Towards a Minimalist Machine: Combining Linguistic Theories
Jason Ginsburg, Sandiway Fong

1. Introduction
Theoretical syntacticians, working within the framework of Generative Grammar, investigate
the nature of the human grammatical system (i.e., Universal Grammar). Most of this work
involves developing theories that predict and explain the structures and well-formedness/illformedness of constructions found in natural language. Theoretical linguists generally do notuse computer models to test the validity of their theories. In this chapter, we show how acomputer model can be a useful tool for combining components of different theories into asingle unified model, which also clarifies the inner workings of the target theories.
We have developed a Minimalist Machine that automatically constructs detailed
derivations of over 140 examples from recent important work in the Minimalist Program. We
discuss particular modifications that are necessary to combine the target linguistic theories intoa single unified model. This is an important and necessary step towards making the Minimalist
Machine viable because there is no guarantee that theories in the same framework are indeed
compatible; for example, they might rely on contradictory assumptions.
This Minimalist Machine is a useful tool for finding and overcoming problems that arisein Minimalist theories. In order for the Minimalist Machine to construct the successfulderivation of a target sentence, all operations must converge successfully. Inconsistencies in
the model will cause a derivation to crash, or the computer program to halt, and thus, problems
that otherwise might be difficult to notice become immediately apparent. In a derivational
theory, both crashes and computation convergence are key components of the framework that
communicate important information about grammar. Convergence will admit valid examples.
Crashes are used to rule out illicit examples. In other words, one can use this system to figure1

out why a particular derivation does or does not converge. Hence, it is important to demonstratethat the grammar does “compute”.
The Minimalist Machine has the unique property of demonstrating how Minimalist
Theories work in extreme detail, beyond what is normally possible via typical paper-and-pencil
linguistics. This model automatically constructs detailed step-by-step derivations of target
constructions that can be read in a web browser. This output displays charts and tree diagrams
that show all core feature-checking operations, Merge operations, and Spell-Out operations(see http://elmo.sbs.arizona.edu/sandiway/mpp/mm.html). This model is thus useful forclarifying exactly how derivations work, as well as for elucidating problems within target
Minimalist theories, so this work can benefit theory development in linguistics.
The notable components of this probe-goal model 1 are as follows. The model utilizes
feature unification, which simplifies cases of multiple agreement, in which a single probe must
Agree with multiple goals. The model incorporates a low-Merge position for the expletive there,
thus accounting for how there is licensed in certain core expletive constructions. To accountfor thematization/extraction, we utilize a light verbal head that must be checked via Agree witha theta-bearing DP. Edge Features, specified for various functional heads, play a role in driving
movement. Economy also plays a role in derivations, so that simpler operations block more
complex operations – if multiple features on a head can be checked via Agree with a single
goal versus Agree with multiple goals, the more economical Agree relation with the single goalis required. Economy plays an important role in accounting for that-trace effects and thepresence/absence of that in relative clauses.
We demonstrate how this model implements the following types of target constructions inaunifiedmanner:expletives

andmultiple

agreement(Chomsky2001),

1

This model does not incorporate the recent labeling-based framework of Chomsky (2013, 2015). For discussionof labeling-based models, see Ginsburg (2016), and Fong and Ginsburg (In preparation).

2thematization/extraction (Chomsky 2001; Sobin 2014), that-trace effects and subject vs. object
wh-movement (Pesetsky & Torrego 2001), and relative clauses (Pesetsky & Torrego 2001;
Gallego 2006). We point out certain problems that arise in previous work on these types of
constructions, and we explain how we resolved these problems in our computational
implementation. Also, it is important to note that we created a single computational
implementation that can account for the structures of all of these types of sentences, as well asothers (which we do not have space to discuss).

2. Multiple Agree (Chomsky 2001)
Chomsky (2001) develops an account of language in which agreement between a probe and agoal is crucial. In Chomsky (2001), however, problems arise with respect to multiple agreement— cases in which a probe must Agree with more than a single goal.
Agreement works as follows. A probe, which is the root of a Syntactic Object (SO), has
an unvalued feature (uF) that searches for a goal with a matching valued feature (F). Crucially,
the probe must c-command the goal. Case checking results as a reflex of a phi-feature checking
relation. A probe with unvalued phi-features (uPhi) Agrees with a goal that has valued phifeatures (Phi) and unvalued Case (uCase). Agreement checks the uPhi on the probe and theuCase on the goal. For example, as shown in (1), given a probe X that has uPhi and the ability
to check Case as nominative (Nom), and given a goal Y that has Phi and uCase, Agree between
X and Y results in checking of the uPhi on X. As a reflex of this Agree relation, the uCase on
Y is valued as nominative.

(1) Agree(X[uPhi,Nom] ,Y[Phi,uCase] ) à X[uPhi,Nom] and Y[Phi,Case:Nom]

3

Certain issues arise with respect to checking of uCase on a participle. Chomsky (2001: 17),
citing the fact that certain past participles show agreement in languages such as Icelandic, takes
the position that a past participle requires Case. Thus, in the passive (2), the participle –ed(which combines with award), must obtain Case.

