Proceedings of the 3rd Workshop on Constraints and Language Processing (CSLP-06), pages 1–8,
Sydney, July 2006. c©2006 Association for Computational Linguistics
Constraints in Language Processing: Do Grammars Count?  
 
 
Marieke van der Feen 
Department of Artificial  
Intelligence, 
University of Groningen, 
Grote Kruisstraat 2/1,  
9712 TS Groningen, 
The Netherlands 
mvdfeen@ai.rug.nl 
Petra Hendriks 
Center for Language and 
Cognition Groningen, 
University of Groningen, 
P.O. Box 716,  
9700 AS Groningen, 
The Netherlands 
p.hendriks@rug.nl 
John Hoeks 
Center for Language and 
Cognition Groningen, 
University of Groningen 
P.O. Box 716,  
9700 AS Groningen, 
The Netherlands 
j.c.j.hoeks@rug.nl 
 
  
 
Abstract 
One of the central assumptions of Opti-
mality Theory is the hypothesis of strict 
domination among constraints. A few 
studies have suggested that this hypothe-
sis is too strong and should be abandoned 
in favor of a weaker cumulativity hy-
pothesis. If this suggestion is correct, we 
should be able to find evidence for cumu-
lativity in the comprehension of Gapping 
sentences, which lack explicit syntactic 
clues in the form of the presence of a fi-
nite verb. On the basis of a comparison 
between several computational models of 
constraint evaluation, we conclude that 
the comprehension of Gapping sentences 
does not yield compelling evidence 
against the strict domination hypothesis. 
1 Introduction 
A linguistic framework which has gained a con-
siderable amount of attention in recent years is 
Optimality Theory (Prince and Smolensky, 
1993/2004). Optimality Theory (henceforth OT) 
is not only used for analyzing and explaining 
linguistic phenomena in the domain of phonol-
ogy, but also in the domains of morphology, syn-
tax, semantics and pragmatics. In contrast to 
more traditional linguistic frameworks, OT as-
sumes grammatical constraints to be violable. 
Because constraints are formulated in such a way 
that they are maximally general (and perhaps 
even universal across languages), these con-
straints may conflict. To resolve conflicts among 
constraints, constraints are assumed to differ in 
strength. It is better to violate a weaker constraint 
than it is to violate a stronger constraint. The 
grammatical structure is the one that violates the 
least highly ranked (i.e., strong) constraints. 
A fundamental property of OT is the principle 
of strict domination. This means that each con-
straint has complete priority over all constraints 
ranked lower in the constraint hierarchy. A num-
ber of recent studies, however, have called into 
question this fundamental property of OT. Keller 
(2001) argues that constraint violations must be 
cumulative to account for the pattern of relative 
acceptability with respect to the phenomenon of 
Gapping. Jäger and Rosenbach (to appear) draw 
a similar conclusion on the basis of the observed 
variation with respect to the English genitive (the 
king’s palace versus the palace of the king).  
In this study, we focus on the linguistic phe-
nomenon of Gapping. The central question is 
whether the comprehension of Gapping sen-
tences provides evidence in favor of cumulativity 
of constraint violations. In section 2, we intro-
duce the phenomenon and discuss the possibility 
of an OT model of Gapping. In section 3, we 
consider different kinds of cumulativity. Section 
4 discusses the way we modeled four different 
evaluation algorithms based on these kinds of 
cumulativity. A comparison between our compu-
tational models of constraint evaluation in sec-
tion 5 suggests that the comprehension of Gap-
ping does not provide compelling evidence for 
abandoning the strict domination hypothesis.  
2 Gapping 
Gapping is a grammatical operation that deletes 
certain subconstituents in the second conjunct of 
a coordinate structure, as in (1): 
1
 
(1) Some ate beans, and others rice. 
 
The deleted material always includes the finite 
verb, but may also include further constituents 
such as the direct object. As a result, it may not 
always be possible to uniquely identify which 
elements were left out. As an example, consider 
the following sentence: 
 
(2) John greeted Paul yesterday and George 
today. 
 
This sentence is ambiguous between reading (3), 
where first John greeted Paul, and then John 
greeted George, and reading (4), where first John 
greeted Paul, and then George greeted Paul. 
  
