Continuous or Discontinuous Constituents?
Stefan Müller
DFKI GmbH
Stuhlsatzenhausweg3
66123Saarbrücken
Stefan.Mueller@dfki.de
1Introduction
During the last years,several grammarians have argued for linguistic descriptions of language that use the concept of discontinuous constituents(Reape,1991,1992,1994;Pollard,Kasper and Levine, 1992,1994;Kathol and Pollard,1995;Kathol,1995;Müller,1995,1997,1999a;Richter and Sailer, 1999;Donohue and Sag,1999;Penn,1999).
Reape(1991)notes that it is possible to develop grammars based on the concept of discontinuous cons
tituents which span every subset of an input string.The complexity of the paring problem for such grammars is at least exponential in both time and space.As Reape(1991,p.62)has argued for the processing of grammars with discontinuous constituents and as Carroll(1994)has demonstrated for different parsing strategies for grammars with continuous constituents,such theoretical values are not of much help when it comes to practical systems.In the following I will compare two grammars for German:one that assumes continuous constituents and one that allows for discontinuous con-stituents.I will show different ways to account for the German data and I will explain why I believe that grammars with discontinuous constituents are more appropriate for systems that analyze German sentences.This claim will be supported by a statistics computed from10,000utterances taken from the Verb mobil corpus.1
2The Phenomena
2.1Relatively Free Constituent Order in the Mittelfeld
In German,complements and adjuncts of a head can be ordered relatively freely.For instance,with a ditransitive verb like geben(give),all six permutations of the arguments are possible,provided appropriate context and intonation.In general the possability to permute constituents depends on a br
oad variety of interacting constraints as for instance animateness,heavyness,definiteness.See for instance(Behagel,1930;Drach,1937;Hoberg,1981;Höhle,1982;Uszkoreit,1987).
(1)  a.Deshalb
therefore gab
gave
der
the
Mann
man
der
the
Frau
woman
das
the
Buch.
book
‘Therefore the man gave the woman the book.’
b.Deshalb gab der Mann das Buch der Frau.
c.Deshalb gab das Buch der Mann der Frau.
d.Deshalb gab das Buch der Frau der Mann.
e.Deshalb gab der Frau der Mann das Buch.
f.Deshalb gab der Frau das Buch der Mann.
Verbs like kaufen(buy)take four arguments(see Kunze(1991)),and as Wegener(1985)argued con-vincingly,some of the so-called“free datives”have to be analyzed as complements as well.
(2)Deshalb
therefore kauft
buys
Karl
Karl
von
from
Hans
Hans
für
for
fünf
five
Mark
Marks
seiner
his
Frau
wife
ein
a
Buch.
book
‘Therefore Karl buys a book for his wife from Hans forfive Marks.’
In principle,all permutations of thefive arguments of kaufen are possible.For sentences withfive arguments the number of possible permutations is5!120.
2.2Verb Position
There are three possible verb positions in German sentences:verbfirst position(3a),verb second position(3b),and verb last position(3c).
(3)  a.Liebt
loves der
the
Mann
man
die
the
Frau?
woman
‘Does the man love the woman?’
b.Der Mann liebt die Frau.
The man loves the woman.’
c.daßder Mann die Frau liebt.
‘that the man loves the woman.’
Verb second sentences are usually analyzed as derived from verbfirst sentences by the fronting of one constituent.
2.3The Predicate Complex
Verbs that embed an infinitive without zu and verbs that select for participles form a complex with their verbal complement(Hinrichs and Nakazawa,1989a).Furthermore,some of the verbs that select an infinitive with zu form a complex(Kiss,1995).
(4)  a.Hat
has er
he
den
the
Mann
man
der
the
Frau
woman
das
the
Buch
book
von
from
Karl
Karl
für
for
fünf
five
Mark
Mark
kaufen
buy
lassen?
let
‘Did he let the man buy the book for the woman from Karl forfive marks?’
b.weil
because es
it
ihm
him
jemand
somebody
zu
to
lesen
read
versprochen
promised
hat.
has
‘since somebody promised him to read it.’