(2) Several prizes are likely to be awarded. (Chomsky 2001: 7)

The relevant portion of the derivation of (2) is shown in Figure 1. A participle, indicated as prt,
has a defective set of uPhi, containing unvalued number (uNum) and unvalued gender (uGen),
as well as uCase. The prt is defective in that it does not have a complete set of uPhi, as it lacks
uPerson. Prt Agrees with the object several prizes. The uNum and uGen of prt are checked by
the valued number and gender, Num and Gen, of the object several prizes. The uCase on prt
remains because the object, also an argument, cannot check uCase. The non-finite T, to, isdefective. It has an EPP feature and an incomplete set of uPhi, which Chomsky (2001: 7)
suggests is uPerson. Non-finite T, being defective, cannot check uCase. The non-finite T
Agrees with several prizes, resulting in checking of uPerson (indicated as uPer) on to, and an
EPP on to forces the object to remerge in embedded subject position. The matrix T has uPhi
and can check Case, which it values as nominative. In this case, T forms a probe-goal Agreerelation with several prizes, resulting in uPhi of T being checked. As a reflex of this phi-featureagreement relation, the uCase of several prizes is checked and valued nominative. An EPP
feature on T also forces several prizes to remerge in subject position.
This derivation, however, faces a problem with respect to the participle — it is not clear
how the uCase of the participle is checked. In order for uCase on prt to be checked, the matrix
T must form an Agree relation with prt, shown in step (6) of Figure 1. But the uPhi on T are
already checked via Agree with the higher object several prizes, shown in step 4. Thus, after T

4forms an Agree relation with several prizes, T has no reason to continue probing and further
Agree with prt. Even if T were to Agree with prt, it is notable that the only phi-features that prt
has are checked number and gender, raising the question of whether or not checked uPhi of prt
are capable of further phi-feature agreement with T.

Figure 1

Structure of (2)In order to generate an example such as (2), in which there is multiple agreement, it isnecessary to determine exactly how the uCase of prt is checked. To this end, we implemented
feature unification. If a probe with a uF Agrees with a goal with an identical uF, the uFs unify.

(3) Feature unification
uFs of the same type unify.

With feature unification, checking of uCase on prt is no longer a problem. The derivation of(2) proceeds as shown in Figure 2. An Agree relation established between prt and several prizes
results in checking of uNum and uGen of prt by the Phi of several prizes. Note that both prt
5and several prizes have uCase. Thus, the uCase of prt unifies with the uCase of several prizes,
indicated as uCase1. This is shown in step (1) of Figure 2. When the matrix T is Merged, shownin step (2), T Agrees with the object several prizes, resulting in checking of uPhi (which
includes uNum, uGen, and uPer) on T and checking of uCase1 on several prizes. Crucially,
checking of uCase1 on several prizes also results in checking of the unified uCase1 on prt.
Thus, feature unification crucially does away with the need for T to probe after it is licensed.
In our Minimalist Machine model, we implemented feature unification in this manner.

Figure 2

Structure of (2) with feature unification

2. Expletives (Chomsky 2001)
Expletives raise some problems for Chomsky’s (2001) account. According to Chomsky(cf. Chomsky 2001: 16), the expletive (Expl) there is a defective argument that has uPerson
features and that lacks uCase. The Expl is also Merged directly in the Spec position of T and
the uPerson feature of there is checked via Agree with T. Several issues arise in (4), with thestructure shown in Figure 3, in which there appears in subject position. First, Agree between

6uPhi of T and uPerson of there checks the uPerson of there. Note that this Agree relation holds
between uFs (uPhi of T and uPerson of Expl), but it is not clear how a uF can check a uF.
Second, when T is Merged, T should form a probe-goal Agree relation with the object a train.
Crucially, this Agree relation between T and a train is formed before there is Merged in Spec
position. Thus, after agreement with the object, T should not have any uPhi available for Agreewith there. One possibility, pointed out by Chomsky (2000: 128) is that the Expl there probes
and Agrees with T, but it isn’t clear if the checked uPhi on T could check the uPerson of theExpl. Another issue that arises is whether or not a non-root node can probe. The root node of
the SO is T, so if Expl probes from Spec position, then there is probing from a non-root node.
Richards (2007) points out that probing from a non-root node is problematic — permitting bothroot and non-root nodes to probe is more complex than limiting probing to a root node.
Richards also points out that probing by Expl would go against Chomsky’s (2008) proposalthat only phase heads can probe.

(4) There arrived a train. (Sobin 2014: 386)

Figure 3

Problems with (4)The feature checking and probing problems raised by expletive constructions are resolved
if we assume that a) an expletive is Merged below T, and b) we utilize feature unification, as

7described in (3) above. We follow Richards (2007) who, in order to avoid the problem ofprobing from a non-root node, proposes that there is Merged below T. 2 The successfulderivation is shown in Figure 4. Assume that there is Merged as the specifier of a light v
projection below T. We assume that this v has an Edge Feature (EF) that requires it to have anelement Merged in specifier position.3 Then when T is Merged, uPerson of T Agrees with
uPerson of there, resulting in feature unification, so that T and there have unified uPerson
features, indicated as uPer1 in step 1 of Figure 4. Since there is defective, it cannot check any
uPhi of T. Thus, T continues to probe and Agrees with the object a train. Agree results inchecking of the uPhi on T. Crucially, in addition to uNumber and uGender, the uPhi includes
the unified uPerson feature. Thus, when the uPerson feature of T is checked, the unified
uPerson on there is also checked. As a reflex of this Agree relation, uCase on the object is also
checked. Note that only T probes, so there is no probing from a non-root node. Since theuPerson of there is checked via feature unification, there is no need to rely on uPerson of there
being checked via Agree with T. Also note that an EF of T forces there to raise to the Spec
position of T.