(3) John greeted Paul yesterday and John 
greeted George today. 
(4) John greeted Paul yesterday and George 
greeted Paul today. 
 
The reading in (3) is traditionally analyzed as 
resulting from the operation of conjunction re-
duction, whereas the reading in (4) is analyzed as 
resulting from Gapping of the finite verb and the 
direct object. 
2.1 Functional constraints on Gapping  
Based on previous work on Gapping, Kuno 
(1976) notes that several non-syntactic factors 
affect the acceptability and interpretation of Gap-
ping. One of these factors is the distance between 
the remnants in the second conjunct and their 
counterparts in the first conjunct: 
  
(5) The Minimal Distance Principle: 
 The two constituents left behind by Gap-
ping can be most readily coupled with 
the constituents (of the same structures) 
in the first conjunct that were processed 
last of all.  
 
According to this principle, interpretation (3) 
should be preferred for sentence (2) because it is 
more preferable to couple George in the second 
conjunct to the direct object Paul in the first con-
junct, than to the more distant subject John. This 
preference is confirmed by experimental evi-
dence (Carlson, 2001). A further principle about 
Gapping is that the deleted material has to repre-
sent contextually given information, whereas the 
remnants in the second conjunct have to consti-
tute new information. This is captured in the fol-
lowing principle: 
 
(6) The Functional Sentence Perspective 
(FSP) Principle of Gapping: 
a. Constituents deleted by Gapping 
must be contextually known. On the 
other hand, the two constituents left be-
hind by Gapping necessarily represent 
new information and, therefore, must be 
paired with constituents in the first con-
junct that represent new information.  
b. It is generally the case that the 
closer a given constituent is to sentence-
final position, the newer the information 
it represents in the sentence.  
c. Constituents that are clearly 
marked for nonanaphoricity necessarily 
represent new information in violation of 
(b). Similarly, constituents that appear 
closest tot sentence-final position neces-
sarily represent old information (in vio-
lation of (b)) if coreferential constituents 
appear in the corresponding position in 
the preceding discourse. 
 
This principle explains the observation that in a 
suitable context, interpretation (4) can become 
the preferred interpretation for (2) (but see Hoeks 
et al. (2006) for experimental evidence that in 
addition to context also prosody has to be in ac-
cordance with a Gapping reading to make this 
reading the preferred reading):  
 
(7) When did John and George greet Paul? 
John greeted Paul yesterday and George 
greeted Paul today. 
 
In this example, John, Paul and George are all 
contextually introduced. But only John and 
George are subjects in the context sentence and 
hence can be interpreted as contrastive topics in 
the target sentence. Contrast has a similar effect 
as newness. Because of this effect of context, the 
Gapping reading can become the preferred read-
ing for (2). Two further principles proposed by 
Kuno are (8) and (9). 
 
(8) The Tendency for Subject-Predicate In-
terpretation: 
When Gapping leaves an NP and a VP 
behind, the two constituents are readily 
interpreted as constituting a sentential 
pattern, with the NP representing the 
subject of the VP. 
2
(9) The Requirement for Simplex-Sentential 
Relationship: 
The two constituents left over by Gap-
ping are most readily interpretable as en-
tering into a simplex-sentential relation-
ship. The intelligibility of gapped sen-
tences declines drastically if there is no 
such relationship between the two con-
stituents. 
 
