2.1 Background: Modeling questions and propositions

Our focus-based account is based on the Alternative Semantics account of the compositional semantics of focus (Rooth 1985; 1992b; Hamblin 1973). Under this approach, items such as wh-words and F(ocus)-marked elements introduce alternatives into the derivation. Focus-semantic values ⟦·⟧^f are computed for each node in the syntactic derivation alongside their ordinary value ⟦·⟧^o. Focus-sensitive operators such as only can then use alternatives to different effects.⁴

Our goal in this paper is to provide an account of the identity condition on sluicing in examples such as (1), repeated from above, where a declarative antecedent and a question continuation must somehow be semantically identical.

We adopt the view that questions denote sets of propositions that are possible answers to the question (Hamblin 1973; Karttunen 1977). In (4a), the wh-word who acts as a source of alternatives, here corresponding to relevant individuals in the context (see Hamblin 1973; Ramchand 1997; Kratzer & Shimoyama 2002; Beck 2006; Cable 2010; Kotek 2019), as shown in (4b). The question denotation is given in set form and in function form in (4c–d).

We furthermore adopt the standard assumption that propositions denote sets of worlds that satisfy certain truth conditions:

Finally, we introduce a union operation over propositions, ∪. This operation will be useful when we present our proposal in (8) below.

2.2 Proposal

Our generalized proposal, which will be motivated in greater detail in §5, is given in (7).

We will argue for this proposal stepwise, by first closely examining the licensing conditions on sluicing, and then expanding our discussion to VP ellipsis and to deaccenting. In Sections 2–3 we concentrate specifically on sluicing. We propose that sluicing is licensed provided the antecedent and sluice have the same focus-theoretic propositional content:

For most purposes, this amounts to the following:⁵

This proposal is similar in spirit to Weir’s (2014) licensing condition on sluicing, reproduced in (10), although for Weir, the licensing condition crucially makes reference to a Question under Discussion (QuD) raised by the antecedent. As we will show at length in §3, a QuD account will struggle to account for the data we will discuss in this paper. It will moreover fail to generalize to other types of ellipsis and redundancy reduction, as we will do with our proposal in §5.

We now illustrate how our proposal handles sluicing, using our simple example with an indefinite correlate (11). First, note that condition (a) of our proposal is met: CP_E has a salient antecedent CP_A, as illustrated in (12). Condition (b) of our proposal is also met, as we can demonstrated that the focus-semantic values of the antecedent clause and of the sluice are equivalent: ∪⟦CP_A⟧^f ↔ ∪⟦CP_E⟧^f, (13).

Note that in this simple case, sluicing would also be licensed by simply making reference to the ordinary semantic value of the antecedent, as opposed to its focus value. As will become evident in §3.4.5, we will need to make reference to the focus semantic value of focused material in order to account for contrastive sluices, and therefore we generalize here, as well.

Consider next the phenomenon of sprouting, a sub-case of sluicing, in which the remnant lacks an explicit linguistic correlate (Chung et al. 1995, a.o.). Such cases will become important in our argumentation against Q-equivalence approaches below. As example (14) shows, we find cases of both argument and adjunct sprouting. In particular, example (14b) demonstrates sprouting’s flexibility:

Our proposal can easily capture examples of sprouting. Consider first examples of argument sprouting, as in (14a). Example (15) illustrates how such cases are captured by our analysis:⁸

Importantly here, notice that if Sally ate in w, then she necessarily ate a certain thing x in w. As a consequence, the set of worlds described by the sluice in (15b) and the set of worlds described by the antecedent (15c) must be identical:

Consider next examples of adjunct sprouting, as in (14b). Example (17) illustrates how our proposal works for the adjunct when.

As in the case of argument sluicing in (15), it is important here that if Sally left in w, then she necessarily left at a certain time t in w. As a consequence, the set of worlds described by the sluice in (17b) and the set of worlds described by the antecedent (17c) must be identical:

Matters are more complex in other cases of adjunct sprouting, such as … with whom or … in which car in (14b). As a general rule, not every event of Sally leaving must involve a companion or a car:

Here, we appeal to a process of accommodation, much like the one appealed to by other accounts of sprouting in the literature.⁹ For concreteness, we adopt the definition of accommodation in (20). This allows the antecedent to entail the sluiced question’s existential presupposition.

In (19), the sluice presupposes that all relevant Sally-leaving worlds are Sally-leaving-with-someone worlds. We assume that accommodation of the sluice’s presupposition removes from consideration worlds in the context set that are inconsistent with the sluice’s presupposition. For (19b), worlds where Sally did not leave with anyone are irrelevant, yielding equivalence between the denotation of the sluice and the antecedent proposition, correctly predicting sprouting to be licensed in these cases once accommodation is taken into account.

