Ellipsis licensing and redundancy reduction : A focus-based approach *

The focus of this paper is the characterization of the identity condition on sluicing. While the formulation of this condition remains an open issue, recent work suggests that sluices are anaphoric to an implicit question or issue that the antecedent raises in the discourse (“Q-equivalence approaches,” Ginzburg & Sag 2000; AnderBois 2011; 2014; 2016; Barros 2014; Weir 2014; Kotek & Barros 2018). We highlight several challenges to Q-equivalence accounts, and argue instead for a return to focus-based accounts (Rooth 1992a; Romero 1998; Fox 2000; Merchant 2001). Under such an approach, antecedents are importantly not responsible for raising any particular issue/question themselves, a point we show to be a critical challenge to Q-equivalence accounts. We propose instead that sluicing is possible provided that the antecedent and sluice have the same focus-theoretic propositional content. We show that this account is similar to, but improves upon, Merchant’s (2001) influential e-givenness account. We extend this account to cases of VP ellipsis, and moreover argue in support of the idea that the theory of ellipsis licensing should be integrated into a more general theory of redundancy reduction. In other words, that the semantic condition on identity in ellipsis is the same as the semantic condition on deaccenting (Rooth 1992a; Tancredi 1992). We propose a generalized condition on redundancy reduction, which may replace Schwarzschild’s (1999) givenness condition.


Introduction
Sluicing is clausal ellipsis in a wh-question, leaving only the wh-phrase overt (Ross 1969;Chung et al. 1995;Merchant 2001, among others), as in (1a).For concreteness, we adopt the standard analysis in (1b), where sluicing involves wh-movement followed by PF-deletion/non-pronunciation of TP (Merchant 2001 and many others). 1 Following Merchant, we refer to wh-phrases left overt in sluicing as remnants.Remnants typically correspond to some indefinite XP in the antecedent, the remnant's correlate.(Throughout, strikethrough represents unpronounced material.Here, the correlate is someone and the remnant is who.) (1) A simple example of sluicing in English: a. Sally called someone, but I don't know who.b.Sally called someone, but I don't know who i [ TP Sally called t i ].
Ellipsis is a form of redundancy reduction (Rooth 1992a), one of several mechanisms provided by natural language to mark linguistic material as redundant/recoverable 1 Although what we say below will be largely independent of this assumption.
Glossa general linguistics a journal of Barros, Matthew and Hadas Kotek. 2019.Ellipsis licensing and redundancy reduction: A focus-based approach.Glossa: a journal of general linguistics 4(1): 100.1-36.DOI: https://doi.org/10.5334/gjgl.811 (alongside pronominalization and prosodic reduction, i.e., deaccenting).Intuitively, the missing content in an ellipsis construction must be, in some sense, identical to some salient antecedent in the immediately preceding discourse (Hankamer & Sag 1976).In (1), the string Sally called in Sally called someone makes this same string redundant in the sluiced continuation, licensing its omission.In this paper we explore the properties of this identity licensing condition on ellipsis.Despite the appeal of this intuitive description of the licensing condition, there is currently no consensus on its precise nature (Chung 2013;Barros 2014;Weir 2014, inter alia).Some authors propose to formulate this condition in terms of semantic equivalence, where the literal interpretations of the antecedent and the elided clause are synonymous in some sense (Hardt 1993;Ginzburg & Sag 2000;Merchant 2001; Barros 2014, a.o.).Others state this condition in terms of syntactic equivalence, where the elided structure must match that of its antecedent (Ross 1969;Chung et al. 1995;Chung 2006;Merchant 2013, a.o.).Others yet propose a hybrid condition, involving some degree of syntactic identity alongside a semantic identity condition (e.g.Rooth 1992a;Romero 1998;Chung 2006;2013;Chung et al. 2010;AnderBois 2011;2014;2016;Merchant 2013;Weir 2014).
A growing consensus is that a hybrid condition is needed, such that a limited degree of syntactic identity is required,2 alongside some semantic condition (Merchant 2005;Chung 2006;2013;AnderBois 2011;Weir 2014, a.m.o.). 3 Starting with AnderBois (2011), the literature has increasingly adopted the view that the correct semantic condition is one where sluicing is anaphoric to some abstract question or issue that the antecedent raises in discourse (Ginzburg & Sag 2000;AnderBois 2011;2014;2016;Barros 2014;Weir 2014;Kotek & Barros 2018).The basic idea behind the AnderBoisian (henceforth Questionequivalence or Q-equivalence) approach is that sentences with indefinites or disjunctions introduce implicit questions into the discourse, which may then serve as semantic antecedents for a sluiced sentence.In (1), Sally called someone implicitly raises to salience the question Who did Sally call?.This implicit question is similar enough to the sluiced question Who sally called?, licensing the ellipsis in (1).
In this paper, we focus on the semantic component of the identity condition on ellipsis.Our main claim is that a proposal along the lines of Merchant's (2001) focus-theoretic approach to ellipsis licensing is on the right track.We offer our own formulation of such a focus-theoretic approach, which we believe improves on Merchant's original proposal.We argue against the increasingly popular Q-equivalence approaches on empirical as well as conceptual grounds.While we do not conclusively show that such accounts cannot be rescued, we argue that they lack motivation and face substantial problems.Finally, we entertain the idea that the theory of ellipsis licensing should be assimilated into the theory of redundancy reduction more broadly, focusing on a comparison with deaccenting.
In the remainder of the paper, we first spell out our focus-based proposal in §2, which is similar in spirit and coverage to Merchant's (2001) influential e-givenness proposal.We concentrate in particular on sluicing, as our starting point.In §3 we argue that there is no empirical motivation for Q-equivalence approaches, and additionally highlight several conceptual challenges for such approaches.We show that our focus-based approach is not susceptible to these challenges.In §4, we discuss Merchant's (2001) account and compare it to our own.We highlight a challenge to Merchant's proposal from sluicing with quantified correlates, which our proposal can better handle.In §5, we generalize our account to cases of VP-ellipsis, where we illustrate along the way another advantage of our account over Merchant's.We conclude by suggesting that the theory of ellipsis licensing should be assimilated into the theory of redundancy reduction more broadly-specifically, that the semantic condition on identity in ellipsis is the same as the semantic condition on identity in deaccenting.We propose a generalized condition on redundancy reduction, building on our proposal in §2, and suggest that it may replace Schwarzschild's (1999) givenness condition.

