Proceedings of the 8th International Workshop on Tree Adjoining Grammar and Related Formalisms, pages 73–80,
Sydney, July 2006. c©2006 Association for Computational Linguistics
Quantifier Scope in German: An MCTAG Analysis
Laura Kallmeyer
University of Tübingen
Collaborative Research Center 441
lk@sfs.uni-tuebingen.de
Maribel Romero
University of Pennsylvania
Department of Linguistics
romero@ling.upenn.edu
Abstract
Relative quantifier scope in German de-
pends, in contrast to English, very much
on word order. The scope possibilities of a
quantifier are determined by its surface po-
sition, its base position and the type of the
quantifier. In this paper we propose a mul-
ticomponent analysis for German quanti-
fiers computing the scope of the quantifier,
in particular its minimal nuclear scope, de-
pending on the syntactic configuration it
occurs in.
1 Introduction: The data
(1) A man loves every woman.
∃ > ∀, ∀ > ∃
In English, in sentences with several quantifica-
tional NPs, in principle all scope orders are pos-
sible independent from word order. (1) for exam-
ple has two readings, the ∃ > ∀ reading and the
inverse scope ∀ > ∃ reading. This is different in
German where word order is crucial for scope pos-
sibilities.
(2) a. Viele Männer haben mindestens eine
many mennom have at least one
Frau hofiert.
womanacc flattered.
‘Many men have flattered at least one woman.’
viele > eine, ∗eine > viele
b. Mindestens eine Frau haben viele
at least one womanacc have many
Männer hofiert.
mennom flattered.
‘Many men have flattered at least one woman.’
viele > eine, eine > viele
In German, for quantifiers in base order, the sur-
face order determines scope.1 (2a) has only the
scope order viele > eine corresponding to sur-
face order, that is, the inverse order eine > viele
is not available. In contrast to this, if the word
order differs from the base order, ambiguities are
possible. (2b) for example displays both scope or-
ders, viele > eine and eine > viele.
In the literature, the following generalizations
have been noticed for German: For two quantifiers
Q1, Q2 with Q1 preceding Q2 in the surface order
of a sentence, the scope order Q1 > Q2 is always
possible. Furthermore, the inverse reading Q2 >
Q1 is possible if
(Q1) Q1 has been moved so that Q2 c-commands
the trace of Q1 ((Frey, 1993)), and
(Q2) Q1 is a weak quantifier (e.g., irgendein
‘some’, viele ‘many’, cardinals) ((Lechner,
1998)).
Evidence for (Q2) –and further evidence for
(Q1)– are the examples in (3)–(4). In (3), the (a)-
example is in base order and thus has only surface
scope, but moving the weak quantifier over the da-
tive quantifier in the (b)-version results in scope
ambiguity. This contrasts with (4). In (4), the (a)-
version with base order has only surface scope, as
before. But now we move the strong quantifier
over the dative quantifier, and this does not yield
ambiguity. That is, even though the dative quan-
tifier c-commands the trace of the moved quanti-
fier both in (3b) and in (4b), only when the moved
1Throughout the paper we assume an unmarked intona-
tion. With a different intonation, other scope orders become
available because of the change in information structure. But
this lies outside the scope of this paper.
The base order depends on the verb; in most cases it is Sub-
ject - (Indirect Object) - Direct Object.
73
element is a weak quantifier do we obtain scope
ambiguity.
(3) a. ... dass er [fast jedem Verlag]
... that he almost every publisher
[mindestens ein Gedicht] anbot.
at least one poem proposed_to.
‘... that he proposed some poem to almost every
publisher.’
jedem > ein, ∗ein > jedem
b. ... dass er [mindestens ein Gedicht]1
... that he some poem
[fast jedem Verlag] t1 anbot.
almost every publisher proposed_to.
jedem > ein, ein > jedem
(4) a. ... dass er [mindestens einem Verleger]
... that he at least one publisher
[fast jedes Gedicht] anbot.
almost every poem proposed_to
‘... that he proposed almost every poem to at least
one publisher.’
jedes > einem, ∗einem > jedes
b. ... dass er [fast jedes Gedicht]1
... that he almost every poem
[mindestens einem Verleger] t1
at least one publisher
anbot.
proposed_to.
jedes > einem, ∗einem > jedes
(Kiss, 2000) claims that if two quantifiers have
been moved such that among themselves they re-
main in base order, inverse scope is not possible
between them. Because of this, he argues for a