2This view is also adopted by Sobin (2014), among others.
An Edge Feature (EF) is akin to an EPP feature, and is checked via Merge with any argument (Chomsky2008).
38

Figure 4

Structure of (4) with low Merge of Expl and feature unification

3. Thematization/Extraction (Th/Ex) (Chomsky 2001 & Sobin 2014)
Chomsky (2001: 20) presents the following example in (5), in which the direct object “isextracted to the edge of the construction by an obligatory thematization/extraction rule Th/Ex.”
The direct object several packages undergoes Th/Ex to a preverbal position, as can be seen in(5)b. Note that if the object remains in its base position, the result is ill-formed, as shown in(5)c, indicating that Th/Ex is obligatory.

(5) a. There were several packages placed on the table. (Chomsky 2001: 20)
b. There were [several packages] placed [several packages] on the table.
c. *There were placed several packages on the table.

Chomsky suggests that Th/Ex is phonological, writing “Th/Ex is an operation of thephonological component (Chomsky 2001: 21),” without offering specifics about how Th/Ex
would work as a PF (Phonological Form) phenomenon. However, we follow Rezac (2006) andSobin (2014), who take a syntactic approach to Th/Ex. Sobin, following Rezac (2006), writes

9that “Th/Ex positions are the specifier positions of those functional v heads that are θ-open andallow an argument to appear in them (2014: 398).”4
Sobin’s approach relies on a Split-EPP feature, which has Agree and Merge subfeatures.
In order for a Split-EPP feature to be fully checked, the Agree and Merge subfeatures must be
checked. The Agree subfeature can take the form of uCheckTheta (6), which is checked via
Agree with a theta-bearing DP. The Merge subfeature is checked via Merge of an element inspecifier position, and can have the form uDMrg, shown in (7), which requires Merge of any
type of DP (an expletive or a theta-bearing DP are fine).5(6) Agree subfeatureuCheckTheta — checked via Agree with a theta-bearing DP(7) Merge subfeature
uDMrg — checked by Merge of a DP

Adopting Deal’s (2009) proposed default verbalizing head v~ that appears in unaccusative,
passive, and progressive constructions, Sobin proposes that English v~ has the EPP subfeatures
shown in (8). It has a uCheckTheta, so it must Agree with a theta-role bearing DP, and it also

4

See Rezac (2006) for discussion of why Th/Ex is syntactic. For example, Rezac argues that Th/Ex positions canbe iterated, which requires Th/Ex to apply before PF, as a derivation is constructed. Also, in Swedish, a passive
participle shows agreement with an argument that appears to have undergone Th/Ex. Assuming that agreement is
syntactic in nature, then this too suggests that Th/Ex is not a PF phenomenon.
5
We only include the Agree and Merge subfeatures that are relevant for the examples presented in this paper.
The full set of Agree and Merge subfeatures utilized by Sobin are as follows.
(i) Agree subfeatures
a. uCheckTheta — checked via Agree with a theta-bearing DP
b. uDAgr — checked via Agree with a DP (any DP is okay, including expletive)(ii) Merge subfeatures
a. uDMrg — checked by Merge of a DP
b. uThetaMrg — checked by Merge of a theta-role bearing DP
c. uDMrgExpl — checked by Merge of an Expl
Sobin proposes that light verbs can have different combinations of the Agree and Merge subfeatures. See Sobin(2014) for further details.

10has a uDMrg feature, so a DP must Merge with it in specifier position. Crucially, uDMrg can bechecked by any type of DP, including an Expl.

(8) v~ has [uCheckTheta, uDMrg] (Sobin 2014: 393)
a. uCheckTheta is checked via Agree with a theta-bearing DP
b. uDMrg is checked via Merge of a DP

The v~ head provides a way to account for Th/EX in English.
The split-EPP feature of v~ accounts for the possibility of either the Expl there or theobject a train appearing in subject position in (9)a-b.

(9) a. There arrived a train.
b. A train arrived. (Sobin 2014: 393)

In (9)a, as shown in Figure 5, when v~ is Merged, its uCheckTheta subfeature Agrees with thetheta-role bearing object a train. Then, when the Expl there is Merged, the uDMrg subfeature ofv~ is checked. Note that uDMrg can be checked via Merge of any DP, regardless of whether or
not it bears a theta-role. Thus, Expl is sufficient.

11Figure 5

Derivation of (9)aThe structure of (9)b is shown in Figure 6. Assume that there is no Expl available for Merge.
Thus, both the uThetaAgr and uDMrg subfeatures of v~ are checked by the same object, a train.
In this case, the need to check the uDMrg subfeature of v~ results in the object a train undergoing
Th/Ex.