The principle in (8) is meant to account for a dif-
ference in preference with object control verbs 
versus subject control verbs. The principle in (9) 
reflects the observation that Gapping cannot 
leave behind remnants that are part of a subordi-
nate clause. Kuno notes that this latter constraint 
seems to be the strongest of the four principles, 
being nearly inviolable, but does not make the 
interaction between his principles explicit. 
2.2 An OT model of Gapping  
As Kuno already observes, the FSP Principle 
seems to be able to override the Minimal Dis-
tance Principle. This observation is regarded by 
Keller (2001) as evidence that Gapping is subject 
to constraint competition in an optimality theo-
retic sense. Based on Kuno’s principles, Keller 
develops an OT model of Gapping, which is able 
to account for the pattern of relative acceptability 
of Gapping sentences. According to this model, 
the degree of acceptability of a candidate struc-
ture depends on the number and type of re-
rankings required to make the structure optimal 
(Keller, 1998). 
Keller’s OT model differs from standard OT 
in a number of ways. Firstly, a distinction is 
made between soft and hard constraints. Hard 
constraints cause strong acceptability when vio-
lated, while violation of soft constraints causes 
only mild unacceptability. According to Keller, 
the Requirement for Simplex-Sentential Rela-
tionship is such a hard constraint. The distinction 
between soft and hard constraints is needed in 
Keller’s model to avoid the problem of overgen-
eration of acceptability differences.  
Secondly, Keller’s model assumes that con-
straint violations are cumulative. According to 
his model, the degree of unacceptability in-
creases with the number of constraints violated. 
In standard OT, on the other hand, no number of 
violations of weaker constraints can override one 
violation of a stronger constraint, in accordance 
with the principle of strict domination. 
The aim of Keller’s OT model is to account 
for the pattern of relative acceptability of Gap-
ping sentences. The aim of the present study, on 
the other hand, is to account for the comprehen-
sion of Gapping sentences. Nevertheless, we fol-
low Keller in adopting Kuno’s functional princi-
ples (reformulated as OT constraints) for our OT 
model because Kuno’s principles are principles 
of comprehension. 
Our model differs from Keller’s model in sev-
eral essential aspects, though. We assume that all 
constraints are violable, in accordance with the 
basic assumptions of OT. Because certain strong 
constraints are not violated by the data under dis-
cussion, they simply appear to be inviolable. 
Keller’s second assumption, the assumption that 
constraint violations are cumulative, is the topic 
of investigation of this study.  
3 Cumulativity of constraint violations 
In this section we discuss the different ways OT 
constraints can interact. In principle, OT con-
straints can interact in an unrestricted way, or in 
one of several more or less restricted ways.  
3.1 Unrestricted constraint interaction  
OT as a linguistic theory is derived from Har-
monic Grammar (Legendre et al., 1990). In Har-
monic Grammar (henceforth HG), each con-
straint is associated with a positive or negative 
numerical weight value. For each candidate, a 
so-called Harmony value is calculated by sum-
ming the numerically weighted constraints. From 
the set of candidates, the candidate with the 
highest Harmony value is selected as the optimal 
candidate. Consequently, the interaction among 
constraints in HG is cumulative. Each constraint 
violation lowers the Harmony value of the can-
didate. This type of constraint interaction is es-
sentially unrestricted.  
To account for natural language interpretation, 
however, unrestricted cumulativity is too liberal, 
as is shown by OT analyses of other phenomena. 
With respect to Gapping, if Kuno and Keller are 
right, no amount of violations on weaker con-
straints of an interpretation satisfying Simplex-
Sentential Relationship can make an interpreta-
tion violating Simplex-Sentential Relationship 
the preferred one:  
 
(10) Who did John promise to examine who?  
John promised Paul to examine George, 
and Ringo Bob. 
 
If Simplex-Sentential Relationship indeed is a 
strong constraint, (10) should only mean that 
3
Ringo promised to examine Bob (satisfying Sim-
plex-Sentential Relationship but violating the 
Minimal Distance Principle and the FSP), and 
never that John promised to examine Bob (vio-
lating Simplex-Sentential Relationship).  
For the analysis of natural language, therefore, 
but also for the establishment of cross-linguistic 
generalizations (see Legendre et al., 2006), we 
seem to require a type of constraint interaction 
which is more restricted than simple numerical 
constraint weighting. 
3.2 Restricted constraint interaction  
In this section we discuss four ways to restrict 
constraint interaction: (1) strict domination, (2) 
local restricted cumulativity, (3) global restricted 
cumulativity, and (4) Keller’s counting cumula-
tivity.  
 
 A B C D 
  Candidate 1  * * * 
      Candidate 2 *!    
 
Tableau 1: Strict domination 
 
Strict domination is illustrated in tableau 1. The 
constraints are ordered from left to right in the 
top row in order of descending strength. Under 
strict domination, no number of violations of the 
weaker constraints B, C and D is able to override 
a violation of the strongest constraint A. 
 
