Focus association by movement: Evidence from binding and parasitic gaps1
Michael Yoshitaka ERLEWINE — National University of Singapore
Hadas KOTEK — Yale University

Abstract. Under the influential Roothian proposal for focus association, focused phrases remain in-situ at LF (Rooth, 1985, 1992). However, a recent line of work has resurrected theidea that focus association involves covert movement: specifically, the associate of English
sentential only must covertly move to only, with the possibility of covert pied-piping (Drubig,
1994; Krifka, 1996, 2006; Tancredi, 1997, 2004; Wagner, 2006; Erlewine and Kotek, 2014,2018). In this paper we contribute to this emerging consensus view with additional evidence
from reflexive binding and parasitic gap licensing.
Keywords: focus association, only, covert movement, binding, parasitic gaps
1. Two approaches to focus association
The problem of focus association concerns the relationship between focus-sensitive operatorssuch as only and focused constituents such as Fridays or chocolate in (1). The semantics ofonly quantifies over the focused constituent and its contextual alternatives: for example, (1a)asserts that there is no day other than Friday where John eats chocolate, whereas (1b) assertsthat John eats nothing other than chocolate on Fridays (see e.g. Horn, 1969).
(1)

a. John only eats chocolate on [Fridays]F .
b. John only eats [chocolate]F on Fridays.

How does only’s semantics make reference to this focused constituent? One family of approaches posits the existence of covert focus movement so that the focused constituent becomesa local argument of the only operator at LF. A sample LF for example (1b) under the covert focus movement view is given in (2) below. Here we illustrate the non-quantificational subject
John in its VP-internal base position. The movement in (2) makes the focus chocolate a local
argument of a two-place only operator.2(2)

Covert movement LF for (1b):only [chocolate]F l x . John eats x on Fridays

The alternative approach — popularized by Rooth (1985, 1992) and adopted in much contemporary work on focus semantics — assumes that focused constituents remain in-situ at LF. The
operator (only) makes indirect reference to the choice of focus and its alternatives through aprocess of alternative computation. Each syntactic node a is associated not only with its ordinary semantic denotation JaKo but also with a set of alternatives, JaK f , defined recursively as in(3) below. Focused (F-marked) constituents introduce non-trivial alternatives into their focus1 We thank Aron Hirsch and anonymous reviewers for comments on the material here. Errors are each other’s.

2 The precise geometry of this movement could vary. See footnotes 7 and 8 in Erlewine and Kotek (2018) for

detailed discussion of this movement and alternative formulations.

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alternative denotations (3c), which are then propagated up through the process of pointwise
composition (3b).
(3)

Focus alternative computation:a. For non-focused terminal nodes:
JaK f = {JaKo }b. For non-focusedbranching nodes (pointwise
composition):noJ[a b ]K f = a b a 2 JaK f , b 2 Jb K f

where is the appropriate composition operation for JaKo and Jb Ko .
c. For focused nodes:
JaK f is a contextually-determined subset of Dt where t is the type of JaKo

The result of this procedure is that the contextual alternatives to chocolate in (4b) will bereflected indirectly in the set of alternatives at VP (4c), which is a local argument of only.
(4)

Interpreting (1b) with focus in-situ:
a. only [VP John eats [chocolate]F on Fridays ]b. J[chocolate]F K f = {chocolate, fish, pizza, ...}
8
9
< John eats chocolate on Fridays, =c. JVPK f = John eats fish on Fridays,:;
John eats pizza on Fridays, ...
d. [only VP] ) John doesn’t eat fish on Fridays,
John doesn’t eat pizza on Fridays, ...

As an empirical argument for the in-situ view, Rooth (1985) following Anderson (1972) notesthat focus association is apparently insensitive to syntactic islands. For example, in (5) based on
an example from Kratzer (1991), only successfully associates narrowly with the focused constituent the Zoning Board inside a relative clause island. Under the covert movement approach— so the argument goes — covert movement of the Zoning Board should be impossible, justas the corresponding overt focus movement in (6) is ungrammatical.3(5)Focus association is apparently island-insensitive:
I only contacted [island the person who chairs [the Zoning Board]F ].

(6)

Corresponding overt focus movement of the Zoning Board: (Kratzer, 1991: 831)
* It was [the Zoning Board]F that I contacted [island the person who chairs ].