We take this solution to provide an answer to a related challenge from Chung et al. (2010) to (then-extant) semantic identity approaches in general, and in particular to the proposal in Merchant (2001). Some examples are given below:

In none of the examples in (21) is it clear that the antecedent renders the ellipsis clause GIVEN in the sense required by Merchant’s account (see §4). For example, finishing one’s homework does not entail doing so with someone’s help. However, such data can be straightforwardly explained by our semantic approach, provided that we allow accommodation of the sluiced question’s existential presupposition, along similar lines to our explanation for (19).

In general, we propose that the nature of the remnant is behind whether any sort of accommodation is required. Remnants like when and where correspond to implicit arguments in the denotation of an eventive antecedent, since events must happen at certain times and places in any world. Likewise for what in (14): every eating event presumably includes an object of eating. Sprouting remnants with contentful head nouns like what time last Tuesday or in which room, on the other hand, require some accommodation, for the reasons discussed above: not every event will necessitate such a component, and therefore, unless already provided by the prior discourse, such information will need to be accommodated.¹⁰

To summarize our proposal, in this section we sketched a focus-based account, where sluicing is possible provided that the antecedent and sluice have the same focus-theoretic propositional content. In §4 we will compare this proposal with Merchant’s (2001) influential e-GIVENness account, which is also focus-theoretic. We will show that in many cases, the two accounts achieve similar results, but that our account allows for wider overall coverage of data.

In the following section, we show in detail that Q-equivalence approaches to identity in ellipsis licensing face serious obstacles. In the process of making this case, we will introduce more complex cases of sluicing and sprouting. We will show how our proposal captures these cases below.

3.1 On empirical motivations for Q-equivalence

3.1.2 Barros (2013) and the Answer Ban

In this section we highlight an additional argument put forth in Barros (2013) for Q-equivalence, and present novel empirical evidence that challenges it.

Barker (2013) describes a generalization dubbed The Answer Ban, where the sluicing antecedent cannot provide an answer to the sluiced question. In (28), the antecedent Jack left provides an answer to the sluiced question who left?, and therefore sluicing is ruled out:

(28)	*Jack left, but Sally doesn’t know who left.

Barros (2013) argues that the Answer Ban follows from Q-equivalence approaches. Following Roberts (2012), Questions under Discussion (QuDs) are live questions in discourse, which interlocutors are committed to answering. Once a question is answered, it is no longer a live QuD. If sluicing requires anaphora to QuDs (i.e., if sluices must be semantically identical to QuDs), it follows that the antecedent cannot have already answered the question raised by the sluice—because in that case there would be no live QuD for the sluice to be anaphoric to. Consequently, Answer Ban violations are correctly ruled out on the grounds that the sluice lacks a semantically identical antecedent. Data supporting the Answer Ban, then can be seen as additional empirical evidence in favor of Q-equivalence.

We present new data here that undermines this argument. Example (29) shows that sluicing may obtain even when the required QuD has, in fact, already been answered in the discourse. Instead, what seems to be important is that the antecedent itself cannot address the sluiced question, but prior discourse may. Note, importantly, QuDs are only live questions if they have not yet been answered. Consequently, there can be no semantically equivalent QuD at the time of sluicing in the discourse in (29). (In Roberts’s 2012 terms, such a QuD has been “popped off the stack.”) Nonetheless, this example is judged as grammatical.

(29)	Jack left at 5 PM, so we know both that someone left, and who.

Barker’s Answer Ban generalization remains intact, since the antecedent doesn’t answer the sluiced question. Nonetheless, Barros’s explanation of the Answer Ban as stemming from Q-equivalence fails, insofar as QuDs must be askable questions in the relevant discourse, as per Roberts (2012). This is explicit in Roberts (2012), and Q-equivalence approaches such as AnderBois (2011), Barros (2014), and Weir (2014).¹⁵

Under our approach, on the other hand, in making no reference to QuDs, sluicing is correctly predicted to go through in examples like (29), and ruled out in examples like (28). In (28), ∪⟦antecedent⟧^f ∪⟦sluice⟧^f. This will be the case whenever the antecedent answers the sluice:

(30)	Deriving the Answer Ban:
	*Jack left, but Sally doesn’t know who left.
	a.	∪⟦Jack left⟧f = λw . Jack left in w
	b.	∪⟦who left⟧f = λw . ∃x (x left in w)
	c.	(30a) (30b)

