) Mary's picture won the photography contest, and [Bob's _] got many small prizes (= picture, pictures)

(73) Mary's pictures won the photography contest, and [Bob's _] got many small prizes (= picture, pictures)

This makes perfect sense. NPs denote properties, not entities. Whether the DP refers to a singular entity or a plurality of entities should be calculated at the level of the DP, not the NP. The identity condition is satisfied for examples like (70)/(71) then:

$NP_A : \lambda x [ car(x) ]$
$NP_E : \lambda x [ car(x) ]$
$\textrm{F-Clo}(NP_A) = \lambda x [ car(x) ]$
$\textrm{F-Clo}(NP_E) = \lambda x [ car(x) ]$
modulo existential type-shifting,
$NP_A \Rightarrow NP_E$ and
$NP_E \Rightarrow NP_A$, so $NP_E$ can be elided.

Singularity in vanilla contexts

There seems to be a preference for the singular interpretation in the absence of anything to push the interpretation in the direction of the plural interpretation. For example, (70) and (72), at the beginning of a discourse, would probably be interpreted as ellipsis sites in singular DPs. With plural antecedents, both interpretations seem equally available. So it seems that this preference is for singulars absent anything to indicate a plural, not for an ellipsis matching the antecedent in number.

However, if we know that Mary is a car collector, or that Bob entered many pictures in the contest, the plural interpretation is suddenly available. Even though one interpretation of the ellipsis site is more salient or preferred, both are available in the appropriate context, so the grammar should not rule out either interpretation.

Eliminating the ambiguity

There are, however, a range of exceptional circumstances in which the plurality/singularity ambiguity of the elided DP is eliminated.

Partitives, for example, mandatorily take a DP complement which is plural or denotes a group. So an elided NP in a DP complement to a partitive is only interpretable as a plural.

(74) Bob's car is in the shop, but I would prefer to drive [one of [Mary's _]] anyway. (= cars, $\neq$ car)

(75) Mary's picture won the photography contest, and [some of [Bob's _]] got several lesser prizes. (= pictures ,$\neq$ picture)

But an elided NP in a DP complement to a partitive which has a group noun as its antecedent remains ambiguous, since both the plural and the singular are possible complements to the partitive:

(76) Mary's team left, but [one of [Sam's _]] didn't. (_ = team, teams)

(77) Frank's research group were all fired, but [some of [Mary's _]] might still work here. (_ = research group, research groups)

Subject-verb agreement also seems capable of eliminating this ambiguity. Although speakers vary on their judgments somewhat, no one judges these kinds of examples to be completely ungrammatical.

(78) Mary's brother has graduated, but Bob's _ haven't graduated. (_ = brothers)

(79) Bob's brothers have graduated, but Mary's _ hasn't graduated. (_ = brother)

(80) ?Mary's single submission has won the grand prize, but Bob's _ have won several lesser prizes. (_ = submissions)

(81) Bob's several submissions have won many small prizes, but Mary's _ has won the grand prize. (_ = submission)

We should not attempt a syntactic or even a semantic analysis of these facts because context or knowledge about the world can interfere to limit the available interpretations as well.

(82) Jack's got blue eyes. Bart's _ might have been blue or green. (_ = eyes)

(83) Mary's wedding was beautiful, but I didn't enjoy Cindy and Tina's _. (_ = weddings)

Since most people have two eyes, and since two women don't ordinarily get married, there is a tendency to assume that these ellipsis sites are in plural DPs. But if we know, for example, that Bart was a battle-scarred pirate, or that Cindy and Tina were gay, then the singular interpretations suddenly become available interpretations.

So NP Ellipsis is insensitive to the morphological form of the noun, allowing ambiguity between plural and singular interpretations of the ellipsis site. There seems to be a preference for a singular ellipsis site in the absence of information to the contrary. And syntactic and contextual factors can interfere and push the interpretation in one direction or the other. But in general, this insensitivity to plurality parallels the insensitivity of VP Ellipsis to the morphological form of the verb in the ellipsis site.

Negation

The identity condition on VP Ellipsis is insensitive to negation:

(84) Bob finished his vegetables, but Mary didn't _. (_ = finish her vegetable(s))

(85) Bob didn't finish his vegetables, but Mary did _. (_ = finish her vegetable(s))

We would expect the same thing in NP Ellipsis, and it does seem to happen:

(86) Mary ate no vegetables, but [Bob's _] were all eaten. (_ = vegetables)

(87) Mary has no dogs, but [Bob's _] might have bit Frank. (_ = dogs)

This is not surprising at all, given the pattern in VP Ellipsis. A naive account would simply insure that NP Ellipsis targeted some node below the negative morpheme, which would sit in a functional projection above NP:

Split Antecedents

Fiengo and May notice that elided VPs can have split antecedents. It is significantly more difficult to generate split antecedents for NP Ellipsis. With just a single noun in both antecedent NPs, there is no clear way to tell if the ellipsis site has both or only one of the possible antecedents.

(88) Mary's brothers climbed Kilimanjaro, and Bob's brothers swam the English Channel, but [Elmer's _] did both these things. (_ = brother, brothers)

(89) Mary's brother climbed Kilimanjaro, and Bob's brother swam the English Channel, but [Elmer's _] did both these things. (_ = brother, brothers,)

With two very semantically similar nouns, however, it is difficult to get NP Ellipsis to resolve to a split antecedent.

(90) Mary's brother climbed Kilimanjaro, and Bob's sister swam the English Channel, but [Elmer's _] did both these things. (_ = brother, sister, brothers, sisters, ?= brothers and sisters)

(91) Mary's brothers climbed Kilimanjaro, and Bob's sisters swam the English Channel, but [Elmer's _] did both these things. (_ = brother, sister, brothers, sisters, ?= brothers and sisters)

And even with a deverbal noun, it seems difficult to get a split antecedent:

(92) Godzilla's destruction of Tokyo frightened me, Mothra's destruction of Osaka amused me, and Gamera's _ both amused and frightened me. (_ = destruction of Tokyo, destruction of Osaka, ?= destruction of Tokyo and Osaka)

It seems that NP Ellipsis may not allow split antecedency at all.

Summary

I have shown that a great deal of the same patterns present in the syntax and semantics of VP Ellipsis are present in the syntax and semantics of NP Ellipsis, and that the identity condition of Merchant accounts for the data.