 A B C D 
      Candidate 1   *! *! 
  Candidate 2  *   
 
Tableau 2: Local restricted cumulativity 
 
Tableau 2 illustrates local restricted cumulativity. 
When the weaker constraints C and D are simul-
taneously violated, their joint effect can be 
stronger than their linear sum. As a result, to-
gether they are able to override the immediately 
dominating constraint B. This type of cumulativ-
ity is similar to the effects of local conjunction. 
The result is a conjoined constraint C&D, which 
is ranked immediately above constraint B in the 
hierarchy.  
 
 A B C D 
      Candidate 1   *! *! 
  Candidate 2 *    
 
Tableau 3: Global restricted cumulativity 
An illustration of global restricted cumulativity is 
given in tableau 3. In this case, the weaker con-
straints C and D together are able to override a 
stronger, but not necessarily immediately domi-
nating, constraint A. Again, this type of cumula-
tivity is similar to the effects of local conjunc-
tion. The result is a conjoined constraint C&D, 
which is ranked anywhere above C and D in the 
hierarchy. 
 
 A B C D 
      Candidate 1  * *! * 
  Candidate 2 *    
 
Tableau 4: Keller’s counting cumulativity 
 
Keller’s counting cumulativity is illustrated in 
tableau 4. For Keller’s cumulativity, the hierar-
chical relation between the constraints is irrele-
vant. The candidate with the fewest constraint 
violations is always optimal. In Keller’s model, 
constraint violations are assumed to result in a 
gradient pattern. The more constraints are vio-
lated by a given Gapping construction, the less 
acceptable the construction is predicted to be. Of 
course, this type of cumulativity will greatly 
overgenerate in production as well as in compre-
hension if every constraint violation counts as an 
equally serious violation. For this reason, a sys-
tem employing this type of cumulativity must 
make a distinction between soft and hard con-
straints. Hard constraints cause strong unaccept-
ability. This extra assumption serves to restrict 
the overgenerating power of this type of cumula-
tivity. 
The four types of cumulativity discussed here 
differ in the amount of freedom they allow. Strict 
domination is the most restricted type of con-
straint interaction, local restricted cumulativity 
the one but most restricted type, global restricted 
cumulativity the two but most restricted type, 
and Keller’s cumulativity the least restricted 
type. As a result, strict domination yields the 
strongest  hypothesis, and Keller’s cumulativity 
the weakest hypothesis. The question we set out 
to answer in the next section is how strongly 
constraint interaction must be restricted to ac-
count for the comprehension of Gapping sen-
tences. 
4 Testing the evaluation algorithms 
To test the predictions of the four types of cumu-
lativity discussed in the previous section, a com-
puter model was developed in Prolog. The input 
4
to the model is a Gapping sentence in Dutch. The 
first conjunct is manually parsed. Information 
about the givenness of its constituents, the selec-
tional restrictions of the main verb of the first 
conjunct, and featural information for all NPs is 
added. The output of the model is formed by the 
possible couplings of constituents in the second 
conjunct with constituents in the first conjunct. 
In addition, for each possible coupling the con-
straint profile is given. For each possible cou-
pling, the model also gives a reconstruction of 
the second conjunct by placing the constituents 
from the second conjunct in the position of the 
constituents they are coupled with in the first 
conjunct. 
4.1 Constraint ranking 
The constraints implemented in the model were 
Kuno’s principles, reformulated as OT con-
straints, augmented with constraints on parallel-
ism (cf. Carlson, 2001), thematic selection 
(Hoeks and Hendriks, 2005) and word order 
(Lamers and de Hoop, 2004). The constraint 
ranking used is: 
 
(11) Categorial Parallelism >> Simplex-
Sentential Relationship >> FSP >> The-
matic Selection >> Subject Precedes Ob-
ject >> Syntactic Parallelism >> Mini-
mal Distance >> Subject-Predicate In-
terpretation >> Featural Parallelism 
 