A focus-based proposal
We begin by presenting the main proposal that we defend in this paper.This is a focustheoretic account of identity for ellipsis licensing, inspired by similar proposals by Schwarzschild (1999) and Merchant (2001) et seq.Our main goal in this paper is to argue for a focus-based approach and against Q-equivalence ones.We spell out our variant of the focus-based approach here for concreteness, focusing on sluicing to allow for direct comparison with Q-equivalence accounts.We extend our discussion to VP-Ellipsis and deaccenting in §5.

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.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.
(3) Sally called someone, but I don't know who i [ TP Sally called 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).
(4)  We furthermore adopt the standard assumption that propositions denote sets of worlds that satisfy certain truth conditions: (5) The denotation of a proposition: ⟦Sally ran⟧ o = λw .Sally ran in w ⇝ the collection of all of the worlds in which Sally ran.
Finally, we introduce a union operation over propositions, ∪.This operation will be useful when we present our proposal in (8) below.
( ⇝ the collection of all of the worlds in which either Sally ran or Mary ran (or both).

Proposal
Our generalized proposal, which will be motivated in greater detail in §5, is given in ( 7).
(7) A generalized licensing condition for redundancy reduction: XP E may be reduced (elided or deaccented) provided that it has a salient antecedent, XP A , and 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: (8) Ellipsis licensing condition (sluicing, to be expanded): Sluicing may apply in CP E provided CP E has a salient antecedent, CP A , and the set of worlds used to construct the alternatives in ⟦CP E ⟧ f ↔ the set of worlds used to construct the alternatives in ⟦CP A ⟧ f .
For most purposes, this amounts to the following:5 (9) The licensing condition on sluicing, in brief: 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.
(10) 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: 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: Here, we appeal to a process of accommodation, much like the one appealed to by other accounts of sprouting in the literature. 9For concreteness, we adopt the definition of accommodation in (20).This allows the antecedent to entail the sluiced question's existential presupposition.
(20) Accommodation (Lewis 1979: 340): If at time t something is said that requires presupposition P to be acceptable, and if P is not presupposed just before t, then, ceteris paribus and within certain limits, presupposition P comes into existence at t.
In (19), the sluice presupposes that all relevant Sally-leaving worlds are Sally-leaving-withsomeone 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: a. Jack finished his homework, but I don't know with whose help he finished his homework.b.She went to the movies, but I don't know who with she went to the movies.c.He put in a bid, but I don't know on who's behalf he put in a bid.
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.

