On Domain Minimization
Prepositional Phrase Ordering Revisited
Daniel Wiechmann — RWTH Aachen University
Arne Lohmann — Leibniz Universität Hannover
METHODS & RESULTS
INTRODUCTION
Language users have a choice concerning the relative ordering of
prepositional phrases.
Efficiency-based accounts (Hawkins 1994, 2000, 2004, also
Gibson 1998, 2000), assume that speakers prefer arrangements
that have optimal processing properties. The principle of domain
minimization (Hawkins 2004) predicts that more efficient variants
are preferred in proportion to the minimization difference between
the competing sequences.
Values < 0 mean
actual order is less optimal
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The results show that both syntactic (PCD) and semantic
(LDD) domain minimization significantly influence the
order of prepositional phrases.
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i. The astronomer gazed [ into the sky ] [ through his telescope ].
ii. The astronomer gazed [ through his telescope ] [ into the sky ].
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Our comparison of the relative strengths of the two
principles suggests that Hawkins’ (2000) claim of a
generally higher importance of PCD (see above) should
be revised:
Values > 0 mean
actual order is more optimal
0
5
Values < 0 mean
actual order is less optimal
iii. John counted [ on your support ] [ in his old age.]
SUBJ Vdep
PPdep
PPindep
iv. John counted [ in his old age] [ on your support. ]
SUBJ Vdep
PPindep
PPdep
Verb entailment test
Does [X V PP] entail [X V]? If so, then assign Vindep.
If not, then assign Vdep & PPdep
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Syntactic domain minimization principle:
Minimize Phrasal Combination Domains (PCD)
Semantic domain minimization principle:
Minimize lexical dependency domains (LDD)
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Figure 2: Observed PCD length differentials (in words)
SYNTACTIC & SEMANTIC DOMAIN MINIMIZATION
Figure 1: PCD length difference resulting from different orders
CONCLUSIONS & OUTLOOK
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 It is true that PCD minimization is the most general
principle, which is reflected in a much greater
coverage (78% of the data versus 30% coverage of
semantic constraint)
 Yet it is the LDD minimization which is the strongest
principle, as it has a much greater effect size
(Regression coefficientSEM = 0.67 versus regression
coefficientSYN = 0.39)
The stronger effect size of LDD shows that speakers are
more reluctant to separate semantically dependent
combinations of verb+preposition, than to produce long
syntactic dependencies.
We are currently exploring if this predominance of
semantic minimization is a general one, in extending the
present study to other order alternations which are
influenced by both principles, e.g. particle placement.
Values > 0 mean
actual order is more optimal
0
5
10
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25
Figure 3: Observed LDD length differentials (in words)
FURTHER ISSUES
STATISTICAL ANALYSIS:
Binomial logistic regression w/o intercept (Levy, in progress)
 model evaluates distributional information
 & tries to predict the ACTUAL PP-order as a function of
syntactic and semantic domain minimization
Verb specific behavior
(Do effects vary across different verbs?)
Regression Coefficients:
Estimate Std. Error z-value Pr(>|z|)
semantic minimization 0.65
0.06
11.32 <2e-16 ***
syntactic minimization 0.39
0.03
11.39 <2e-16 ***
v. John accounted [ for this fact ] [ in his book]
SUBJ Vindep
PPdep
PPindep
Model predictions (fitted values)
vi. John accounted [ in his book] [ for this fact ]
SUBJ Vindep
PPindep
PPdep
Pro-verb entailment test
Does [X V PP] entail [X Pro-V PP]*, then assign Pindep.
If not, assign PPdep.
_________________________________________________
*Pro-V sentences: X did something PP; X was PP; something
happened PP; something was done (by X) PP.
Model predictions from
syntactic
minimization
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1.0
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800
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Individual verbs are effected differently:
Some words (e.g. be) are strongly affected by the
semantic constraint but not by the syntactic one.
Others (e.g. arrive) show a reverse image of that
behavior: these are strongly affected by the syntactic
constraint but not by the semantic one.
Still others (e.g. come) are equally affected by both
constraints.
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jitter(sample(fitted(sem.model), 1060), amount = 0.03)
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jitter(sample(fitted(syn.model), 1060), amount = 0.03)
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most general and the strongest is Early Immediate
Constituents (~PCD), which defines a preference for minimal
domains of phrase structure recognition (and production). A
second factor is lexical dependency, […] “
(Hawkins 2000:257)
0.0
“The
0.8
0.8
Figure 3: Mean fitted values for all verbs w/ N ≥ 10
jitter(sample(fitted(model), 1060), amount = 0.03)
Research Question:
What are the relative strengths of syntactic (PCD) &
semantic (LDD) domain minimization?
Model predictions from
semantic
minimization
1.0
Overall model
predictions
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Index
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Index
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800
WORKS CITED
1000
Index
Removing all cases where no predictions are being made
1.0
1.0
jitter(sample(fitted(sem.model)[fitted(sem.model) != 0.5], 406),
amount = 0.03)
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jitter(sample(fitted(syn.model)[fitted(syn.model) != 0.5], 977),
amount = 0.03)
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mean fitted = 0.62
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mean fitted = 0.70
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Index
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406 fitted values ≠ 0.5
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977 fitted values ≠ 0.5
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1060 fitted values ≠ 0.5
0.0
CODING:
o Annotation of each example with respect to syntactic and
semantic properties:
o Syntax: Assess length of actual PCD & alternative PCD
o Semantics: Is there a semantic dependency?
o If so, assess length of actual & alternative LDD
mean fitted = 0.81
jitter(sample(fitted(model)[fitted(model) != 0.5], 1060), amount = 0.03)
CORPUS SAMPLE:
o Extraction of all ―V PP PP‖-sequences from ICE-GB
o  manual weeding out of false hits
o N FINAL DATA SET = 1,256
1.0
DATA
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Index
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Hawkins, John. 1994. A performance theory of order
and constituency. Cambridge: CUP.
-- 2000. The relative order of prepositional phrases in
English: Going beyond manner-place-time. Language
Variation and Change 11: 231-266.
-- 2004. Efficiency and Complexity in Grammars.
Oxford: OUP.
Gibson, Edward. 1998. Linguistic complexity: Locality
and syntactic dependencies. Cognition 68:1-76.
-- 2000. The dependency locality theory: a distancebased theory of linguistic complexity. In A.
Marantz, Y. Miyashita, & W. O’Neil (Eds.), Image,
language, brain (pp. 95–126). Cambridge, MA:
MIT Press.
Levy, Roger. in progress. Probabilistic Models in the
Study of Language. Cambridge, MA: MIT Press.