On the other hand, examples such as (29) are predicted to be acceptable, because the sluice and antecedent are equivalent in our terms:

(31)	Deriving Answer Ban violations:
	Jack left at 5 PM, so we know both
	[CPA that someone left at 5 PM], and [CPE who left at 5 PM].
	a.	∪⟦someone left at 5PM⟧f = λw . ∃x (x left at 5PM in w)
	b.	∪⟦who left at 5PM⟧f = λw . ∃x (x left at 5PM in w)
	c.	(31a) ↔ (31b)

What’s important in our approach is that an antecedent with an indefinite correlate is semantically identical to the sluiced question. As we’ve defined the relevant notion of semantic identity, this is achieved.

3.2 Issues and QuDs: A closer look at Q-equivalence

In this section we give a more detailed description of the two main approaches to Q-equivalence, those based on issues raised by the Inquisitive denotation of a sentence, and those based on Questions under Discussion in the sense of Roberts 1996/2012.

Q-equivalence approaches take as their starting point the intuition that antecedents with expressions such as indefinites and disjunctions implicitly raise questions as to which alternative holds. For instance, in (32), an assertion like Sally ate something intuitively raises the question What did Sally eat?. Likewise, Sally ate either a hamburger or a hotdog raises the question Which of the two did Sally eat?. Relevantly, assertions with indefinites and disjunctions make for natural sluicing antecedents, with the indefinite or disjunction serving as the remnant’s correlate, (33):¹⁶

Sluicing is possible when the question denoted by the sluice is equivalent to the question raised by the antecedent (Ginzburg & Sag 2000; AnderBois 2011; Barros 2014; Weir 2014; Kotek & Barros 2018). The goal, then, is to determine precisely what question is raised by the antecedent.

We find two types of ways to approach this issue. For AnderBois (2011) et seq, the question raised by the antecedent is its Inquisitive-Semantic inquisitive denotation (called an issue, Groenendijk & Roelofsen 2009). This is the most explicit implementation of Q-equivalence, as it provides an explicit semantics in the Inquisitive Semantics framework, where antecedent assertions have compositionally derived question-like meanings.

In Inquisitive Semantics, a sentence is a proposal to update the common ground, and may be inquisitive, informative, or both. The informative contribution of a sentence, S, is its classical denotation, whereas a sentence’s inquisitive contribution, [S], is a multi-alternative proposal, raising an issue as to which alternative that it proffers we should update the common ground with. AnderBois (2011) provides the following semantics which achieves inquisitive denotations of this sort for sentences with indefinites (e.g., sluicing antecedents).¹⁷

In a toy model with two individuals, a and b, a sentence like someone left has the following inquisitive denotation: { that a left, that b left }. This is the same as the inquisitive denotation of a wh-question of the form Who left?.

Inquisitive mutual entailment is proposed as the relevant semantic condition on sluicing, requiring that the inquisitive denotation of the antecedent and the sluice be mutually entailing. Given two sentences, A, and E, A entails E if for every alternative, α, in [A], there is some alternative, β in [E] that α entails.

(35)	Symmetric inquisitive entailment condition on sluicing:
	TPE can only be elided if there is some salient antecedent CPA such that:
	a.    CPE |= CPA, and
	b.    CPA |= CPE

Of course, if two inquisitive denotations are identical, they will be mutually entailing, so sluicing is predicted to go through given a simple antecedent/sluice pair like Someone left, but I don’t know who.

Alternatively, and more commonly, the question raised by the antecedent might be the QuD relevant in the context, in the sense of Roberts 1996/2012 (cf Büring 2003; Barros 2012; 2014; Weir 2014). Following Roberts (2012), we take QuDs to be semantico-pragmatic objects—live questions in a discourse with interrogative force. Their role in discourse is to shape the flow of information exchange, as interlocutors engage in the cooperative task of addressing the QuD. The QuD may be made salient implicitly or explicitly (e.g., by asking a direct question).

However, implementations of QuD-based accounts are largely proof of concept, often taking a particular QuD for granted, but failing to address how the QuD actually comes about. An exception is Barros (2014), which provides an explicit algorithm for calculating the current QuD raised by an antecedent in an ellipsis construction:¹⁸

This algorithm can apply in simple cases to derive semantic identity and correctly predict licit cases of sluicing:

The QuD raised by the antecedent CP_A in (33a) is calculated to be as in (37c): ‘What Sally ate?’ Q-equivalence then requires that this question meaning be identical to the meaning of the sluiced question CP_E. This is indeed the case in (33a), and therefore sluicing is correctly predicted to be acceptable in this case.¹⁹ However, heuristic approaches are explicitly so—they go a step further than intuitionistic approaches, but are just heuristics after all, sidestepping important questions as we will see.