Revisiting Q-equivalence
In this section, we argue that there is little motivation for the move to Q-equivalence approaches.We demonstrate this by first revisiting the empirical motivations in AnderBois (2011), and recap the results reported in Collins et al. (2015) that challenge AnderBois's 2011 data.We then consider an additional argument for Q-equivalence from Barros (2013), and present novel data challenging Barros's 2013 conclusions.Our conclusion is that Q-equivalence approaches are empirically unmotivated.
Importantly, Q-equivalence approaches, following AnderBois (2011), would have it that sluicing (and following especially Weir 2014, clausal ellipsis more generally) is subject to a distinct semantic identity condition from VP ellipsis and NP ellipsis that makes crucial reference to question meanings (a two-pronged approach).11This much is intuitive on an analytical level; sluices are questions, so perhaps it makes sense that their antecedents should also be questions.12However, a unified theory of semantic identity in ellipsis in general (encompassing clausal ellipsis, VP ellipsis, and NP ellipsis) is more parsimonious on its face, and the idea that clausal ellipsis shares the same character as other (smaller) kinds of ellipsis also has intuitive purchase.We argue that in the absence of empirical motivations that force us to adopt a two-pronged approach, any theory that successfully provides a unified account of the data is to be preferred on (at least) conceptual grounds.
That this state of affairs obtains is what we show in this section.After demonstrating that Q-equivalence approaches lack empirical motivation, we proceed to highlight new empirical and conceptual challenges to such approaches.Importantly, we do not suggest that Q-equivalence approaches cannot be modified, elaborated, or complicated, to meet these challenges.We even suggest ways in which Q-equivalence approaches may be modified to meet some of these challenges (though we refrain from fully fleshing out such suggestions for space reasons).
We show, below, that it remains the case that there are no compelling empirical arguments supporting a split in semantic identity conditions for ellipsis-one for clausal ellipsis/sluicing, on one hand, and another for VP ellipsis and NP ellipsis, on the other.We moreover show that our account can be further extended to account for deaccenting.As such, complications of Q-equivalence approaches, elaborations, or modifications thereof, amount to empirically unmotivated moves to save a conceptually unnecessary analysis in the face of a conceptually and empirically better motivated alternative: our proposal here.2015) Collins et al. (2015) presents results that challenge AnderBois's (2011) empirical motivations for Q-equivalence.They nonetheless adhere to Q-equivalence as a means of licensing sluicing-despite stripping the force of AnderBois's empirical arguments, their experimental results undermining those arguments at every turn-for reasons that are orthogonal to our aims and which we will not repeat here.Here we will use the results in Collins et al. (2015) as undermining the empirical motivation for Q-equivalence, and providing support for our claim that a unified focus-theoretic semantic approach to ellipsis identity should be favored on conceptual grounds.

On empirical motivations for Q-equivalence
In empirically motivating Q-equivalence, AnderBois (2011) takes as a starting point the proposal in Merchant (2001), where the sluice is licensed provided it is e-given.The definition of e-givenness is provided below.(See additional discussion of Merchant's 2001 e-givenness in §4.) Focus Condition on Ellipsis (FCE, Merchant 2001: 26) a.
A constituent E can be deleted iff E is e-given.
b.An expression counts as e-given iff E has a salient antecedent A and, modulo ∃-type shifting, i.A entails F-clo(E), and ii.E entails F-clo(A) c. F-clo(α) is the result of replacing F-marked parts of α with ∃-bound variables.

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Deriving simple sluicing using Merchant's FCE: AnderBois (2011) makes the claim that the reliance on truth conditional semantics in Merchant's system makes the wrong prediction when it comes to antecedents with double negation.(Judgements as in AnderBois 2011.) and vice versa.Therefore, e-givenness is met.( 24a) is predicted to be grammatical, contrary to fact.This is a misprediction of Merchant's (2001) proposal.AnderBois (2011) uses such data as an empirical motivation for Q-equivalence.Specifically, AnderBois makes use of the fact that in the Inquisitive Semantics framework (Groenendijk & Roelofsen 2009), double negation is not semantically vacuous.Section 3.2 will spell out this proposal in greater detail.
Indeed, if the data in (24) really do bear on the analysis of sluicing, AnderBois's analytical move counts as an empirically well motivated one.However, Collins et al. (2015) report experimental results where participants rated sluices with doubly negated antecedents poorly, and importantly, just as poorly as those same examples without sluicing, 13 so that AnderBois's reported judgements with double negation do not bear on sluicing at all, but instead have to do with the oddness of double negation more generally.
Another sort of data AnderBois (2011) brings to bear on the issue of the semantic identity condition on sluicing comes from appositives.AnderBois highlights the following paradigm, where in (26a), sluicing fails when its antecedent (in brackets) is contained inside an appositive.In (26c), on the other hand, VP ellipsis is possible. (26) VPE, but not sluicing antecedents may be contained in appositives a. *Joe, [who once killed a man in cold blood], doesn't even remember who he killed in cold blood.
(Sluicing) b.Joe once killed a man in cold blood and he doesn't even remember who he killed in cold blood.c.Joe, who [murdered a man in cold blood], convinced Bill to murder a man in cold blood too.
(VPE) e-givenness fails to predict this asymmetry, as nothing about being contained in an appositive influences the truth conditional content of the antecedent in examples like (26a).AnderBois (2011) capitalizes on the observation, going back to Potts (2005), that appositive content is not at-issue, and assumes that non-at-issue content is non-inquisitive (i.e. has no issue-raising capacity).In other words, antecedents contained in appositive relative clauses fail to raise a question which can serve as a Q-equivalent sluicing antecedent.VPE, on the other hand, is claimed to be subject to a distinct licensing condition, taken to be e-givenness in AnderBois (2011).Collins et al. (2015) reports on the results of an experimental study that showed that sluicing was in fact possible when the antecedent was contained in an appositive.An important factor in predicting acceptability is whether the indefinite correlate and whremnant have the same informativity status (to borrow the term from Collins et al. 2015).Syntactically, if the correlate has a contentful head NP (and is not just an indefinite pronoun, such as someone, for instance), then the wh-remnant should have one as well (or they should both lack such a contentful head noun).(This generalization is independently made in Dayal & Schwarzschild 2010.)Examples like those in ( 27) were rated significantly more acceptable by experimental participants than those like AnderBois's (2011) (26a), where the sluicing remnant and its correlate mismatch in informativity.(See Collins et al. 2015  In other words, once the preference for matching in informativity across remnants and correlates is controlled for, sluicing becomes acceptable with appositive-contained antecedents.Collins et al. (2015) take their results as evidence that appositive clauses do, in fact, (contra AnderBois 2011) have the capacity to raise issues/questions, which may then serve as antecedents for sluices, provided that informativity is controlled for. 14Here, we adopt an alternative understanding of these results.Specifically, we argue that Collins et al.'s (2015) results undermine AnderBois's (2011) empirical arguments for positing a split in the identity conditions between VPE and sluicing, opening up an alternative understanding of the facts surrounding antecedents contained in appositives.