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Hinrichs and Nakazawa(1989a)suggested analyzing these verbal complexes via argument attraction, essentially a lexical variant of a functional composition combining the two verbal functors.For(4b) this means that zu lesen and versprochen form a verbal complex.The complex inherits all arguments of the verbs that are involved in the complex ,for the complex zu lesen versprochen we have jemand,ihm,and es as arguments.Since all arguments are dependents of the verbal complex, it can be explained why these elements can be permuted in the same way as normal complements of one single verb can be(see the discussion of(1)).2Note that the number of arguments of the complex kaufen lassen hat is six.In principle,this addition of arguments can be iterated.
(5)weil
because Hans
Hans
Cecilia
Cecilia
John
John
das
the
Nilpferd
hippo
füttern
feed
helfen
help
läßt.
let
‘because Hans lets Cecilia help John feed the hippo.’
Füttern is a transitive verb.Helfen takes a subject,a dative NP and a verbal complex.The complex füttern helfen has three arguments.Lassen takes a subject,an accusative object(which is linked to the subject of füttern helfen)and a verbal complex.The complex füttern helfen läßt has four arguments. Restricting the number of complements that a verbal complex may take is no less ad hoc than limiting the number of center self-embeddings.Restrictions on the number of arguments should not be part of
a competence grammar.
2.4Extraposition
Extraposition is a dependency,which is nonlocal in nature,even if the the constraints which are im-posed on this dependency differ from those found with fronting as the classical nonlocal dependency: (6)  a.Karl hat mir[ein Bild[einer Frau_i]]gegeben,
[die schon lange tot ist]i.
b.Karl hat mir[eine Fälschung[des Bildes[einer Frau_i]]]gegeben,
[die schon lange tot ist]i.
c.Karl hat mir[eine Kopie[einer Fälschung[des Bildes[einer Frau_i]]]]gegeben,
[die schon lange tot ist]i.
‘Karl gave me a copy of a forgery of the picture of a woman who has been dead for a long
time ago.’
Relative clauses can be extraposed from an arbitrarily deeply embedded NP.The same holds for com-plement clauses,as I have shown in(Müller,1999a,Ch.13.1.1).
The number of extraposed constituents is unlimited in principle,as(7)shows.
(7)Ich
I habe
have
gearbeitet
worked
[an
at
diesem
this
Abend]
evening
[in
animate下载安装in
der
the
Kneipe]
pub
[als
as
Kellnerin].3
barmaid
‘I worked as a barmaid in the pub that evening.’
In (7),three PPs are extraposed.The PPs are adjuncts and are as such not subcategorized by the ,they are not predictable.4See section 3.1.4for the consequences of this fact for some analyses.3Continuous Constituents
3.1Linguistic Theory
Like GPSG,HPSG divides the grammar into Immediate Dominance and Linear Precedence rules (LP rules).In GPSG,LP statements play the role of constraining order in local trees.While in HPSG larger linearization domains are possible,as is discussed in section 4,most HPSG publications have implicitly adopted the GPSG conception of applying LP rules to local trees only.
3.1.1
Relative Free Constituent Order in the Mittelfeld 3.1.1.1Flat Structures
To account for the constituent order freedom in (1),Uszkoreit (1987)suggested a flat structure.Since all complements in figure 1are in the same local tree,they can be permuted as long as no LP rule is
violated.
Gab V[fin, SUBCAT < 1 , 2 , 3 >]    3 NP[dat]mir das Buch
1 NP[nom]
2 NP[acc]
S[fin, SUBCAT <>]
H C C C
Maria Figure 1:Flat Structure:Gab mir Maria das Buch?
The problem with this approach is that the number of rules that is needed is quite big.There have to be rules for intransitive verbs,for transitive verbs,for ditransitive verbs,and for verbs with four arguments.If the verb appears in initial position,it is possible that there is a verbal complex at the right periphery of the clause.In order to account for this,the number of rules has to be increased again.In German,adverbs can be placed anywhere between the complements.The number of adverbs is not restricted.If this has to be reflected in the grammar rules,the number of rules is infinite.Even if one restricts the number of adverbs in an ad hoc way,the set of rules will be huge.
3.1.1.2Binary Branching Structures
The problems that one has with flat structures disappear if one uses binary branching structures.A head is combined with one complement at one projection step.At each projection step it is possible to combine the projection with an adjunct.So it is trivial to account for the free appearance of adjuncts in the German Mittelfeld .