Despite the intuitive appeal of these approaches, in what follows we raise a conceptual challenge and further empirical challenges to Q-equivalence. These ultimately lead us to reject these approaches to semantic identity, and advocate for a return to a focus-theoretic approach.

3.3 A conceptual challenge

Recall again the case of sprouting: sluicing which takes place in the absence of a correlate.

In these examples, there is no indefinite or disjunction correlate with an issue raising capacity in the antecedent. Moreover, different issues or QuDs must be raised by the antecedent to license ellipsis in each one of the cases illustrated in (38a–b). We must therefore ask how the antecedent makes salient or raises any of these (possibly infinitely many) imaginable issues.

For AnderBois (2011) et seq, this is done through the process of issue bridging, which is explicitly designed to allow different issues to be relevant, depending on the nature of the sprouted continuation. Issue Bridging is a form of accommodation, where the sprout determines what the relevant issue or question must have been to license the sluice.²⁰ AnderBois (2011) appeals to existential quantification over events in these cases, so that a sentence like Sally left, has an inquisitive denotation consisting of alternatives varying with respect to values for an event variable.

A subsequent sprout of the form when Sally left determines that the relevant issue is one whose alternatives vary with respect to choices of times at which Sally may have left. Accommodation of this issue allows the alternatives in (39) to be re-sorted along the relevant dimension, yielding an issue sufficiently similar to the sluice to license ellipsis:

Barros (2014) adopts a similar set of assumptions in a QuD approach to Q-equivalence, where the accommodated presuppositions of a particular sprout on a case-by-case basis have consequences for the interpretation of the antecedent, with corresponding consequences for which QuDs the antecedent may raise.

At this point, the reader may suspect that this process of accommodation/Issue Bridging is not unlike the proposal for accommodation we have argued for in §2.2 for examples such as (19) and (21). However, here we highlight a crucial distinction between the two views.

Importantly, in both AnderBois’s Inquisitive implementation, and in QuD implementations, what is accommodated is a particular discourse structure—one where the antecedent in context did in fact manage to raise the accommodated QuD or issue. Only once this state of affairs is accommodated, has the antecedent managed to raise a QuD or issue capable of serving as the antecedent for the sprout.²¹

We argue that this seems intuitively incorrect when it comes to sprouting. There is no sense, for instance, in (38b), that the antecedent is at all responsible for raising the question of when Sally left. In AnderBois’s (2011) Inquisitive approach, issue bridging renders the inquisitive denotation of the antecedent equivalent to a question about when Sally left, but such a hypothesized inquisitive denotation is at odds with intuitions about whatever issues (if any) the sentence Sally left may raise.

Instead, we argue that it is the sprout, and not the antecedent, that is responsible for raising the relevant issue.²² This raises the following question:

Our response to this question is that the antecedent is in fact not responsible for raising any questions/issues at all.

More precisely, although it is clearly possible for antecedents to raise issues—as is the case in sentences containing indefinites and disjunctions—we argue that they need not necessarily be responsible for raising the sluiced issue. This follows if sluicing is simply not anaphoric to QuDs/issues or any question-like meanings.²³ As a consequence, Q-equivalence theories contain a fatal flaw: they crucially rely on an object—the issue/QuD raised by the antecedent—that may not always exist at all, or in the right form.

In the next section, we discuss five cases in which the antecedent cannot or should not be thought of as raising a salient issue/QuD which can then be used to calculate semantic identity, but nonetheless sluicing is possible. We conclude that any approach that ties ellipsis licensing to a particular question/issue raised by the antecedent faces very serious challenges.

3.4 Five empirical challenges

3.5 Interim summary

To summarize the discussion in this section, Q-equivalence approaches attribute ellipsis licensing to QuDs/Issues raised by the antecedent. We began this section by surveying two empirical arguments which have been proposed in the literature in favor of Q-equivalence, from sluicing with doubly-negated antecedents (AnderBois 2011) and from the Answer Ban (Barros 2013). We diffused both arguments and concluded that neither in fact motivates Q-equivalence.³¹,³²

We additionally raised several new empirical challenges to Q-equivalence: We showed that non-issue antecedents can license sluicing, resolved questions can license sluicing, and a single antecedent can license multiple sluices. We moreover spelled out challenges from else modification and from contrast sluicing. In each of these cases, extant Q-equivalence approaches run into trouble.