Figure 6v~ in (9)bNote that in (9)a-b, the v~+arrive complex is pronounced as arrived (assuming that a pasttense T is Merged). The v~ has no pronunciation, which turns out to be an issue, since v~ ispronounced in other examples (see below).
The progressive construction with an expletive (10) has two instances of v~, as shown in
Figure 7, where prog represents a progressive head that combines with v~ and a verbal root toform an -ing construction. The lower v~1 has both its uThetaAgr and uDMrg subfeatures checked
by a train. Checking of the uDMrg subfeature forces a train to remerge in specifier position ofv~1, and thus undergo Th/Ex. The uCheckTheta subfeature of the higher v~2 then is checked
via Agree with a train. Then Merge of an Expl with v~2 satisfies the uDMrg subfeature of v~2,
thus also preventing a train from moving higher.

12(10) a. There is a train arriving. (Sobin 2014: 399)
b. A train is arriving.

Figure 7v~ in (10)aIf the derivation lacks an Expl, then the structure results as shown in Figure 8. In this case, theobject a train moves all the way to matrix subject position, due to the lack of an Expl, to checkthe uDMrg subfeature of v~2. Thus, a train checks the uThetaAgr and uDMrg features of both v~1
and v~2.

Figure 8v~ in (10)b

13

Note that pronunciation of v~ in (10)a-b, as shown in Figure 7-Figure 8, is complex because
the higher v~2 is pronounced as is but the lower v~1 lacks any pronunciation, assuming thatthe progressive head Prog and v~ are pronounced as arriving. But it isn’t clear how to
distinguish the pronunciations of v~.
Sobin’s analysis also accounts for the impossibility of (11), as shown in Figure 9. In thiscase, the uThetaAgr of v~1 is checked via Agree with the object a train, and the uDMrg featureof v~1 is Checked by Merge of the Expl there. A problem then arises when v~2 is Merged
because the Expl blocks the uThetaAgr subfeature of v~2 from Agreeing with a train; since anExpl lacks a theta-role, it cannot check uThetaAgr. Sobin (2014) argues that this type of example
is ruled out because a phase boundary intervenes between v~2 and its potential goal. But even
if there were no phase boundary, this could be ruled out as an intervention effect caused by theExpl.

(11) *There is arriving a train.

Figure 9

Structure of (11)While Sobin’s analysis accounts for Th/Ex of an object to pre-verbal position, as well as
for the distribution of the Expl in English, there are some issues that arise with respect to SpellOut. In (10)a-b, as shown in Figure 7 and Figure 8, the higher v~1 is pronounced as is but the14lower v~2 lacks any pronunciation, as it combines with arrive and the progressive, to form
arriving. Thus, sometimes v~ is pronounced, and other times it is not, as shown in Figure 10.
If both of these are identical v~ elements, then the question arises of how the Spell-Out
component determines the correct pronunciation of v~. Another problem arises from theplacement of a train in constructions such as (10)a, in which a train undergoes Th/Ex topreverbal position. As a result, a train intervenes between the progressive head prog and thelower v~1, which need to combine to form arriving, as shown in Figure 10.

Figure 10v~ pronunciation in (10)aThese Spell-Out problems are resolved in our model as follows. First, since sometimes v~
is pronounced and other times it is not, we propose that there are actually two different typesof v~. One type, which we refer to as v~, is simply a light verb that is pronounced as a form ofbe, (12)a. Another type, (12)b, which we refer to as v~unacc, Merges with an unaccusative
verbal root, and lacks any pronunciation. Both types of v~ have the same Agree and Merge
features, (12)c. We utilize CheckTheta, which is essentially the same as Sobin’s uThetaAgr, torefer to a feature that is checked by a theta-bearing argument. Instead of uDMrg we simply utilize
an Edge Feature (EF). To deal with the affix-hopping problem, in which an object intervenes
between the progressive and v~, we assume that the progressive head (prog) has an EF, (13).

15

Thus, the EF on prog forces an object to move to the edge of prog, which enables affix-hoppingto occur without an intervening overt argument.

(12) v~ types
a. v~ is pronounced as beb. v~unacc has no pronunciation. (v~unacc Merges with an unaccusative verbal root)c. v~ and v~unacc have CheckTheta and EF(13) prog has an EF

With these proposals, we next explain how we implemented Sobin’s v~ analysis with our
computer model. The derivation of (10)a, as generated by our model, is shown in Figure 11.
This construction contains a v~unacc and a separate v~. The CheckTheta feature of v~unacc ischecked via Agree with the object a train and the EF feature of v~unacc is checked via remergeof a train. Then the higher prog head is Merged, and prog has an EF that forces a train to
remerge again in specifier position of prog. Note that because the object moves to the Spec ofthe prog projection, it no longer intervenes between prog and the v~unacc+arrive complex, sothat prog can affix-hop onto v~unacc+arrive. Then the higher v~ is Merged, and the
CheckTheta of v~ is checked via Agree with a train, which is in the Spec of the next lower
projection, and thus is accessible. The EF of v~ is checked via Merge of the Expl there. The
Expl has uPhi (unvalued Phi), indicated as !phi in the figure. These uPhi are eventually checked
via Agree with a higher T. The final structure and Spell-Out steps are shown in Figure 11b.
Crucially, the higher v~ is pronounced as a form of be and the lower v~unacc is silent, andprog affix hops onto v~unacc+arrive, forming arriving.

16

Figure 11

Derivation of (10)aWith our assumptions about v~ combined with our previous assumptions about feature
unification, we can now account for the core examples of Chomsky (2001), including thosewith Th/Ex.
The derivation of (2), repeated below as (14), is shown in Figure 12.