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). 15nder 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: 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.

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 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 multialternative 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).17AnderBois's (2011) inquisitive semantics: a. Atomic Formulas: 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.

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Symmetric inquisitive entailment condition on sluicing: Given a structure: CP E C 0 TP E TP E can only be elided if there is some salient antecedent CP A such that: a. CP E |= CP A , and b.CP A |= CP E 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 (36) A QuD-calculation algorithm ( 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. 19However, 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.

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

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Argument and adjunct sprouting: 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.20AnderBois (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. (39) [Sally left] = { e 1 is an event of Sally leaving, e 2 is an event of Sally leaving, … } 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: 8 20 e -e are events of Sally leaving at 5 PM, e -e are events of Sally leaving at 5:30 PM ,… 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. 21e 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. 22This raises the following question: (41)

A crucial question:
To what extent is the antecedent responsible for raising any particular issue/QuD, which can then serve to license ellipsis?
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. 23As 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.

(42) A crucial conclusion:
There is no compelling empirical evidence in favor of adopting Q-equivalence approaches to semantic identity for sluicing.An alternative unified focus-theoretic semantic identity condition capable of handling VPE and sluicing is conceptually and empirically more attractive.
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.

Five empirical challenges
3.4.1The Answer Ban and else modification In §3.1.2,we challenged Barros's (2013) empirical argument from Barker's (2013) Answer Ban in favor of Q-equivalence approaches by providing novel evidence showing that Q-equivalence approaches fail to predict the acceptability of sluicing in examples like (29), repeated below.
(29) Jack left at 5 PM, so we know both that someone left, and who.
The acceptability of sluicing in ( 29) is surprising under the view that the sluice must be semantically identical to some QuD that the antecedent makes salient; the first clause in (29) answers the would-be QuD, thereby precluding the question who left? from being a QuD in the discourse since it has been answered.As we showed in §3.1.2,focus-theoretic implementations of semantic identity do not run into this issue.
Here, we highlight that this challenge to Q-equivalence approaches is particularly problematic for QuD-based accounts that rely on Roberts's (2012) definition of what it means for a question meaning to count as a QuD in discourse: QuDs must be askable questions in discourse, and answered questions cannot be asked.As we alluded to in footnote 15 above, an anonymous reviewer suggests that it may be possible to re-cast Q-equivalence in terms of pure salience, so that even answered questions may be made salient enough to license sluicing.While such an analysis would circumvent the challenge our data in (29) raises, it would mark a significant departure from the standard assumptions in Q-equivalence treatments thus far.Such a proposal would hopefully lead to other novel empirical predictions for ellipsis licensing quite generally, as it would be important to motivate such a move beyond the need to deal with the Answer Ban.We will not attempt to pursue such an amendment or spell out its implications here.
Next, notice that in addition to (29), else-modification can also rescue would-be Answer Ban violations: (43)

Else-modification can rescue Answer Ban violations:
Chris knows that Jack left, but Sally doesn't know who else left.
Following Romero (1998), 24 else introduces an additivity presupposition into the discourse: the question in the sluice in (43) presupposes that there is some answer to the question Who left?, other than Jack left, that is true, and is a request for the hearer to provide that true answer.When this additive presupposition is explicitly denied, a subsequent else-question is unacceptable, as shown in (44).
(44) Else-wh-questions have an additive presupposition: *Jack i didn't leave.Who else i left?(cf.Jack i left.Who else i left?) In the discourse in (43), accommodating the sluiced question's presupposition ensures that only worlds where Jack wasn't the only leaver are considered. 25In terms of our focusbased proposal, this ensures equivalence between the union of the sluiced question (i.e., the set of worlds such that Jack left, and someone other than Jack also left) and the antecedent proposition (i.e. that Jack left).These meanings are spelled out in (45a-b), correctly predicting that ( 43) is grammatical: After accommodation, equivalence holds in (43): For Q-equivalence approaches, however, we again encounter a problem: to account for cases such as (43), the antecedent, Chris knows that Jack left, must somehow raise the QuD 'Who other than Jack left?'.Likewise, Issue Bridging would require us to accommodate that all Jack-leaving events are Jack-leaving-with-someone events.This is, of course, possible, but we claim again that there is no sense in which the antecedent is responsible for triggering this accommodation process, or raising the relevant issue.