non-movement-based theory of German quantifier
scope. However, Kiss’ claim is not true as can be
seen with the example (5) from (Frey, 1993):
(5) a. weil der freundliche Museumsdirektor
because the friendly curatornom
[mindestens einer Frau]1
at least one womandat
[fast jedes Gemälde]2 gezeigt hat
almost every paintingacc has shown
‘because the friendly curator has shown almost ev-
ery painting to at least one woman’
Q1 > Q2, ∗Q2 > Q1
b. weil [mindestens einer Frau]1 [fast jedes
Gemälde]2 der freundliche Museumsdi-
rektor t1 t2 gezeigt hat
Q1 > Q2, Q2 > Q1
In both cases, (5a) and (5b), the two quanti-
fiers are in base order. According to Kiss there
should be, contrary to fact, no ambiguity in (5b).
The difference between the two is that in (5a) the
quantifiers are in base position while in (5b) both
of them have been scrambled with the result that
Q2 c-commands the trace of Q1. We assume with
(Frey, 1993) that this is why the inverse scope or-
der becomes available.
We therefore stick to the above-mentioned gen-
eralizations (Q1) and (Q2) and try to capture them
in our LTAG analysis. This means that, in order to
capture (Q1), we need a syntactic analysis of Ger-
man NPs that takes into account movement and
base positions.
2 English quantifier scope in LTAG
We use the LTAG semantics framework from
(Kallmeyer and Romero, 2004; Kallmeyer and
Romero, 2005). Semantic computation is done on
the derivation tree. Each elementary tree is linked
to a semantic representation (a set of Ty2 formu-
las and scope constraints). Ty2 formulas (Gallin,
1975) are typed λ-terms with individuals and situ-
ations as basic types. The scope constraints of the
form x ≥ y specify subordination relations be-
tween Ty2 expressions. In other words, x ≥ y
indicates that y is a component of x.
A semantic representation is equipped with a
semantic feature structure description. Semantic
computation consists of certain feature value iden-
tifications between mother and daughter nodes in
the derivation tree. The feature structure descrip-
tions do not encode the semantic expressions one
is interested in. They only encode their contribu-
tions to functional applications by restricting the
argument slots of certain predicates in the seman-
tic representations: They state which elements are
contributed as possible arguments for other se-
mantic expressions and which arguments need to
be filled. They thereby simulate lambda abstrac-
tion and functional application. A sample feature
for this simulation of functional application is the
feature I that serves to pass the individual con-
tributed by an NP to the predicate taking it as an
argument. Besides this functional application as-
pects, the feature structure descriptions also con-
tain features that determine the scope semantics,
i.e., features specifying boundaries for the scope
of different operators. Sample features for scope
are MINS and MAXS encoding the minimal and
74
maximal scope of attaching quantifiers.
Features can be global (feature GLOBAL, here
abbreviated with GL) or they can be linked to spe-
cific node positions (features S, VP, . . . ). The latter
are divided into top (T) and bottom (B) features.
The equations of top and bottom features linked
to specific node positions in the elementary trees
are parallel to the syntactic unifications in FTAG
(Vijay-Shanker and Joshi, 1988). The global fea-
tures that are not linked to specific nodes can be
passed from mothers to daughters and vice versa
in the derivation tree.
(6) Everybody laughs.
As a sample derivation let us sketch the anal-
ysis of quantificational NPs in English from
(Kallmeyer, 2005). Fig. 1 shows the LTAG anal-
ysis of (6). More precisely, it shows the deriva-
tion tree with the semantic representations and fea-
ture structure descriptions of laughs and every-
body as node labels. The feature identifications
are depicted by dotted lines. The semantic repre-
sentation of the NP everybody contains the gen-
eralized quantifier every that binds the variable x
and that has a restrictive scope 4 and a nuclear
scope 5. Furthermore, it contains the proposi-
tion person(x) that must be part of the restrictive
scope (constraint 4 ≥ l3). Concerning functional
application, the NP provides the individual vari-
able x in the global feature I as a possible argu-
ment for the verb predicate laugh.
l1 : laugh( 1 ),
2 ≥ 3