(14) Several prizes are likely to be awarded. (Chomsky 2001: 7)
17

When prt is Merged, Agree between prt and several prizes results in unification of uCase of prt
and several prizes, as well as checking of uNumber and uGender of prt. An EF of prt forces
several prizes to remerge in Spec position. Then when v~ is Merged, the CheckTheta featureof v~ is checked via Agree with the theta-role bearing several prizes. An EF on v~ also forces
several prizes to remerge in Spec position. Next, the non-finite Tinf has an EF that forces
several prizes to remerge in Spec position. The higher light verb be, vbe, also has an EF thatforces remerge of several prizes. When the matrix T is Merged, T Agrees with several prizes,
resulting in checking of the uPhi of T and the uCase of several prizes. Crucially, the uCase of
several prizes is unified with uCase of prt, so the unified uCase of prt is also checked. Then an
EF of T is checked by remerge of several prizes and the derivation eventually converges. The
final tree and Spell-Out are shown in Figure 12(b).

18

Figure 12

Derivation of (14)We next explain how we extended this model to account for completely different types ofexamples (that-trace effects, wh-movement, and relative clauses).

4. That-trace effects and subject vs. object wh-movement (Pesetsky & Torrego 2001)
Pesetsky & Torrego (2001), hereafter P&T, present an analysis that accounts for, in a unified
manner, the English subject/object wh-movement asymmetry and the that-trace effect. We
explain how we implemented their proposals.
P&T’s analysis relies on the idea that certain C heads have a uT feature that must be
checked in the most economical manner. P&T propose that a uT feature on C can be checkedby T or by nominative Case, which is checked uT on D, as summarized in (15). Nominative
Case can check uT because Nominative is a checked uT feature.

19(15) Certain C heads have a uT featurea. uT can be checked by T
b. uT can be checked by Nominative Case

P&T also propose that T in C is pronounced as that. Thus, when that appears in an embedded
clause, T has checked a uT feature on C. In a wh-question, they assume that an interrogative C
has uWh and uT features that need to be checked in order for a derivation to converge. Fromthe perspective of economy, Agree between an interrogative C and a single goal that can check
both uWh and uT features is most economical. This is stated in (16), where we utilize uQ
instead of uWh; we assume that a wh-phrase is headed by Q (cf. Hagstrom 1998; Cable 2007)
and it has an iQ feature that checks a uQ feature on an interrogative C. If the option of checking
both uT and uQ features is not available, then it is possible for C to form two separate Agreerelations, one which checks the uT feature and one which checks the uQ feature.

(16) Economy
Given C[uQ,uT], if goal X can check uT but not uQ, and goal Y can check both uQ and uT,then Agree with Y blocks Agree with X.

This analysis accounts for the optionality of that in embedded clauses, as in (17).

(17) Mary thinks (that) Sue will buy the book. (P&T 2001: 373)

The embedded clause is shown in Figure 13a. The embedded non-interrogative C is indicatedas Ce (our notation). P&T assume that Ce has a uT feature. Thus, one option is for the uT feature
to be checked via Agree with the subject Sue, in which case Nominative Case of the subject

20

checks the uT feature. P&T assume that uT has an EPP subfeature that forces remerge ofwhatever uT Agrees with. We utilize an Edge Feature (EF), assuming that whatever Agrees
with Ce must remerge with the Ce projection to check the EF. Thus, an EF of Ce forces the
subject Sue to remerge. Since the subject is in Ce, there is no pronunciation of that, as can beseen in the final structure, shown in Figure 13b. Note that the matrix clause contains what werefer to as vunerg, which occurs with a verbal root such as think that takes a clausal complement.
This vunerg is an unergative light verb that assigns a subject theta-role, but does not check Caseor have uPhi.6

6

Another possibility is that if v* doesn’t assign Case to an argument, then its uPhi don’t have to be checked.
Also see Epstein, Kitahara, and Seely (2016) for an account that relies on pair-Merge.

21Figure 13

Derivation of embedded clause of (17) without that22

Another possibility is for that to be pronounced in (17), as shown in Figure 14. In this case,the uT feature of Ce is checked via Agree with T and an EF forces T to raise to Ce.7 T in C is
pronounced as that, as shown in Figure 14b.

7

For P&T, an EPP subfeature of uT forces raising.

23

Figure 14

Derivation of embedded clause of (17) with thatWe next demonstrate how P&T (2001) account for wh-movement in an example suchas (18). Although P&T do not discuss this exact example, it is important for demonstrating theneed for a verbal element to raise to T.

(18) What will Mary buy?

Initially, shown in Figure 15a, after T is Merged, the modal will raises to T, which is necessary
so that the modal can eventually raise to C. We implemented this movement by giving T an
unvalued v feature, uv, that requires checking by the closest verbal head. The interrogative C,
which we indicate as CQ, has uQ, uT, and EF features. The EF feature forces whatever Agrees
with CQ to remerge with CQ. Initially, CQ forms an Agree relation with T, resulting in checkingof uT. An EF on CQ then forces T to remerge. Furthermore, the modal will is pied-piped with
T. This has the desired effect of bringing the modal into pre-subject position. Thus, we assume
that the highest verbal element raises to T (to check a uv feature) and that when T raises to CQ,
this verbal element also raises. While movement of the verbal element to T may seem like animperfection, this is necessary to account for the correct word order. If T alone were to move
to C, without the highest verbal element, then the result would be the ill-formed (19) in which
will remains below the subject, and T in C is pronounced as do.