The constraint Categorial Parallelism is added to 
ensure that constituents are coupled with con-
stituents of the same syntactic category only. It 
prevents, for example, that in (2) today is cou-
pled with Paul. Thematic Selection expresses the 
selectional restrictions verbs may impose on their 
arguments. For example, the verb bake requires 
an inanimate object, the verb introduce requires 
an animate object, and the verb take can combine 
with either an animate or an inanimate object 
(see section 4.3). The constraint Thematic Selec-
tion is violated if the candidate interpretation 
does not satisfy these selectional restrictions, for 
example if the object of the verb bake is animate. 
According to the constraint Subject Precedes Ob-
ject, the subject must linearly precede the object. 
Syntactic Parallelism requires the two conjuncts 
to have the same syntactic structure. The con-
straint Featural Parallelism, finally, promotes the 
coupling of constituents which share features 
such as animacy, definiteness, number and gen-
der. The ranking of these constraints was deter-
mined on the basis of the literature (Carlson, 
2001; Kuno, 1976) and via comparison of rele-
vant sentences and their meanings. 
4.2 Computational considerations 
The different types of cumulativity were compu-
tationally modeled as different ways of evaluat-
ing the constraint profiles.  
Strict domination can be modeled as numeri-
cal weighting with exponential weights.  
Local restricted cumulativity can be modeled 
as numerical weighting as well, if the weights are 
chosen in such a way that the sum of two adja-
cent constraints is larger than the weight of the 
directly dominating constraint. This is the case if, 
for example, B is 0.50, C is 0.26, and D is 0.25 in 
tableau 2. In our model, local restricted cumula-
tivity only applies to the constraints Thematic 
Selection, Subject Precedes Object and Syntactic 
Parallelism, and allows the constraints Subject 
Precedes Object and Syntactic Parallelism to-
gether to override the directly dominating con-
straint Thematic Selection.  
Global restricted cumulativity, on the other 
hand, cannot be captured straightforwardly in a 
system with weight values. To implement this 
evaluation method, therefore, we made explicit 
use of constraint conjunction. The newly formed 
conjoined constraint C&D was located in the 
hierarchy somewhere above its constituting con-
straints C and D. Because violation of this con-
joined constraint is dependent on the violation of 
each of the constituting constraints, the new con-
straint can only be evaluated in a second round 
of evaluation after all other constraints have been 
evaluated. This is an unfortunate complication of 
our implementation. Legendre et al. (2006: 352) 
show that this type of cumulativity can be im-
plemented with weight values if constraint con-
junction is assumed to involve a superlinear 
combination of weights (through summation as 
well as multiplication). In our model, only the 
constraints Minimal Distance and Subject-
Predicate Interpretation were allowed to conjoin. 
The resulting conjoined constraint was located 
above Categorial Parallelism in the hierarchy.  
For the fourth method of evaluation, Keller’s 
counting cumulativity, simply counting the num-
ber of constraint violations suffices. By applying 
one of these four evaluation algorithms, the 
computational model yields an optimal interpre-
tation for each combination of input and evalua-
tion algorithm. 
5
4.3 Input sentences 
To test the four evaluation algorithms, we fed the 
model three types of input: (i) 10 Gapping sen-
tences taken from a corpus, (ii) test sentences 
taken from all five conditions of Carlson’s 
(2001) study on Gapping, and (iii) 15 hand-
crafted sentences. 
The Eindhoven corpus (uit den Boogaart, 
1975) is an annotated corpus of Dutch written 
text of about 750 000 words. We scanned the 
corpus for suitable Gapping sentences, which 
had to occur unembedded, contain an overt con-
junction, and should not involve other deletion 
operations as well. Unfortunately, we only found 
10 such Gapping sentences in the corpus, pre-
sumably because Gapping is quite rare. For all 
ten sentences, all evaluation methods produced 
the same outputs. Nine out of the ten optimal 
interpretations did not violate any of the con-
straints. One sentence involved a constraint vio-
lation by all models, namely a violation of the 
constraint Featural Parallelism: 
 
(12) Groep 1 trok de arm na vijftien minuten 
uit de testkamer, en groep 4 na een uur. 
Group 1 pulled the arm after fifteen 
minutes from the test room and group 4 
after an hour. 
 