Drubig (1994) however notes that this island-sensitivity problem can be avoided if covert focus
movement can trigger pied-piping. That is, instead of the logically focused constituent moving
alone to become a local argument of only, a focus-containing phrase can instead move to only.
This possibility is illustrated schematically for the case of example (5) in (7) below.
3 A possible response may be to say that covert (focus) movement is not sensitive to the same island constraints

as overt movement, but this is ultimately incorrect. See Wagner (2006) and Erlewine and Kotek (2016, 2018) for
evidence that covert focus movement is sensitive to syntactic islands.
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Focus association by movement: Binding and parasitic gaps

LF for (5) using covert focus movement with pied-piping:
only [island the person who chairs [the Zoning Board]F ] l x . I contacted x

The interpretation of the pied-piped constituent in (7) then must utilize Rooth’s mechanismof in-situ alternative computation in order to yield the observed sensitivity to the position of
focus within the pied-piped phrase. Pied-piping of the constituent in (7) is also independently
observed in overt focus movement, as in example (8):4(8)

Corresponding overt focus movement with pied-piping:
X It was [island the person who chairs [the Zoning Board]F ] that I contacted(cf (6)).

This hypothetical possibility of pied-piping in covert focus movement thus defuses Rooth’s
argument from island-insensitivity for the in-situ approach to focus association. Independent
evidence is then necessary to adjudicate between these two possible options. A series of works
in the past decade have introduced new arguments for the idea that focus association withEnglish only necessarily involves covert focus movement with the possibility of covert piedpiping.5 The gist of each of these arguments is summarized here in (9).
(9)

Previous arguments for covert focus movement with pied-piping:a. Krifka (2006): Restrictions on association of only with multiple foci are sensitive
to islands, in a manner predicted by the covert movement with pied-piping view.
b. Wagner (2006): The distribution of NPIs licensed by adverb only is sensitive to theplacement of islands, in a manner predicted by covert movement with pied-piping.
c. Erlewine and Kotek (2014): The distribution of focus intervention effects (Beck,2006) in focus association is explained by covert focus movement with pied-piping,with intervention affecting just the covertly pied-piped material.
d. Erlewine and Kotek (2016, 2018): The distribution of so-called Tanglewood configurations, where alternatives apparently co-vary between a pronounced focus andwithin an ellipsis site (Kratzer, 1991), is sensitive to syntactic islands. Tanglewood
readings are best explained using covert focus movement with pied-piping.

In this paper, we contribute two new arguments to this growing body of evidence. Following
related diagnostics for covert wh movement by Nissenbaum (2000a, b), we will show that covert
focus movement in English can feed reflexive binding and the licensing of parasitic gaps. These
effects too are unexplained by the in-situ approach to focus association.

4 In some cases, however, the pied-piping that we would need to posit for covert focus movement may be larger

than what is observed with overt pied-piping. There is however independent evidence that pied-piping can belarger with covert movement than with overt movement: see Kotek and Erlewine (2016).
See also Horvath (2000, 2007) for discussion of pied-piping in overt focus movement.
5 All of these works in (9) look exclusively at focus association with English sentential only. A significant open
question is whether this claimed necessity of covert movement in focus association extends to other focus-sensitive
operators or languages.
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2. Binding
Nissenbaum (2000b: pp. 124ff) shows that covert wh-movement in English allows reflexives tobe bound by an antecedent outside of their surface local binding domain: that is, covert phrasal
movement feeds reflexive binding. Consider the contrast in (10):(10) Covert wh-movement feeds reflexive binding:(Nissenbaum, 2000b: p. 126)
a. * Whoi thinks [Mary was looking at a picture of himselfi ]?
b.
Whoi thinks [Mary was looking at which picture of himselfi ]?
The masculine reflexive himself does not have a local antecedent within the embedded clause,as the ungrammaticality of the baseline (10a) indicates. However, when this reflexive is contained within an in-situ wh-phrase, it can be bound by a higher antecedent, as long as thecontaining wh-phrase takes scope under the antecedent. In this case, assuming that movements
triggered by the same head (here: matrix C) will “tuck in” (see also Richards, 1997; Pesetsky,
2000), (10) will have a LF representation as in (11).6(11) Covert wh-movement LF for (10):[CP Whoi [which picture of himselfi ] [TPthinks [CP Mary was looking at]]