GL
bracketleftbigg
MINS l1
MAXS 2
bracketrightbigg
S
bracketleftBig
B
bracketleftbig
P 3
bracketrightbigbracketrightBig
VP
bracketleftBigg
T
bracketleftbig
P 3
bracketrightbig
B
bracketleftbig
P l1bracketrightbig
bracketrightBigg
NP
bracketleftBig
GL
bracketleftbig
I 1
bracketrightbigbracketrightBig






np
l2 : every(x, 4 , 5 ),
l3 : person(x),
4 ≥ l3,
6 ≥ 5 , 5 ≥ 7



GL
bracketleftbig
I xbracketrightbig
NP
bracketleftBigg
GL
bracketleftbigg
MINS 7
MAXS 6
bracketrightbiggbracketrightBigg



Figure 1: LTAG analysis of (6) everybody laughs
Quantificational NPs in English can in princi-
ple scope freely; an analysis of quantifier scope
must guarantee only two things: 1. the proposition
corresponding to the predicate to which a quanti-
fier attaches must be in its nuclear scope, and 2. a
quantifier cannot scope higher than the first finite
clause. (Kallmeyer and Romero, 2005) model this
by defining a scope window delimited by some
maximal scope (global feature MAXS and some
minimal scope (global feature MINS) for a quanti-
fier. In Fig. 1, the nuclear scope 5 of the quantifier
is delimited by the maximal and minimal scope
boundaries provided by the verb the quantifier at-
taches to (constraints 6 ≥ 5, 5 ≥ 7 ). The feature
identifications in Fig. 1 lead then to the constraints
2 ≥ 5, 5 ≥ l1.
Applying the assignments following from the
feature identifications and building the union of
the semantic representations leads to the under-
specified representation (7):
(7)
l1 : laugh(x),
l2 : every(x, 4, 5), l3 : person(x)
2 ≥ l1,
4 ≥ l3, 2 ≥ 5, 5 ≥ l1
As the only possible disambiguation, we obtain
2 → l2, 4 → l3, 5 → l1 which yields the seman-
tics every(x,person(x),laugh(x)).
3 Syntax of German quantificational NPs
Recall that, according to criterion (Q1), not only
the position of an NP but also -if the NP was
moved- the position of its trace are crucial for the
scope properties. In order to capture this, our anal-
ysis needs to take into account movements (scram-
bling, topicalization, etc.) of NPs including traces
at base positions. We therefore cannot adopt the
analyses proposed by (Rambow, 1994) in V-TAG
where the slot for the NP is generated at the sur-
face position and there is only one initial tree for
NPs, whether moved or not.2
(8) a. . . . dass jeder/irgendeiner
... that everybody/someone
irgendein Buch/jedes Buch liest
some book/every book reads
‘... that everybody/someone reads some
book/every book’
SUBJ > DOBJ
b. . . . dass [jedes Buch]1 irgendeiner t1 liest
. . . that every book someone reads
DOBJ > SUBJ
2To avoid misunderstandings, let us emphasize that in
LTAG, there is no movement outside the lexicon. Therefore,
either the NP or the slot of the NP must be localized together
with the corresponding trace inside one elementary structure.
This elementary structure can be a tree or, in MCTAG, a set
of trees.
75
c. . . . dass [irgendein Buch]1 jeder t1 liest
. . . that some book everybody reads
SUBJ > DOBJ, DOBJ > SUBJ
To illustrate our analysis, in this and the follow-
ing section, we restrict ourselves to the sentences
in (8). For the syntax, we adopt a multicompo-
nent analysis for NPs that have been moved con-
sisting of an auxiliary tree for the moved mate-
rial and an initial tree for the trace. Our analysis
can be adopted using V-TAG (Rambow, 1994) or
something in the style of SN-MCTAG (Kallmeyer,
2005). Note that, in order to account for scram-
bling, we need some type of MCTAG anyway, in-
dependent from quantifier scope.
VP
NP VP
NP V
liest
for each NP, e.g., irgendein Buch:
α1
NP
irgendein Buch