Cross-speaker sprouting
A second challenge to Q-equivalence approaches comes from cases where sluicing/sprouting happen across speakers.That is, speaker A may utter an assertion, which speaker B may then treat as an antecedent for a sluice.This is possible in both sprouting and nonsprouting sluices.In our presentation of this material, audiences report the intuition that it seems entirely up to speaker B to choose which issue to sluice, and furthermore, that there is no requirement that speaker A share speaker B's intention to raise this issue at the time of utterance.
Once speaker A accepts speaker B's discourse move (raising the sluiced issue), then the QuD can be said to have been raised, but this falls short of the expectations of Q-equivalence approaches, where the antecedent must raise the relevant issue with which the sluice must be semantically identical.Facts like those in (46) cast doubt on the notion that the antecedent assertion/speaker A is somehow responsible for raising the relevant QuD.Instead, it seems as if it is the sluiced question that raises the relevant QuD.In other words, the sluicer/asker is responsible for the issue raised.
An appeal to accommodation will not easily get around this problem.To see this, consider what such an accommodation account would have to look like.The discourse in (46b) fails to provide the necessary ingredients in the right order in order for sluicing to go through.For sluicing to go through, there must be an antecedent, which must raise an issue, which can then be sluiced.An appeal to accommodation in (46b) might look as follows: even though, according to our intuitions about discourses like that in (46b), the antecedent fails to raise the sluiced issue, we must nonetheless retroactively assume that the antecedent did, in fact, raise this issue.Once this is achieved, sluicing may go through provided the sluice is identical semantically to this issue.We find to be this a very strange sort of accommodation, and one which is additionally empirically unmotivated given our intuitions about the exchange in (46b).
The issue of speaker intentions in making discourse moves seems relevant here.In a simpler case of non-sprouting with an antecedent like Sally met someone, where there is an indefinite or some expression with an issue-raising capacity, we can imagine that the speaker intends to raise the corresponding issue: Who she met?, which may then license a sluice downstream.In the discourse in (46b), however, and perhaps in sprouting more generally, there is an intuition in which it is speaker B (the sluicer), instead, who is responsible for and intends to ask the sluiced issue explicitly, and no such corresponding intuition about speaker A's intentions at all. 26n support of this point, notice that speaker A may explicitly raise a specific issue with an antecedent, but speaker B is not then limited to sluicing that issue: (47) Sluicing is not constrained by the QuD raised by the antecedent: A: Sally left.Do you know how long ago she left?I don't care about who she left with.B: No, sorry, I only know who with she left.
On the other hand, our account can deal with such cases without any difficulty.Under our proposal, the union of the sluiced question's meaning must be equivalent to the set of worlds denoted by the antecedent.With example (46a), this is straightforward and follows the procedure we introduced in §2.The antecedent is a set of worlds where Sally met someone.The sluice is a set of propositions of the form That Sally met x, where x is a member of the domain in the model.The union of this set of propositions is the set of worlds where Sally met someone.Semantic equivalence is straightforwardly met.The procedure similarly goes through in (46b), under the assumption that if Sally left in w, then she left at a certain time t in w (see our discussion of ( 17) and the discussion of accommodation in ( 19)).

Antecedent sharing
A third challenge to Q-equivalence approaches comes from cases that we dub Antecedent Sharing.In (48), we observe a single antecedent followed by a sluiced continuation as well as a sprouted continuation: (48) Sluicing with antecedent sharing: Sally met someone, bidk who she met, or when she met them.
Q-equivalence accounts struggle to explain the availability of cases such as (48).Examples like the above require that antecedents be associated with multiple issues/questions simultaneously-one for each sluice.However, current proposals don't allow for more than one question/issue to be raised to salience at a time, since it's the antecedent that must raise the question/issue.On a QuD-based account, there can only be one current QuD that interlocutors strive to resolve at a time, since the QuD is modeled as a stack (Roberts 1996(Roberts /2012)). 27An alternative proposal, where the sluice is responsible for raising the question that licenses the sprout, is also not viable-the QuD raised by a question is the question itself.No QuD theory we are aware of allows a who question to raise a when QuD; a who question instead always raises a who QuD.
Alternatively, on an Inquisitive Semantics based account, if we follow the common assumption that any given antecedent has one single inquisitive denotation, this denotation must somehow be one that licenses both a who issue and a when issue simultaneously; but there is no way to do this in a way that matches the interpretations of each independent sluice in the current theory.Specifically, in (48), the sprouted inquisitive denotation is a set of events sorted by times, whereas the non-sprouted inquisitive denotation has alternatives sorted by individuals met.These are, then, two distinct denotations that must at the same time match the inquisitive denotation of a single antecedent sentence-a contradictory requirement.
Under our approach, on the other hand, antecedent sharing is no different than any other case of sluicing/sprouting.We can easily show that equivalence holds between the denotation of the antecedent and that of both sluices, provided that meeting x in w necessitates meeting x at some time t in w (cf 17): An anonymous reviewer notes that Q-equivalence approaches may circumvent this problem by appealing to the idea that perhaps sentences may be associated with a number of QuDs or issues (call them potential QuDs).In Inquisitive Semantics terms, sentences would be associated with multiple inquisitive denotations, a subset of which may be explicitly taken up/made salient by interlocutors in subsequent discourse.We agree with the reviewer that this would be one way to understand the phenomenon of antecedent sharing in a Q-equivalence approach, but once again highlight the fact that it is not clear how this modification of Q-equivalence theories makes any new empirical predictions that would help us distinguish them from a focus-theoretic approach like the one defended here.