We acknowledge that it may be possible to address some—or perhaps even all—of these challenges by amending the current Q-equivalence approaches in some way or another.³³ For example, Onea’s (2016) view of QuDs, which decouples them from speaker intentions, may account for cross-speaker sprouts and non-at-issue antecedents. Alternatively, if we adopt Ginzburg’s (1994) view of QuDs, more than one QuD may be simultaneously available in the context, explaining antecedent sharing. Issue Bridging, within AnderBois’s (2011) Inquisitive Semantic account, may account for some cases of sprouting. However, no one current Q-equivalence account possesses all of these properties, and we do not see an obvious way to extend one account to meet all of the challenges we have posed.

Moreover, we have argued, on conceptual grounds, that Q-equivalence makes irrecoverably bad predictions about the shape of the discourse: it is simply not the case that antecedents must raise a question or issue, which then licenses a sluice. This was especially clear in cases of sprouting, where the question is intuitively accommodated posthoc, once the sprout is uttered, and in cases of cross-speaker sluicing, but we argue that this is true for all cases of sluicing. That is, we have argued that we shouldn’t necessarily place the burden of raising an issue/question on the antecedent, contra the very foundation of Q-equivalence approaches.

At the same time, we showed how our focus-based proposal (8), repeated below, accounts for all of the data and challenges presented here.

Crucially for our account, whether it is the antecedent or the sluice that is responsible for raising the relevant issue/question—indeed, whether a relevant issue/question has been raised at all—is an orthogonal question to whether ellipsis can be licensed in the clause.

Like others, our account must resort to accommodation to explain some cases of sprouting. However, we argue that this is implemented in our account in a principled way: accommodation is triggered by a contentful head noun in a remnant, which was not supported by previous context. Unlike Issue Bridging or the QuD-based version of this account, there is crucially no need to assume post-hoc that the accommodated meaning was somehow already raised by the antecedent. We take this last step, which must be assumed by Q-equivalence accounts but not by focus-based ones, to be a fatal flaw in the former type of accounts, regardless of any details of the accounts.

We conclude that a unified theory of semantic identity in ellipsis, encompassing clausal ellipsis, VP ellipsis, and NP ellipsis, is both better motivated and more parsimonious than the alternative, and therefore to be preferred. In §5 we show how our proposal in (8) extends to VP ellipsis, and, more generally, to deaccenting.

4.1 Merchant’s (2001) truth conditional mutual entailment

Having argued against Q-equivalence approaches, we now return to Merchant’s (2001) influential focus-theoretic implementation of semantic identity in ellipsis. As we noted above, our proposal (8) is inspired by—and is very similar to—Merchant’s account. In this section, we show that Merchant’s proposal runs into trouble in a subset of sluices which are handled straightforwardly by our account. A second challenge for Merchant’s (2001) account, from VP-ellipsis with relational opposite predicates, will be discussed in §5.

Merchant’s (2001) proposal builds on theories of focus and deaccenting (prosodic reduction). Following Rooth (1992a), ellipsis can be seen as a form of radical deaccenting—that is, deaccenting and ellipsis form a natural class, as two cases of redundancy reduction.³⁴ As a form of redundancy reduction, therefore, conditions on deaccented material would be expected to apply to ellipsis constructions, as well. However, Rooth shows that the conditions on deletion appear to be stronger than those relevant for prosodic deaccenting. To account for this, Rooth proposes two distinct redundancy relations; one which applies to both ellipsis and deaccenting, and one which applies only to ellipsis, essentially requiring syntactic identity between the elided structure and some linguistic antecedent (in the spirit of e.g., Fiengo & May 1994, among others).

Merchant (2001) defends the claim that there is no syntactic parallelism condition at work in ellipsis, and proposes, instead, a semantic parallelism condition on ellipsis which is stronger than that for deaccenting.³⁵ Instead of having a syntactic condition that applies only to ellipsis, and a semantic parallelism condition that applies to both deaccenting and ellipsis, we end up with two semantic parallelism conditions: a weaker one for deaccenting, and a stronger one for ellipsis.

Merchant adopts the theory in Schwarzschild (1999), where a constituent, XP_E, may be deaccented provided it is GIVEN. GIVENness is defined in (58):

For example, VP_A in (60b) counts as GIVEN, since VP_A entails F-clo(VP_E). (Deaccenting is represented throughout in small font.)

The condition on ellipsis is dubbed e(lliptical)-GIVENness, and essentially requires GIVENness to be checked twice; first, the ellipsis constituent must be GIVEN with respect to its antecedent, and likewise, the antecedent must also be GIVEN with respect to the ellipsis constituent.