The most plausible interpretation of this sentence 
is the interpretation that group 4 pulled the arm 
from the test room after an hour. The interpreta-
tion selected by all evaluation methods, however, 
was that group 1 pulled group 4 from the test 
room after an hour, thus satisfying Minimal Dis-
tance but violating Featural Parallelism. It may 
be that the strong parallelism between group 1 
and group 4 sets up a contrast which evokes the 
constraint FSP even in the absence of an explicit 
linguistic context. If this is true, Minimal Dis-
tance must be violated in order to satisfy FSP.  
We also fed the models test sentences taken 
from Carlson’s (2001) written questionnaire. 
Carlson studied the interaction between The-
matic Selection, Featural Parallelism and Mini-
mal Distance by varying verb type (see the dis-
cussion of Thematic Selection in section 4.1) and 
properties of the noun phrases. She distinguished 
five conditions: the Bake A condition (Alice 
bakes cakes for tourists and Caroline for her 
family), the Bake B condition (Alice bakes cakes 
for tourists and brownies for her family), the 
Take A condition (Josh visited the office during 
the vacation and Sarah during the week), the 
Take B condition (Josh visited Marjorie during 
the vacation and Sarah during the week) and the 
Introduce condition (Dan amazed the judges with 
his talent and James with his musicality).  
The four evaluation algorithms behaved ex-
actly the same on all five conditions of Carlson 
because none of Carlson’s sentences involves a 
simultaneous violation of Subject Precedes Ob-
ject and Syntactic Parallelism (which would give 
rise to local restricted cumulativity in our model) 
or a simultaneous violation of Minimal Distance 
and Subject-Predicate Interpretation (which 
would give rise to global restricted cumulativity 
in our model). As a result, all models yielded a 
100% Gapping response for Carlson’s Bake A 
condition (compared to Carlson’s subjects 81%) 
because for all models a violation of Thematic 
Selection is more serious than a violation of 
Minimal Distance. Furthermore, all models 
yielded a 100% non-Gapping response for her 
Bake B condition (compared to Carlson’s sub-
jects 97%) because a Gapping response violates 
Thematic Selection, Minimal Distance and Fea-
tural Parallelism whereas a non-Gapping re-
sponse satisfies all three constraints. Finally, all 
models yielded a 100% non-Gapping response 
for Carlson’s Take A condition (compared to 
Carlson’s subjects 60%), her Take B condition 
(compared to Carlson’s subjects 96%) and her 
Introduce condition (compared to Carlson’s sub-
jects 79%) because for all models a violation of 
Minimal Distance is more serious than a viola-
tion of Featural Parallelism, given the constraint 
ranking in (11).  
So all models correctly predicted the interpre-
tational preferences found in Carlson’s experi-
ment. However, subjects’ percentages of non-
Gapping responses on the Take A, Take B and 
Introduce condition varied considerably. This 
variation seems to be due to differences between 
the features of the NPs involved. In particular, in 
the Take A condition the feature animacy played 
a role, which seems to have a stronger effect than 
the other grammatical features that were manipu-
lated. However, our constraint Featural Parallel-
ism does not distinguish between animacy and 
other grammatical features. Moreover, our OT 
model is unable to capture the gradience that 
seems to result from the interaction between fea-
tures. 
4.4 Generating different predictions 
Because the four evaluation algorithms behaved 
identically on all sentences taken from the corpus 
as well as on all sentences types from Carlson’s 
6
study, we had to construct sentences on the basis 
of expected constraint violations in order to gen-
erate different predictions for the four evaluation 
algorithms. The following sentence is predicted 
to distinguish between strict domination and lo-
cal restricted cumulativity: 
 
(13) John picked a rose, and a tulip Paul. 
 
If hearers interpret this sentence as meaning that 
a tulip picked Paul, they will have violated the 
stronger constraint Thematic Selection in order 
to satisfy the two weaker constraints Subject 
Precedes Object and Syntactic Parallelism. This 
then would constitute evidence for local re-
stricted cumulativity. If, on the other hand, hear-
ers interpret this sentence as meaning that Paul 
picked a tulip, then this is evidence for strict 
domination. Sentence (14) distinguishes between 
strict domination and global restricted cumulativ-
ity: 
 
(14) John asked him to get Paul, and George 
to bring Ringo. 
 
Because him is a pronoun, it counts as given for 
evaluating the constraint FSP. If hearers interpret 
this sentence as meaning that John asked George 
to bring Ringo, they will have violated the 
stronger constraint FSP in order to satisfy the 
weaker constraints Minimal Distance and Sub-
ject-Predicate Interpretation. Because FSP does 
not immediately dominate the weaker con-
straints, this would be evidence for global re-
stricted cumulativity. To distinguish between 
strict domination and Keller’s counting cumula-
tivity, consider the following sentence: 
 
(15) The children promised John to stop, and 
the neighbors to continue. 
 