(19) *What does Mary will buy?

If there is no overt auxiliary/modal that can raise to T, then the default do is inserted.
Continuing on, the uQ feature of CQ is checked via Agree with the Q-phrase what, and an EF

24

of CQ forces what to remerge. Note that two operations are required to check the uT and uQfeatures of CQ. The derivation then converges as shown in Figure 15b.

Figure 15

Derivation of (18)25

P&T (2001) present an economy-based account for the subject/object wh-question
asymmetry, exemplified in (20)a-c. When the object what undergoes wh-movement, did is
pronounced (generally considered to be an indication of T to C movement), but when thesubject who undergoes wh-movement, did is not permitted, as in (20)b-c.

(20) a. What did Mary buy?
b. Who bought the book?
c. *Who did buy the book? (unless did is focused) (Koopman 1983, per P&T: 357)

The relevant portions of the derivation of (20)a are shown in Figure 16. As with theprevious example, the highest verbal element, in this case v*, remerges with Tpast (past tense).
An Agree relation between CQ and Tpast checks the uT feature of CQ and an EF forces Tpast
to remerge. When Tpast remerges, v* is also pied-piped. Then CQ forms a second Agreerelation with the Q-phrase what, resulting in checking of the uQ feature of CQ, and an EF forces
what to remerge. In this case, Tpast in CQ is pronounced as did, assuming that when T in CQ
lacks a phonological form, a form of do is required. As in the previous example, separate Agree
operations are required to check the uQ and uT features of CQ.

26

Figure 16

Derivation of (20)aThe subject wh-question in (20)b has the structure shown in Figure 17. In this example,
the subject who is a Q-phrase, and thus it can check a uQ feature. Furthermore, the subject has
Nominative Case, which it obtains from T. When Tpast Agrees with who, both the uT and uQ

27

features are checked. Then an EF of CQ forces remerge of who. The other option would be forthe uT feature of CQ to be checked by Tpast, and then for the uQ feature to be checked via aseparate Agree relation with who. But P&T argue that this latter derivation is ruled out by
economy. Since the uQ and uT features of CQ can be checked via a single Agree relation formed
with who, the less economical derivation involving two separate Agree relations is blocked. As
a result, T cannot move to C, and (20)b is ruled out.88Note that according to P&T’s analysis, a subject can also check uT on CQ, as in (i) in which the subject Marychecks the uT, but this is ruled at Spell-Out for reasons of interpretation — only an exclamative subject (not a whphrase) can appear in a specifier of a CQ resulting in an exclamative. Thus, P&T rely on what is essentially aconceptual interface well-formedness condition to block (i).
(i) *What Mary bought (P&T: 358)

28

Figure 17

Derivation of (20)b

We next explain how we implemented P&T’s account of the that-trace effect, as found in(21)a-b.

(21) a. Who did John say will buy the book?
b. *Who did John say that will buy the book? (P&T: 371)

29

The embedded clause contains what we refer to as CeQ, which is an embedded non-interrogative
C that hosts a wh-phrase. CeQ contains uT and uQ features, but it cannot fully license a Qphrase. Rather, it hosts a Q-phrase that undergoes movement from an embedded clause to ahigher clause. The embedded clause of (21)a is shown in Figure 18a. Assume that a Q-phrase
has an unvalued scope feature, uScope, which is indicated as !scope in Figure 18a. This uScopeis not checked via Agree with CeQ — uScope must be checked by a truly interrogative CQ. As
in the previous example, CeQ forms an Agree relation with who, thereby checking the uT anduQ features via a single Agree relation, since who can check a uQ feature and the Nominative
Case of who can check the uT feature. The other option of checking the uT feature via Agreewith T, which would result in pronunciation of that, and the uQ feature via Agree with who isless economical, and thus banned. Therefore, the ill-formedness of (21)b is blocked due toeconomy. The final output and Spell-Out are shown in Figure 18b. Note that in the matrix
clause, the uT feature of CQ is checked via Agree with T, assuming that the Nominative Caseof who, from the embedded clause, is not available to check uT in the matrix clause.

30

Figure 18

Derivation of (21)a

In a construction such as (22)a, there is no that-trace effect because economy is not an
option for checking the uT and uQ features of the embedded CeQ, since there is no single
element that can check both uT and uQ features.

(22) a. What did John say that Mary will buy?
b. What did John say Mary will buy? (P&T: 370)

In (22)a, as shown in Figure 19a, the embedded CeQ forms an Agree relation with T, whichchecks the uT feature. As a result, an EF of CeQ forces T to remerge, and T in C is pronounced
as that. In (22)b, as shown in Figure 19b, CeQ forms an Agree relation with the subject Mary
instead of T. Thus, Mary remerges with CeQ to check an EF. Since there is no T in C, there is31

no pronunciation of that. In both examples (22)a-b, CeQ also forms an Agree relation with theobject what, which checks the uQ feature of CeQ and forces what to remerge.