Merchant treats traces of wh-phrases in sluiced TPs as ∃-bound variables (see also Schwarzschild 1999). For a simple sluice like that in (62), F-clo(TP_E) entails its antecedent TP_A, and F-clo(TP_A) entails TP_E, satisfying the FCE.³⁶

4.2 e-givenness reconsidered

Taking the union of the Roothian focus-semantic value of some XP, as we propose in §2, comes very close to Merchant’s (2001) appeal to Existential Focus Closure.³⁷

For the most part, e-GIVENness will achieve the same results as our account has. However, e-GIVENness falls short for sluices with quantified correlates.

Consider first cases of multiple sluicing (Takahashi 1994), where more than one remnant survives ellipsis. In (64a–b) we see examples of multiple sluicing in Russian and English, respectively. See Lasnik (2014) and Kotek & Barros (2018) for a discussion of the felicity of English multiple sluicing.

Examples (64a–b) involve a quantified antecedent on its surface scope (∀ > ∃) reading, with a pair-list multiple question in the sluiced continuation. These antecedent/sluice pairs in pair-list multiple sluices fail to be mutually entailing with their quantified antecedents. We show this here for example (64a):

The same holds true for any pair-list multiple sluice whenever the antecedent has a wide-scope universal: ∃-closure or Focus closure of wh-traces in TP_E, as assumed by Merchant (2001), will inevitably lead to a failure of mutual entailment.³⁸

We entertain next a possible solution to this problem under Merchant’s account, which we show faces problems of its own: if we take quantifiers in examples (64a–b) to be F-marked, we predict sluicing to go through. In that case, all we need is to be able to find quantifiers to plug in in place of everyone and someone in the antecedent (65a), which can lead to semantic identity with the clause in (65b)—a task that we are easily able to perform. However, this approach faces two problems.

First, there is no cue in the prosody suggesting that quantifiers in the antecedent are F-marked. (Or, in other words, that all such sluices are necessarily contrastive.) Worse, this proposal leads to over-generation. There is nothing stopping this procedure from going through in examples involving inverse scope in the antecedents, such as (66–67) from Grebenyova (2009) and Kotek & Barros (2018), respectively. These are ungrammatical but would be predicted to be acceptable under this account.³⁹ See Kotek & Barros (2018) for a detailed recent account of this restriction.

The problem of quantified antecedents extends beyond multiple sluicing to sluices with unambiguously quantificational correlates. We show this in example (68), where e-GIVENness is not met, and hence sluicing is incorrectly predicted to be impossible. This problem will extend to any remnant with a non-existential correlate.

Under our approach, the multiple sluicing facts and those with quantified correlates are predicted. We adopt the approach to pair-list questions in Dayal (1996) (see also Kotek 2019): pair-list questions denote families of questions.⁴⁰

(69)	Representing multiple questions:
	Everyone was dancing with someone, but I can’t recall who was dancing with whom.

As we can see, each alternative in the set is a graph of the dance-with relation. This is the set of worlds where a, b, c, and d each danced with someone. The union of the multiple sluice meaning, then, is equivalent to the union of the proposition everyone danced with someone, ∪⟦Everyone danced with someone⟧^f. As a result, we correctly predict multiple sluicing to be possible in (64a–b).⁴¹

This adds to existing arguments against a characterization of the semantic condition on sluicing in terms of truth conditional mutual entailment. In the next section, we see how the FCE leads to an over-generation problem, following observations in Hartman (2009). We show that our proposal does not face the same problem.

To account for the data, we entertain the idea that the semantic licensing condition on ellipsis is exactly the same as the condition on deaccenting. This is not a novel claim, but the consensus in the literature, following Rooth (1992a) and Merchant (2001), is that the semantic conditions on ellipsis and deaccenting are distinct. Fox (2000), on the other hand, holds that the semantic conditions on deaccenting and ellipsis are the same. Here, we defend this claim, and illustrate how our proposed semantic condition in (8) may function as a general condition on redundancy reduction, encompassing both ellipsis and deaccenting.

5.1 A generalized account of ellipsis licensing

Q-equivalence approaches imply a conceptually unattractive conclusion about identity in ellipsis: that VP-ellipsis and sluicing must be subject to independent licensing conditions (Chung et al. 1995; 2010; AnderBois 2011). Conversely, focus-based accounts as in Merchant (2001) have broad empirical coverage, deriving VP-, NP-, and TP-ellipsis from the same principles.⁴² In this section we show how to extend our proposal to achieve similar coverage, and in fact improve on, e-GIVENness.