However,it is not trivial to account for the free ordering of complements.Since er ,and das Buch ,
and
das Buch
2  NP[acc]
gab
3  NP[dat]C H
dem Mann  1  NP[nom]
er V[fin, SUBCAT < 1 , 2 >]V[fin, SUBCAT < 1 , 2 , 3 >]
H
C H
C V[fin, SUBCAT < 1 >]V[fin, SUBCAT <>]
Figure 2:Binary Branching Structure:er das Buch dem Mann gab.
dem Mann are not sisters in a local tree,they cannot be permuted freely.There are several solutions t
o this problem:Gunji (1986),Hinrichs and Nakazawa (1989b),Pollard (1990),and Engelkamp,Erbach and Uszkoreit (1992)suggested using a set rather than a list to represent valence information.In head-complement structures,two elements can be combined if the complement is an element of the subcat set of the head.
The problem with such an approach is that one gets spurious ambiguities for constructions where the head is in the middle.An example would be the head noun in an NP analysis.
(8)  a.der the Entschlußdecision zu to gehen
go
b.seine his Behauptung,claim daßthat Gysi Gysi ein a Spitzel spy war
was
‘his claim that Gysi was a spy’
c.das the Bild picture von of Maria
Maria
In sentences like (8)the head noun could be combined with its complement (zu gehen ,daßGysi ein Spitzel war ,von Maria )or with the deteminer (der ,das )or subject (seine )first.To solve this problem
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one had to assume either a DP ,an analysis where the determinator and the subject is the head,or introduce a special valence feature for determiners and subjects of deverbal NPs.
Another example of a case where spurious ambiguities arise is the conjunction in coordinated struc-tures,if they are treated as the head of the construction,as suggested by Paritong(1992).
A further problem with the subcat set approach is that one needs a second list for principles and mechanisms that rely on the order of the subcat list,as for instance the Binding Theory,some versions of Case Principles(Heinz and Matiasek,1994;Müller,To Appear),and other prominence related phenomena like Vorfeldellipse(so-called‘Topic Drop’)(Fries,1988)and free relative clauses(Müller, 1999b).
An alternative with almost the same problems is a relaxation of the subcat principle.If one allows the subcat principle to take an arbitrary element from the subcat list,it is not possible anylonger to formul
ate principles that refere to elements at a certain position of the subcat list of a phrase.As Detmar Meurers pointed out,that with this approach principles that rely on the order of the subcat list possibly may be formulated at word level,since there the order information is undisturbed. Uszkoreit(1986)suggested using a lexical rule that for each verb licences lexical entries with permuted elements in the subcat list for all possible permutations of these elements.This means that at least six lexical entries are licensed for a ditransitive verb like geben.5This considerably increases the lexical ambiguity.Furthermore the approach has problems with spurious ambiguities that cannot be solved without stipulatations.To see this consider the example in(9).
(9)Dem
the Mann
man dat
gab
gave
er
he nom
das
the
Buch.
book acc
‘He gave the man the book.’
The fronting of constituents in German is usually analyzed in terms of a nonlocal dependency:A complement of the verb is removed from the subcat list by the saturation by a trace,a unary projection, or by a lexical rule.The complement is introduced into a list(SLASH)and percolated up the tree and then realized to the left of thefinite verb.The problem with(9)is that it can be analyzed with two lexical entries that have the subcat lists shown in(10a)and(10b).
(10)  a.NP[nom],NP[dat],NP[acc]
b.NP[nom],NP[acc],NP[dat]
Only the nom and acc are realized to the right of thefinite verb and nom and acc have the same order in both orderings in(10).With an analysis of extraction based on lexical rules an order for rule application could be ,the extraction lexical rule could be restricted to apply before the permutation lexical rule.With the other two approaches one is forced to assume exception features that block the extraction of an element that was permuted by the lexical rule.
Note,that the problem would disappear if permuted elements were extraction islands as is assumed in various GB publications.Then all reordered elements could be marked as islands simultaneously blocking the extraction of the element in the subcat list itself.I have shown in(Müller,1999a,p.101) that permuted elements are not islands.Therefore the spurious ambiguities in(9)can only be avoided by ad hoc features.

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