In this higher LF position, himself is close enough to the intended antecedent, who. We therefore conclude that Binding Condition A is evaluated at LF.
We can similarly use reflexive binding to test whether or not focused material — or material
pied-piped together with focused material — can include reflexives bound by a higher antecedent than regularly possible, as long as it is within the scope of the associating only. We
begin with the baseline in (12), where the intended antecedent of myself is the matrix subject,outside of the relevant binding domain (BD).
(12) Baseline: *I want [BD the museum to display a picture of myself].
Now consider example (13), which differs minimally from (12) in the addition of only above
want, associating with the F-marked picture. The reflexive myself is now successfully boundby its intended antecedent, which is outside of myself ’s surface local binding domain (cf (12)).
(13) Covert focus movement feeds reflexive binding:Context: I commissioned many paintings and pictures of myself. The museum is interested in displaying both a painting and a picture that I had made, but in fact,
X I only want [BD the museum to display [a [picture]F of myself]].
The grammaticality of the reflexive binding in (13) is explained by the availability of covert
focus movement with pied-piping. The proposed LF for (13) is given in (14). Here the overt
6 Following Kotek (2016), this covert wh-movement need not always move all the way up to the interpretingcomplementizer, but it suffices here that, in (10b) but not (10a), attraction of the surface in-situ wh-phrase has theoption of covertly moving out of the embedded clause.
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A-movement of the subject from its predicate-internal position to its surface position, above
only, is critical and therefore illustrated.
(14) LF for (13) using covert focus movement with pied-piping:Ii l y . only [a [picture]F of myselfi ] l x . y want [BD the museum to display x]
If a different constituent is focused which will not trigger covert movement of the reflexive, thelong-distance binding in (13) is not licensed:(15)* I only want [BD the [museum]F to display a picture of myself].

Notice that the solution here is not to simply say that focused constituents themselves canviolate locality in reflexive binding: what is focused in (13) is picture, not myself. It is necessary
for covert focus movement of the F-marked constituent, picture, to trigger pied-piping of thewhole reflexive-containing DP, a picture of myself.
Note too that it is not simply the case that focus on the head noun picture in (13) somehow allows myself to be bound long-distance, by an antecedent outside of the surface binding domain(BD). This long-distance binding facilitated in (13) is limited to the scope of only. If we attach
only lower, within the surface binding domain of the reflexive, the long-distance antecedent
option disappears:(16)* I want [BD the museum to only display a [picture]F of myself].

To summarize, we find that association with only feeds reflexive binding, as would be predictedby a theory of covert movement with pied-piping: the F-marked constituent moves (possiblywith pied-piping) to become the first argument of only. This movement can put this constituent
in a local relationship with a binder that is otherwise absent, licensing a binding relation. This
result is unexpected under an in-situ account of Association with Focus, which predicts nodifference between (12) and (13).
3. Parasitic gap licensing
The literature on parasitic gaps has largely followed Engdahl (1983) in assuming that wh-in-situ
never licenses parasitic gaps. Engdahl’s examples are reproduced in (17) below. Assuming thatin-situ wh-phrases must or can move covertly (Karttunen, 1977; Huang, 1982; Pesetsky, 2000;
Kotek, 2016; a.o.), this claim is commonly (re)interpreted as a claim that covert movements
cannot license parasitic gaps.
(17) Wh-in-situ does not license parasitic gaps: (Engdahl, 1983: p. 14)
a. * John filed which articles without reading pg ?
b. * Who filed which articles without reading pg ?
Nissenbaum (2000a, b) shows that Engdahl’s generalization is not exceptionless: although it
is true that covert movement alone does not license parasitic gaps, overt movement together
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with covert movement through the same vP edge can together license two parasitic gaps. An
in-situ wh-phrase can license a secondary parasitic gap (18), which is not simply licensed by
the presence of a non-wh phrase in the same position (19).
(18) Wh-in-situ licenses a secondary parasitic gap: (Nissenbaum, 2000a: p. 542)
Which senatori did you persuade i to borrow which car j[after getting an opponent of pg i to put a bomb in pg j ]?
(19)

* Which senatori did you persuade i to borrow a Prius j[after getting an opponent of pg i to put a bomb in pg j ]?

It is also possible to license an adjunct with just one parasitic gap bound by the overtly-moved
wh-phrase (20a), but not with one corresponding to the in-situ wh-phrase (20b). The mainclauses in both examples here are identical to that in (18). The secondary parasitic gap pg j asin (18) is, then, itself parasitic on the first parasitic gap pgi which corresponds to the overtly
moved wh-phrase.
(20) Secondary parasitic gap is parasitic on the first parasitic gap:a.
Which senatori did you persuade i to borrow which car j(Ibid. p. 552)
[after talking to pg i for an hour]?
b. * Which senatori did you persuade i to borrow which car j[after putting a bomb in pg j ]?
To license the adjunct with two parasitic gaps, both the overt and covert A-movement steps mustcross the same vP edge. This is accomplished in (18) at the vP edge associated with persuade,as which senator is overtly A-moved from within it. Subjects which are first A-moved out ofvP do not license their own parasitic gaps (Engdahl, 1983; a.o.) and similarly do not license
secondary parasitic gaps:(21)* Which terroristi

i persuaded the senator to borrow which car j[after getting a friend of pg i to put a bomb in pg j ]?