β VP
NP VP∗
irgendein Buch
α2 NP
ǫ







Figure 2: Elementary trees for (8)
The elementary trees for (8) are in Fig. 2. α1
is used for NPs in base position, while the set
{α2,β} is used for moved NPs. We assume that,
if possible, α1 is used. I.e., starting from the verb,
trees of type α1 are substituted to its left as long
as possible. {α2,β} sets are used when α1 could
not possibly yield the desired surface word order.
Fig. 3 shows a derivation of a sentence of type (8a)
(with no movement). Fig. 4 shows the derivation
of (8b). ((8c) is similar to (8b).)
NP
irgendeiner
NP
jedes Buch
VP
NP VP
NP V
liest
derivation liest
tree: np1 np2
irgendeiner jedes_Buch
Figure 3: Derivation for (8a)
VP
NP VP
NP V
liest
NP
irgendeiner







VP
NP VP∗
jedes Buch
NP
ǫ







derivation liest
tree: np1 np2 vp1
irgendeiner tjedes_Buch jedes_Buch
Figure 4: Derivation for (8b)
Note that, in the derivation trees, each node rep-
resents a single elementary tree, not a set of el-
ementary trees from the grammar. An MCTAG
derivation tree as defined in (Weir, 1988) with each
node representing a set is available only for tree-
local or set-local MCTAG, not for the MCTAG
variants we need (SN-MCTAG or V-TAG). There-
fore we take the undelying TAG derivation tree
as the derivation structure semantics will be com-
puted on.
4 Semantics of German quantificational
NPs
Because of the generalizations above, the fol-
lowing must be guaranteed: i) Strong quantifiers
scope over the next element in surface order (take
scope where they attach).3 ii) The minimal nu-
clear scope of a weak quantifier is the closest “un-
moved” element following its base position. Con-
sequently, we need different lexical entries for
weak and strong quantifiers.
We characterize the scope possibilities of a
quantifier in terms of its minimal scope. Consider
first the verb tree for liest ’read’ in Fig. 5. In con-
trast to English, MINS is not a global feature since,
depending on the position where the quantifier at-
taches, its minimal scope is different. In the liest-
tree, MINS appears in the feature structure of dif-
ferent nodes, with each MINS value determined in
the following way: the value of MINS at the NP2
address is the label l1 of the verb; the value of
MINS at the NP1 address depends on what is at-
tached at NP2 (see variables 4 and 0, which in
this case will be identified with each other); and
the value of MINS at the top VP address depends
on what is attached at NP1 ( 5 ).
3But see section 5, where more complex examples show
that this generalization needs to be refined.
76
VP
NP1 VP
NP2 V
liest
l1 : read( 1, 2 )
3 ≥ l1










GL
bracketleftbig
MAXS 3
bracketrightbig
VP1
bracketleftBig
B
bracketleftbig
MINS 5
bracketrightbigbracketrightBig
NP1
bracketleftBigg
T
bracketleftbigg
MINS 0
NEXT 5
bracketrightbiggbracketrightBigg
VP2
bracketleftBigg
T
bracketleftbig
MINS 0
bracketrightbig
B
bracketleftbig
MINS 4
bracketrightbig
bracketrightBigg
NP2
bracketleftBigg
T
bracketleftbigg
MINS l1
NEXT 4
bracketrightbiggbracketrightBigg










Figure 5: Semantics for liest
NP
l2 : quant(x, 6 , 7 )
l3 : restriction(x)
6 ≥ l3,
8 ≥ 7 , 7 ≥ 9

NP

GL
bracketleftbig
MAXS 8
bracketrightbig
B
bracketleftbigg
MINS 9
NEXT l2
bracketrightbigg