Non-issue antecedents
A related challenge can be identified when we consider examples such as in (50a-c), where the sentences themselves explicitly state that the would-be issue/QuD raised by the 27 We take Roberts's system to be one in which there is only one QuD at the top of the stack.The alternative tree model may fare slightly better, but this model, too, only entertains one question at a time as the current QuD.See Rojas-Esponda (2014).As an anonymous reviewer notes, however, a model that allows QuDs to be an ordered set of unordered sets of questions-that is, one that allows the top QuD to be a set of questions-would not run into this problem.See Ginzburg (1994) for such a model.To our understanding, this view hasn't been adopted in more current writing on QuDs.In particular, QuD approaches which calculate a single QuD deterministically, such as AnderBois (2011) and Barros (2014) do run into the problem described here.
antecedent (under the Q-equivalence approach) is not relevant or not interesting.Despite this fact, sluicing and sprouting are licensed: (50) Non-issues can license sluicing: a. Jack would date anyone, it doesn't matter who! b. (Lucas Champollion p.c.) There's going to be another faculty meeting, but no one cares what about.c.Someone, anyone, needs to make sure the plants get watered daily, it doesn't matter { who, when }.
As discussed above, issues/QuDs are discourse moves, accepted by conversational participants, who have agreed to collaboratively address the issue.However, when we consider (50a), does the antecedent really raise a who question, despite the fact that the sentence explicitly asserts that any person x we might choose would verify the predicate Jack would date x?Likewise, in (50b), we would have to accommodate that the antecedent raises a what about question-i.e., that what about matters, despite our explicit denial of this fact.
Here one might argue that the issues or questions raised by the antecedents in (50a-c) are salient, even if the speaker explicitly opts out of asking them.See Onea (2016) for such an attempt (see also footnote 26 above).Nonetheless, we note that this goes counter to the idea that QuDs should be accepted by conversational participants as salient and relevant issues, which they together seek to resolve (Roberts 2012), and will still face some of the other criticisms we have raised in this section.(51) Contrast sluicing: a.She has five cats F , but I don't know how many dogs F she has.b.I know which books F she read, but not which articles F she read.
It is not clear how Q-equivalence approaches handle antecedents as in (51a-b).The antecedent clearly doesn't raise the sluiced issue/question needed to license the sluice on its own, since it explicitly raises a different issue/question.In (51a), the intuition is not that the antecedent itself is raising the subsequent sluiced issue, but that the antecedent utterance and the sluice, together, address some superordinate question paraphrasable as How many pets/cats or dogs does she have?
Here we present one attempt to account for such cases in a Q-equivalence approach, along the lines of Barros (2014): In a context where Mary's pets are discussed, we can imagine a QuD with sub-QuDs such as in (52) guiding the conversation, and licensing ellipsis: (52) A discourse strategy for generating an appropriate QuD for (51a): How many pets does she have?a.How many cats does she have?b.How many dogs does she have?
Given this assumption, we are able to use the context and focus structure of the antecedent to generate the right QuD to license our sluice, predicting (51a-b) to be available.
However, we argue that such an explanation is in danger of over-generating QuDs, which would license unwanted sluices.Consider the examples in (53-54) below (from Jason Merchant, p.c.).It seems plausible to assume that Sally didn't call ALEX F in (53) raises the QuD Who did Sally call?.Yet this QuD cannot license sluicing in this example. 28A similar concern affects example (54).How would QuDs be constrained to rule these examples out? (53) Ungrammatical sluices which Q-equivalence over-generates: # Sally didn't call Alex F { but, and } I dont know who Sally called t.
(54) A: Did(n't) Sally call Alex F ? B: # I dont know who Sally called t.
Our approach can handle such cases.Take (51b), for instance.We assume that the denotation of a wh-question with a contrastively focused remnant is a family of questions (that is, set of questions, see Büring (2003); Kotek (2019), among others). 29(55) A family of questions denotation for contrast sluices: a.
F which books she read, which books she read which magazines she read, which articles she read,… The union of both questions in (55a) and ( 55b) is an identical set of propositions, as shown in (56a).The union of this set is a set of worlds, as in (56b).Since, again, this set is identical for (55a) and (55b), we predict sluicing to be allowed in (51b).Notice that we had to take the union of each question twice to yield a set of worlds-since our proposal compares sets of worlds, not sets of propositions. 30Once this move is granted, we correctly predict these examples to be acceptable.