The correct generalization regarding the licensing of parasitic gaps by covert movement is thenas in (22). Nissenbaum (2000a, b) gives an explanation for this generalization in terms of thederivational timing of overt vs covert movement and adjunction of the parasitic-gap-containing
adjunct. We refer interested readers to those works.
(22) The Engdahl/Nissenbaum generalization:
Covert A-movement by itself does not license parasitic gaps. However, covert Amovement does license a secondary parasitic gap when it crosses a vP edge that is
also crossed by an overt A-movement step.
We now show that focus association with only also licenses secondary parasitic gaps, as predicted by the covert focus movement approach to Association with Focus. Example (23) below
is based on the ungrammatical baseline (19) above, but with the addition of an only associating
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with the object of drive — here, a Jaguar:(23) The focus associate of only licenses a secondary parasitic gap:
X Which senator could you only persuadeii to drive [a [Jaguar]F ] j[after getting an opponent of pg i to put a bomb in pg j ]?
Both the overt movement of which senator and the covert movement of a Jaguar to only in (23)will cross through the vP edge associated with persuade, to which the after-adjunct adjoins. If
only is introduced lower so that the path of covert focus movement does not overlap with theovert wh-movement path, as in (24), the secondary parasitic gap becomes ungrammatical, as
also predicted by the generalization in (22).
(24) The position of only marks the height of covert focus movement:* Which senatori could you persuade i to only drive [a [Prius]F ] j[after getting an opponent of pg i to put a bomb in pg j ]?
Just as we saw with wh-movement, parasitic gap licensing by covert focus movement is only
possible when crossing a vP edge that is also crossed by overt A-movement, as per the Engdahl/Nissenbaum generalization (22). The generalization also predicts that a single parasitic
gap is not licensed by the covertly moved focus of only alone. This prediction is borne out in(25):(25) Covert focus movement alone does not license parasitic gaps, as predicted by (22):a. * I only criticized [[this]F book] without reading pg .
b. * I only want to read [[this]F book] without buying pg .
We include another set of secondary parasitic gap contrasts, similar to the examples above.
Example (26a) shows the ungrammaticality of a secondary parasitic gap with a referential DP,
the placebo; example (26b) shows the availability of a secondary parasitic gap with a wh-phrase
in that position; and (26c) shows the parallel licensing of a secondary parasitic gap with an only
associating with a focused placebo.
(26)

a.
b.
c.

* Which patientsi did the doctors assign i to the placebo j[after showing the families of pg i how to administer pg j ]?
Which patientsi did the doctors assign i to which drug j[after showing the families of pg i how to administer pg j ]?
Context: Following FDA regulations, patients’ families were shown how to administer all the drugs that might be associated with the trial. After some patients began exhibiting unexpected symptoms, the families wrote the FDA anddemanded to know:
Which patientsi did the doctors only assign i to [the [placebo]F ] j[after showing the families of pg i how to administer pg j ]?

In examples (19) and (26a), the secondary parasitic gap is not licensed. The presence of thesecondary parasitic gap is not by itself able to force the covert movement necessary to license
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the gap. Instead, this movement must be independently licensed — covert wh-movement in(18) and (26b) and covert focus movement in (23) and (26c).
We conclude that — like in the case of covert wh-movement — parasitic gaps on F-marked material are licensed in Association with Focus constructions. This is predicted if association with
only requires covert focus movement but is unexplained by the common, in-situ association
approach of Rooth (1985) and others.
4. Conclusion
Evidence from reflexive binding and parasitic gap licensing shows that the focus associate of
only is interpreted in a higher position at LF through covert movement. This is predicted under
the covert movement theory of only, where the F-marked constituent moves (possibly withpied-piping) to become the first argument of a two-place only (Drubig, 1994; Krifka, 1996,
2006; Tancredi, 1997, 2004; Wagner, 2006; Erlewine and Kotek, 2014, 2018). It is inconsistent
with the influential in-situ analysis of association with only (Rooth, 1985, 1992), and hence
serves as an argument against this view.
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