If hearers interpret this sentence as meaning that 
the neighbors promised John to continue, they 
violate the single stronger constraint Minimal 
Distance in favor of satisfaction of the two 
weaker constraints Subject-Predicate Interpreta-
tion and Featural Parallelism. Because these con-
straints would all be considered soft constraints 
according to Keller’s distinction between hard 
and soft constraints, Keller’s counting cumulativ-
ity predicts that this interpretation is preferred. 
The strict domination hypothesis, on the other 
hand, predicts that the interpretation is preferred 
according to which the children promised the 
neighbors to continue, since it is more important 
to satisfy the stronger constraint Minimal Dis-
tance than any number of weaker constraints.  
5 Results and discussion 
For all Gapping sentences occurring in the Eind-
hoven corpus and all Gapping sentences taken 
from the written part of Carlson’s psycholinguis-
tic study, the four evaluation algorithms yielded 
identical results. These sentences therefore do 
not shed any light on the central question of this 
study, namely whether the strict domination hy-
pothesis should be abandoned in favor of a 
weaker cumulativity hypothesis. 
To determine which evaluation algorithm 
models the way comprehenders process language 
best, we must look at the interpretations of sen-
tences such as (13), (14) and (15). We presented 
10 participants with a written questionnaire, 
which included 15 sentences distinguishing be-
tween the four evaluation algorithms. The reader 
is referred to van der Feen (2005) for the com-
plete list of sentences. The results show that 
there does not seem to be a clear preference in 
interpretation for sentences such as (13), leaving 
the distinction between strict domination and 
local restricted cumulativity undecided. For sen-
tences such as (14), on the other hand, there 
seems to be a clear preference for the reading 
supported by global restricted cumulativity. Sen-
tences such as (15), finally, show no effects at all 
of Keller’s counting cumulativity. For only one 
sentence only one subject preferred the interpre-
tation according to which the neighbors promised 
John to continue, which favors the strict domina-
tion hypothesis and goes against Keller’s cumu-
lativity algorithm. This suggests that constraints 
on comprehension may be different from the 
principles governing acceptability judgments. 
Boersma (2004) argues that the paralinguistic 
task of providing acceptability judgments in-
volves comprehension, but under a reverse map-
ping between meaning and form. An alternative 
view is that acceptability judgments involve a 
mapping from the given form to its optimal 
meaning (‘what do I think the sentence means?’), 
followed by a mapping from that meaning to the 
optimal form for that meaning (‘how would I 
express that meaning?’), thus involving princi-
ples of comprehension as well as production.  
To conclude, there seems to be a slight indica-
tion of global restricted cumulativity in the com-
prehension of Gapping, but further study with a 
larger pool of subjects is required to confirm 
these initial findings.  
7
However, a few remarks are in place here. 
First, note that for hearers to prefer the interpre-
tation that Paul picked a tulip for (13), the hearer 
has to find some motivation in the linguistic con-
text of the utterance for why the speaker chose to 
put the object first. In the absence of such a con-
text supporting a non-canonical word order, the 
reading that Paul picked a tulip might be dis-
preferred anyway. 
Also in sentence (14), context seems to play a 
crucial role. Although in general pronouns may 
be used to refer to given material, in certain con-
texts pronouns can be emphatically stressed. If 
the pronoun in (14) is stressed, it is much easier 
to couple George to him to obtain the reading 
that John asked George to bring Ringo. This ef-
fect of context and prosody may have been the 
main reason for the observed preferences. 
6 Conclusion 
A central principle of Optimality Theory is the 
hypothesis of strict domination among con-
straints. In this paper we investigated whether 
this hypothesis should be abandoned in favor of 
the weaker hypothesis that constraint violations 
are cumulative. Studying the effects of four dif-
ferent evaluation algorithms (three of which dis-
play some kind of cumulativity) on the compre-
hension of Gapping sentences, we found a slight 
indication of cumulativity effects. However, 
these effects are likely to disappear if the context 
and prosodic structure of the utterance are taken 
into account. 
Acknowledgments 
The authors thank three anonymous reviewers 
for their useful comments and suggestions. This 
research was funded by grant # 015.001.103 
from  NWO, awarded to Petra Hendriks.  

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