Figure 19

Derivation of (22)aWe have thus demonstrated how we implemented the core proposals of P&T. We changeda few of the formalisms of P&T (e.g., we used an EF instead of EPP subfeatures, and uQ insteadof uWh). We also had to implement raising of a verbal element to T in matrix interrogative
clauses, which, although not discussed by P&T, is crucial for producing the correct outputs.
32

Our model thus demonstrates that P&T’s proposals can be successfully implemented, and this
implementation is not in conflict with the constructions, involving multiple agreement andexpletives, presented in the preceding sections. We next explain how we extended this modelto account for relative clauses.

5. Relative Clauses (Pesetsky & Torrego 2001; Gallego 2006)
Gallego (2006) proposes an analysis of relative clauses that follows P&T’s (2001) views about
economy and feature checking. Therefore, it is natural for us to extend our analysis to utilize
Gallego’s insights. Gallego proposes that a relative C has uRel and uT features. Following P&T(2001), the uT feature can be checked by T or by a nominative subject. The uRel feature,
however, must be checked by a relative DP. Gallego also assumes that there is a c head above
C that has uPhi (cf. Bianchi 2000 for a similar proposal), and N raises to c to check uPhi.
Furthermore, these uRel, uT, and uPhi features can have EPP subfeatures, although there issome variation with respect to when an EPP subfeature is present. We explain how Gallego
accounts for subject relative clauses, discuss some problems, and then explain our
implementation.
English subject-relative clauses permit who but not who that, as show in (23)a-b.

(23) a. the man who loves Maryb. *the man who that loves Mary (Gallego 2006: 156)

The relevant portion of the derivation of (23)a is shown in Figure 20. The relative C has uT
and uRel features and each of these features has an EPP subfeature, thus meaning that anythingthat Agrees with uT or uRel must also remerge with C. When C Agrees with who man, the uTfeature is checked by the Nominative Case of who man and the uRel feature is also checked,

33

assuming that who man has an iRel feature. The EPP (which actualy refers to a subfeature ofuT and another subfeature of uRel) is then checked via remerge of who man. Then there is ahigher c head, which has uPhi. The c head Agrees with the phi-feature bearing man. The Phi
of man check the uPhi of c and an EPP subfeature of uPhi forces man to remerge with c. Thenthe determiner the is externally Merged. Note that this derivation involves a single Agreerelation between the relative C and who man. The other option would be for the uT feature of
C to be checked by T and then the uRel feature to be checked by who man, which would involve
two Agree relations, and also result in pronunciation of that, due to T appearing in C. But
economy rules out this option given that a single Agree relation is possible. Thus, economy
accounts for the impossibility of that in subject relatives with a relative D who, thus blocking(23)b.

Figure 20

Derivation of (23)aGallego also accounts for the fact that that is required and a zero relative is banned, in a
subject relative clause such as (24)a-b.

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(24) a. the boy that called Mary (Gallego 2006: 158)
b. *the boy called MaryIn this case, Gallego assumes that a DP with a null D cannot move, following Chomsky’s(2001) view that an empty category cannot be pied-piped. In the derivation of (24)a, as shownin Figure 21, the relative DP does not move. As a result, the relative DP does not remerge with
C. Note also that because the relative DP has a null D, it cannot even move to Spec, T. The uTof C forms an Agree relation with T and an EPP subfeature of uT forces T to remerge. Notethat T in C results in pronunciation of that. The uRel of C forms an Agree relation with therelative DP. But the uRel, conveniently, lacks an EPP subfeature, so the relative DP does not
move. Then, the uPhi feature of c Agrees with boy and an EPP subfeature of uPhi forces boy
to remerge with c. Crucially, because the relative DP cannot move, the uT of C must be checkedby T, which forces pronunciation of that.

Figure 21

Derivation of (24)b35

Gallego’s analysis is not without problems. First of all, it isn’t clear why a DP that has anull D cannot move, but a DP with an overt D can move. Also, it isn’t clear why a uRel featureof C has an EPP subfeature when there is an overt D, as in (23)a, but lacks an EPP subfeaturewhen there is a null D, as in (24)a. The uRel lacks an EPP subfeature only when convenient;i.e. in cases in which the relative DP cannot move. Another consequence of this analysis is thata subject with a null D cannot move to Spec of T, but subjects are generally considered to bein Spec of T. Also, Gallego’s analysis requires a c head, as shown in Figure 20 and Figure 21,
but the question arises of why c Agrees with the relative noun to the exclusion of the relative
D. Also, it isn’t entirely clear why c is necessary.
We implemented a modified and improved version of Gallego’s analysis. We adopt
Gallego’s proposal that a relative C has uT and uRel features. But crucially, we do away withthe c head, and we also do away with the stipulation that a null d can’t move. There is also no
Agree relation that targets the relative N to the exclusion of the D head. Our core assumptions
about relative clauses are as follows.

(25) Relative C (Crel): [uRel,uT,EF](26) N: [uD](27) Relative Ds:
a. drel: [Rel]b. whorel: [Rel,T]

We assume that a relative C, our Crel, has uRel and uT features, as well as an EF, as shown in(25). Our EF serves the purpose of remerging anything that an Agree relation is establishedwith. So if a relative DP Agrees with the uRel of Crel, then the EF of Crel forces remerge of therelative DP. We propose that N, shown in (26), has a uD feature that requires checking via a D

36

element. Therefore, if D and N Merge, the uD feature on N is typically checked by an D featureof D. A relative D, shown in (27), however, is defective in that it is unable to check a uD feature,
as it lacks a D feature. This has the important consequence of leaving the N complement of a
relative D unlicensed. We also assume that the null relative D, indicated as drel, (27)a, has a Rel
feature that can check a uRel, but it lacks what we refer to as a T feature. This T is akin tonominative Case that can check a uT. As a result of lacking a T feature, drel is unable to checka uT feature. Note that we assume that even if a relative DP headed by drel has Nominative Case,it cannot check a uT feature, due to a lack of a T feature. The other relative head whorel, (27)b,
has both Rel and T features. Thus, it can check both uRel and uT. We also assume that there isan operation of Last Resort, (28), whereby an unlicensed argument remerges with the root of
an SO. This serves the purpose of bringing an unlicensed argument into the appropriate position
for forming a relative clause.