Here we extend our proposal to VP-ellipsis, and demonstrate how it accounts for a puzzle noted in Hartman (2009). Hartman points out a set of cases where, for VP-ellipsis, e-GIVENness over-predicts identity when relational opposites (such as beat and lose) are involved.⁴³

e-GIVENness is met in (70a–b), since it is always the case that if someone lost to someone at chess, then someone beat someone at chess, and vice versa.⁴⁴ Ellipsis is therefore incorrectly predicted to be possible in (70).

Hartman appeals to semantic equivalence to prevent these cases. (See Hartman 2009 for details.) Comparing the denotations of VP_A and VP_E rules out VP-ellipsis, since the two are not semantically equivalent:

Our approach in (8) can be generalized to cover VP-ellipsis in the same way as Hartman’s proposal. We provide this generalized condition on ellipsis in (72):

This generalized proposal can explain Hartman’s examples, as shown in (73):⁴⁵

Since the denotations in (73a–b) are not equivalent, our generalized condition achieves the same results as Hartman’s account. Our proposal, then, achieves the same coverage as e-GIVENness—and improves on it by dealing with relational opposites, by virtue of making reference to non-propositional content.⁴⁶

5.2 A theory of redundancy reduction

Can we go even further? Hartman (2009) claims that while ellipsis with relational opposites is impossible, deaccenting in parallel cases appears to be possible, providing the evidence in (74). Consequently, he argues that the licensing conditions on ellipsis are stronger than those on deaccenting, where semantic equivalence is an ellipsis-specific requirement that deaccenting is not subject to.

We agree with Hartman that there is a sharp contrast in acceptability between the elliptical and deaccented versions of the sentences in (74). This is consistent with the Roothian idea that the parallelism conditions on ellipsis are both distinct from and stronger than those on deaccenting—a claim we argue against below. However, to our ear, (74d) is not fully acceptable, as deaccenting the relationally opposite predicate lost strikes the hearer as surprising. We concede that deaccenting in (74b) is better than in (74d), but suspect this is because in (74b), the deaccented predicate belong to is not in relational opposition to its antecedent own.

We turn now to explaining why this is relevant to acceptability of deaccenting in our account of the differences between deaccenting and ellipsis. When we cast the empirical net more widely, it does not appear to be the case that, in general, deaccenting with relational opposites yields acceptable results:

One way to account for the data in (75) is to assume that the semantic parallelism condition on ellipsis is also active in deaccenting (contra Hartman). This is precisely what is proposed in Fox (2000).⁴⁷ Our condition in (72) can be easily extended to deaccenting:

The puzzle is why deaccenting with relational opposites, while generally unacceptable, is nonetheless more acceptable than ellipsis under the same conditions.

In terms of Fox’s (2000) proposal, this follows from constraints on accommodation. Specifically, redundancy reduction requires an antecedent. When a suitable antecedent for some deaccented or elided phrase is missing in the context, as in the cases of relational opposites above, such an antecedent can be accommodated. Importantly, accommodation must be triggered (to adopt Fox’s terminology) by overt phonetically reduced material. In the case of deaccenting, the presence of overt reduced material that lacks a parallel antecedent triggers the requisite process of accommodation. In ellipsis, on the other hand, the trigger is missing from the speech signal. As a result, accommodation does not take place, leading to unrecoverability/unacceptability. We spell this constraint out in (77):

We propose that this process is also behind the pattern we see in (74), where (74b) is more acceptable than (74d). Specifically, in (74b) the deaccented predicate has an advantage over the deaccented predicate in (74d) in that it is not in relational opposition with its antecedent predicate. We assume that this difference aids in accommodation, and is responsible for the difference between these two examples.

At this juncture, we revisit Hartman’s concern regarding whether his semantic identity condition on VP-ellipsis could be extended to sluicing. The challenge from relational opposites for e-GIVENness in VP-ellipsis stems from the fact that e-GIVENness renders XP meanings propositional via existential closure in the calculation of identity, as would be required to check mutual entailment. Hartman’s semantic equivalence condition makes direct reference to VP predicate meanings, avoiding the problem of mutual entailment. Our proposal achieves Hartman’s results in the same way, as the meanings we compare are not propositional for VPs.

Given this solution, however, we encounter a problem: the same issue that plagues e-GIVENness in VP-ellipsis persists in sluicing, since ∃-closure of the sluice and the antecedent would be mutually entailing (if someone lost at chess then someone won at chess and vice versa). Importantly, our proposal runs into the same problem as e-GIVENness, since the set of worlds where someone lost at chess is identical to the set of worlds where someone won at chess.