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 28 A reviewer finds the presluiced version of (53) unacceptable as well.To our ears and to our consultants, this issue rests on the prosody associated with the sentence, and there is a prosody with which the presluiced sentence is felicitous.Note further that this concern does not extend to example (54). 29Example (51a) would receive a similar account, where the collected worlds of the focus semantic values of the antecedent and sluice clause would be roughly paraphrasable as the proposition Sally has some number of things (perhaps with things contextually restricted to types of pets/animals). 30An alternative proposal might be to generalize our analysis to comparing sets of any kind.We prefer the double-application of the union operation we employ here, since to the best of our knowledge, this is the only exception to the generalization that sets of worlds must be compared.
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. (57) Ellipsis licensing condition (sluicing, to be expanded): (= 8) Sluicing may apply in CP E provided CP E has a salient antecedent, CP A , and the set of worlds used to construct the alternatives in ⟦CP E ⟧ f ↔ the set of worlds used to construct the alternatives in ⟦CP A ⟧ f .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. 31Recently, Griffiths (2018) proposes an account of MaxElide effects in ellipsis that fails to predict that sluicing should ever be possible.He takes this result to support the claim that sluicing must be subject to distinct licensing conditions and other kinds of ellipsis.However, we believe that more work is required in order to therefore conclude that Q-equivalence is the right condition for clausal ellipsis licensing.In particular, Griffiths (2018) does not tackle the issues for Q-equivalence approaches that we have highlighted here, since his aims lie elsewhere.Another possible conclusion from this work might be that an alternative account of MaxElide, consistent with our theory, is therefore required.However, pursuing such an account is beyond the scope of this paper. 32An anonymous reviewer points out that another argument in favor of Q-equivalence comes from cases of antecedentless ellipsis (see in particular Weir 2014).How would our account, which makes explicit reference to the focus-semantic value of the antecedent as part of the licensing condition on sluicing, deal with the absence of such an antecedent?Here, we follow Merchant (2004;2010) in assuming that in contexts in which antecedentless ellipsis is licensed, the elided material is trivially recoverable.We can therefore see at least two answers to the puzzle the reviewer raises: our identity condition might not be invoked in such cases at all, since the elided material is trivially recoverable; or, trivially recoverable elided material might automatically satisfy our condition without reference to an explicit linguistic antecedent.We leave adjudicating the issue for future research. 33We are especially thankful to three anonymous reviewers for spelling out some of these solutions and discussing them with us in detail.
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.

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. 35Instead 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): (58) givenness: XP E is given whenever it has a salient antecedent, XP A , and modulo ∃-type shifting, XP A entails the existential focus closure of XP E (F-clo(XP E )).
34 See also Tancredi (1992).See Romero (1998) for an extension of Rooth's (1992a) theory to explain a variety of constraints on sluicing remnants and their correlates.Romero additionally compares Rooth's Alternative Semantic proposal to that of Schwarzschild (1999), demonstrating that they make identical predictions. 35Since Merchant (2001), many authors, including Merchant himself, have scaled back this claim empirically, showing that some degree of syntactic identity appears to be at work in constraining Merchant's (2001) proposal from over-generation.See e.g.Merchant (2005;2013) 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. (

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.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.
(67) a.Every boy likes some girl, bidk which boy which girl. (cf 64b) b. *Some boy likes every girl, bidk which boy which girl.
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. (68) Sluicing with quantificational correlates: She read most of the books, but we don't know which ones she read.a. TP A entails F-clo(TP E ) (there are books that Sally read), but b.TP E does not entail F-clo(TP A ).
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) 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. 40More specifically, families of questions keyed on the first element in the pair.This becomes important in cases in which the domain denoted by the two wh-phrases are distinct; here we take dance to be a reciprocal predicate, and hence the domains of who and whom in (69b) are identical.In cases such as tell me which student read which book, the pair-list answer must pair each student with a book, but some books may not be read by anyone.See Dayal (1996) for further discussion. 41For cases of quantificational correlates such as (68), alternatives must be most of the books alternatives (with different choices of books).This can be achieved via global accommodation, given the antecedent's context-change potential and its effect on the context when the sluice happens.See also the discussion of accommodation surrounding example (19) above.
(79) Comparing abstracted-over TP denotations helps: λx .x lost at chess ≠ λx .x won at chess 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(80) Constraints on the placement of accent a. Givenness: If a constituent is not F-marked, it must be given.b.AvoidF: F-mark as little as possible, without violating givenness.
Importantly, in Schwarzschild's (1999) proposal, any syntactic constituent is subject to these constraints in an utterance. 50s 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. 51As 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): (85) Iterative satisfaction condition: For any reduced (elided or deaccented) XP, not only must XP satisfy (76), but so must all of XP's subconstituents, and any sub-subconstituents therein.
(Modulo accommodation à la Fox 2000) 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.