(28) Last Resort
At a phase boundary, remerge an unlicensed element with the root.

The derivation of (23)a, as produced by our model, is show in Figure 22. The relative DP has
the form whorel man, with the relative head whorel, which has both Rel and T features. Thus,
when Crel Agrees with the relative DP, both the uRel and uT features of Crel are checked. An
EF on Crel forces the relative DP to remerge. Note that the EF feature is not a subfeature ofuRel or uT, contra Gallego. Rather, any element that Agrees with Crel is forced to remerge due
to Crel’s EF. The other option would be to check the uRel feature by the relative DP and the uTfeature by T, but this would involve two Agree relations, which is blocked by economy (16).
This analysis accounts for why that is not possible, as in (23)b. The uT feature cannot bechecked by T, so that, which is T in C, is not permitted. When Crel is complete, the relative N37

man is still unlicensed, assuming that it has a uD feature. At this point, the operation of Last
Resort (28) applies and man remerges with the root node. Since man is a head, and the Crelprojection is an XP, the head man labels.9 Then, when the external D the is Merged, the uDfeature on man is checked and the labels. The D the has an unvalued uCase feature (indicatedas !case), which is eventually checked when the DP obtains Case, for example as a subject orobject of a larger syntactic structure.

9

See Cecchetto and Donati (2015) for a similar head-raising account of relativization, In Cecchetto and Donati’s
account, only heads (not phrases) may raise to relabel a clause. Furthermore, head raising is constrained by Gross
Minimality considerations. We leave comparison of our account with that of Ceccehetto and Donati for future
work.

38

Figure 22

Derivation of (23)a (implementation)

The derivation of (24)a is shown in Figure 23. In this example, the relative DP is headedby drel, which crucially lacks a T feature, so it cannot check uT on Crel. Therefore, there is no
option of the relative DP checking both the uT and uRel features of Crel. As a result, Crel forms
an Agree relation with drel boy, which checks the uRel feature, and Crel must form a separate
Agree relation with T to check the uT feature. An EF feature forces both T and drel boy toremerge. Remerge of T in C results in pronunciation of that. Then when the Crel projection iscomplete, Last Resort applies to force the unlicensed relative noun boy to remerge, due to its
uD feature. Being a head, boy labels. Then when the external D the is Merged, the uD featureof boy is checked and the relative clause is successfully completed as shown in Figure 23b.

39

Figure 23

Derivation of (24)a (implementation)

Following the insights of P&T and Gallego, we have implemented relative clauses without
an extra projection in the left periphery of the clause, and without recourse to optional EPP
subfeatures. Rather, we simply use the idea that a relative C head, Crel, has uT and uRel features,
and a relative D differs in whether or not it can check the uT feature of Crel. When the relative40

D can check uT, then economy requires this operation, thus blocking pronunciation of that.
When the relative D cannot check uT, then T must check uT, thus requiring the presence ofthat.

6. Conclusions
We have highlighted important details of our implementation of expletives and multiple
agreement (Chomsky 2001), thematization/extraction (Sobin 2014), that-trace effects andsubject vs. object wh-movement (P&T 2001), and relative clauses (Pesetsky & Torrego 2001;
Gallego 2010). We explained how we dealt with particular problems that arose in the theories
that we implemented and how these problems can be resolved. Problems arising with respect
to multiple agreement in Chomsky (2001) were dealt with via feature unification. Problems
arising with respect to feature checking and the position of the expletive there were also
resolved with feature unification, as well as with the notion that an expletive is Merged low ina position below T. Problems from Sobin (2014) regarding locality of affixes and spell-out
were resolved via the use of EFs (prt has an EF) and distinguishing v~ into two separate types
that differ in pronunciation (v~unacc and v~). We implemented P&T’s account of whmovement and that-trace effects, and in the process clarified how the fine details work; weutilized an EF instead of an EPP subfeature and we implemented movement of the highest
verbal element to T in a matrix clause. Lastly, we resolved problems with Gallego’s (2010)account of relative clauses. We utilized relative Ds that differ with respect to whether or notthey can check a uT feature. We also incorporated a notion of last resort whereby an unlicensed
relative N can undergo movement, thus doing away with the notion that an extra projection isneeded in the left periphery. Crucially, all of these modifications and improvements of workfrom Chomsky (2001), P&T (2001), and Gallego (2010), were implemented via a single unified

41

model, thus demonstrating that a wide variety of constructions can be accounted for with asingle theory.
In conclusion, we have integrated core components of different linguistic theories to createa single unified theory that accounts for a wide variety of data. Our theory provides possible
explanations for target phenomena, and this theory has been successfully tested.

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