As a solution, Hartman suggests comparing the meanings of the predicate abstract created by wh-movement in the sluice to that of the predicate abstract created by scoping the correlate out of the TP in the antecedent. This would give us the right sort of objects to compare, and would rule out sluicing with relational opposites in much the same way as with VP-ellipsis, as in (71) above.⁴⁸

Although Hartman’s solution works, it faces a conceptual challenge. Hartman’s semantic identity condition is intended to exist alongside Rooth’s (1992a) focus-theoretic parallelism condition on deaccenting. In short, ellipsis is licensed just in case that conditions on deaccenting are met (satisfying Roothian focus-theoretic parallelism) and, in addition, Hartman’s semantic condition is satisfied. This is justified in part by the putative need to posit two distinct parallelism conditions, one for deaccenting, and one for ellipsis.

As our generalized focus-theoretic proposal can extend to redundancy reduction operations beyond ellipsis, in the spirit of Rooth (1992a); Tancredi (1992)—with differences between ellipsis and deaccenting explained by differences in the availability of accommodation, following Fox (2000)—we believe that reducing Hartman’s two distinct parallelism conditions into a single one would lead to a more parsimonious, and therefore a conceptually and intuitively sounder, account.

The solution that saves our approach in the face of data like in (78) comes free, once we adopt the assumption in Schwarzschild (1999) that conditions on accent placement are meant to apply to all levels of structure in an utterance. The challenge from clause-sized ellipsis is that even in an Alternative Semantic implementation like ours or Hartman’s (2009) implementation, we’re forced back to comparing propositional meanings, reintroducing the problem posed by relational opposites.

However, Schwarzschild’s (1999) definition of GIVENness (see (58) and (59)) plays a part in a larger system of constraints governing the distribution of F-marking in the syntax, which is taken to be free, subject to the constraints in (80).⁴⁹

Importantly, in Schwarzschild’s (1999) proposal, any syntactic constituent is subject to these constraints in an utterance.⁵⁰

As we intend to account for both ellipsis and deaccenting, we contend that our generalized condition in (76) should replace Schwarzschild’s (1999) definition of GIVENness in a general theory of accent placement and redundancy reduction. For explicitness, assume Schwarzschild’s (1999) theory otherwise remains intact with respect to the constraints in (80), but with our (76) replacing the Schwarzschildian definition of GIVENness in (58). It follows, then, that sub-constituents of elided constituents are subject to the constraints in (80), and by extension, to our semantic identity condition in (76).

In effect, for some reduced (elided or deaccented) XP, α, not only must α satisfy the constraints in (80), and thereby, also, GIVENness/our (76), but so must all of α’s subconstituents.⁵¹ As a consequence, in TP-ellipsis, our parallelism condition in (76) must be checked at TP as well as its subconstituents, including VP. We summarize this in (81):

Like for e-GIVENness, iterative checking is superfluous in simple cases under our account as well, as shown in (82):⁵²

This requirement becomes crucial only in cases such as the ones of relational opposites discussed in this section. As shown above, in such cases, our condition is met at the TP level in (78). However, since the parallelism condition must be checked at the level of every subconstituent as well, VPs will also be compared. (78) will be correctly ruled out since the union of ⟦lost at chess⟧^f and the union of ⟦won at chess⟧^f are not equivalent at the VP level. In other words, TP-ellipsis with relational opposites in (78) is ruled out for precisely the same reason that VP-ellipsis was in (73). We therefore rules out clause-sized ellipsis with relational opposites, a desirable result, fitting within a general and unified theory of ellipsis and of redundancy reduction in general.

5.3 Summary

We generalized our approach beyond sluicing to account for patterns in VP-ellipsis, in the spirit of Merchant (2001), who provides a unified theory of semantic identity in ellipsis. We then followed Fox (2000) in assuming that both sluicing and deaccenting are subject to this same semantic identity condition. The empirical differences in the distribution of these two redundancy reduction operations, which had led Rooth (1992a) to propose two distinct conditions, are instead explained by appealing to accommodation as in Fox (2000). The result is a better motivated more parsimonious proposal which achieves wider empirical coverage than the previous accounts that it builds on. The generalized proposal is repeated in (83–85).

Finally, note that while we have laid out a theory of parallelism in redundancy reduction, we have not proposed a more general theory of accent placement. In short, our parallelism condition in (83) could be seen as replacing the definition of GIVENness in Schwarzschild (1999), which itself plays a part in a more complex system governing the distribution of accent and deaccenting in English sentences. We leave exploring this more fully to future work.