Conclusion
The precise characterization of the identity condition on sluicing has been the subject of a large and growing body of literature in recent years.In this paper, we have argued against an emerging consensus that sluices must be anaphoric to an implicit question or issue that the antecedent makes salient in the discourse (Q-equivalence approaches, Ginzburg & Sag 2000;AnderBois 2011;2014;2016;Barros 2014;Weir 2014;Kotek & Barros 2018), which is distinct from the licensing condition on other kinds of smaller ellipsis.Instead, we argued for a return to a focus-based approach (Rooth 1992a;Romero 1998;Fox 2000;Merchant 2001), and offered a new formulation of the identity requirement on sluicing couched in Rooth's (1992b) Alternative Semantics framework.
Under our proposal, the set theoretic union of the focus semantic values of the antecedent and the sluice must be equivalent in order for ellipsis to go through.We showed that this proposal handles not only basic sluices, but also contrast sluices and sprouting in a parsimonious and empirically motivated way.Although our proposal is inspired by, and is in many ways similar to, Merchant's (2001) focus-based e-givenness account of ellipsis licensing, we showed that our account fares better in accounting for cases of multiple sluicing and sluicing with quantified correlates.
Along the way, we highlighted conceptual as well as empirical challenges to Q-equivalence approaches-most importantly, that antecedents should not be burdened with the task of raising the question or issue needed for ellipsis licensing-taking the rug from under any Q-equivalence approach.At the same time, we demonstrated that our account is able to straightforwardly meet and explain all of these challenges to Q-equivalence.In sum, our proposal is an argument for a return to the idea in Rooth (1992a) and Merchant (2001) that semantic conditions on sluicing, and ellipsis in general, should be couched in terms of focus-theoretic dimensions of meaning.It is an implementation of the idea that ellipsis is a radical form of deaccenting, both being forms of redundancy reduction operations.
Having established our account of the identity condition on sluicing, we then went a step further and generalized our semantic identity condition to other forms of ellipsis besides sluicing.In particular, we showed that our generalized condition is able to automatically account for challenges from VP-ellipsis to Merchant's (2001) e-givenness raised in Hartman (2009).Finally, we showed that our generalized condition is able to provide a unified account for the distribution of ellipsis and of deaccenting, where the two are subject to the same semantic parallelism condition, modulo accommodation and constraints thereupon (Fox 2000).
Going forward, our proposal opens several fruitful domains of inquiry.For one, it would be important to check how well our proposal fares as a replacement definition for Schwarzschild's givenness.More broadly, although the ellipsis literature makes heavy use, to our minds, of the results from the literature on focus, it is not as clear that results from the ellipsis literature, in turn, inform theories of focus.If this is correct, then our paper can also be seen as giving back in a useful way to the literature on focus, in providing a new definition of givenness as it applies to deaccenting and accent placement. 4 only wears a bow-tie when [teaching] F .≈ David doesn't wear a bow-tie when doing anything else.b.David only wears [a bow-tie] F when teaching.≈David doesn't wear anything else when teaching.

events always involve a time of leaving: ⟦Sally
Sally ate ], bidk [ cp e what Sally ate].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: Sally left ], bidk [ cp e when Sally left ].a. ⟦When Sally left⟧ f = λp .∃t (p = λw .Sally left at time t in w) b. ∪⟦When Sally left⟧ f = λw .∃t (Sally left at time t in w) c. ∪⟦Sally left⟧ f = λw .Sally left in w left⟧ = { w : Sally left in w } = ∪ { λw .Sally left at time t in w | t ∈ D s } Argument and adjunct sprouting: a. Sally ate, but I don't know what.a. ⟦what Sally ate⟧ f = λp .∃x (p = λw.Sally ate x in w) b. ∪⟦what Sally ate⟧ f = λw .∃x (Sally ate x in w) c. ∪⟦Sally ate⟧ f = λw .Sally ate in w d. (15b) ↔ (15c) (16) ⟦Sally ate⟧ = { w : Sally ate in w} = ∪ {λw .Sally ate x in w | x ∈ D e } b. { w : Sally left in w} ≠ ∪ { λw .Sally left with x in w | x ∈ D e } 24) a. *Sally didn't see no one, but I don't know who Sally saw.b. *It's not the case that no student left, but I don't know which student left.e-givenness predicts such cases to be licensed, because double negation is truth conditionally vacuous in dialects where each negation is a separate logical negation.The resulting truth conditions for (24a) are thus: (25)a.Sally didn't see no one antecedent for further details on the results of the study.) a. My cousin Joni, who spent the night with a Beatle in 1962, can't remember which Beatle. b.My cousin Joni, who spent the night with someone in 1962, can't remember who.
14) a. Sally ate, but I don't know what.
XP E ) is the result of replacing F-marked parts of XP E with variables of the same type, and existentially closing the result.For example, VP A in (60b) counts as given, since VP A entails F-clo(VP E ). (Deaccenting is represented throughout in small font.) Barros (2014)2010);Chunget al. (2010); AnderBois (2011);Weir (2014);Barros (2014), among many others.