Figure 6: Quantifiers in base position
The idea is that, when an NP (part) is attached
at a given address, the label of that NP is the new
MINS to be passed up the verb tree; when a trace
(part) is attached instead, the MINS of the verb ad-
dress is passed up unmodified. This feature pass-
ing is technically achieved by articulating the VP
spine with the feature MINS (much like the use
of the P feature in English for adverbial scope in
Kallmeyer and Romero, 2005), and by adding the
feature NEXT for passing between NP substitution
nodes (since substitution nodes do not have T and
B features that allow feature percolations between
mothers and daughters).
The lexical entries for the three types of quanti-
fiers we must distinguish (non-moved quantifiers,
weak moved quantifiers and strong moved quanti-
fiers) are shown in Fig. 6–8. Quantificational NPs
that have not been moved (Fig. 6) receive their
MINS boundary (variable 9 ) simply from their at-
tachment position. Weak and strong quantifiers
that have been moved differ in how their own
MINS is determined: Strong quantifiers (see Fig. 7)
get their MINS from the VP node they attach to,
i.e., from their surface position (see variable 13 ).
In contrast to this, weak quantifiers (see Fig. 8) get
their MINS from the base order position, i.e., from
their trace position (see variable 18 ).













VP
NP VP∗ NP
ǫ













l4 : quant(x, 10 , 11 )
l5 : restriction(x)
10 ≥ l5,
12 ≥ 11 , 11 ≥ 13

NP

GL
bracketleftbig
MAXS 12
bracketrightbig
B
bracketleftbigg
MINS 14
NEXT 14
bracketrightbigg





VPr
bracketleftBig
B
bracketleftbig
MINS l4bracketrightbig
bracketrightBig
VPf
bracketleftBig
B
bracketleftbig
MINS 13
bracketrightbigbracketrightBig


Figure 7: Strong quantifiers that have been moved
As sample analyses consider Fig. 9 and Fig. 10
showing the analyses of (8b) and (8c) where the
accusative object quantifier has been moved. (The
features of the internal VP node are omitted since
they are not relevant here.) In the first case, it is a
strong quantifier, in the second case a weak quanti-
fier. For Fig. 9, we obtain the identifications 12 =
l1 = 4 = 8, 5 = l2 = 11 (depicted with dotted
lines). Consequently, the only scope order is wide
scope of jedes Buch: l4 > 10 ≥ l2 > 7 ≥ l1.
In Fig. 10, we obtain 11 = l1 = 4 = 8, 5 = l2
which leads to the scope constraints l2 > 7 ≥ l1
and l4 > 10 ≥ l1. Consequently, we have
an underspecified representation allowing for both
scope orders.
The analysis proposed in this section has
demonstrated that some features –in this case
MINS– are global in some languages (e.g. English)
while being local in other languages (e.g. Ger-
man). We take this as further evidence that the
distinction between the two kinds of features, ad-
vocated in (Kallmeyer and Romero, 2005) is em-













VP
NP VP∗ NP
ǫ













l6 : quant(x, 15 , 16 )
l7 : restriction(x)
15 ≥ l7,
17 ≥ 16 , 16 ≥ 18

NP

GL
bracketleftbig
MAXS 17
bracketrightbig
B
bracketleftbigg
MINS 18
NEXT 18
bracketrightbigg




bracketleftbigg
VPr
bracketleftBig
B
bracketleftbig
MINS l6bracketrightbig
bracketrightBigbracketrightbigg
Figure 8: Weak quantifiers that have been moved
77
l1 : read( 1 , 2 )






VP
bracketleftBig
B
bracketleftbig
MINS 5
bracketrightbigbracketrightBig
NP1
bracketleftBigg
T
bracketleftbigg
MINS 4
NEXT 5
bracketrightbiggbracketrightBigg
NP2
bracketleftBigg
T
bracketleftbigg
MINS l1
NEXT 4
bracketrightbiggbracketrightBigg






vp np1 np2
l4 : every(x, 9 , 10 )
l5 : book(x)
9 ≥ l5, 10 ≥ 11
l2 : some(x, 6, 7)
l3 : person(x)
6 ≥ l3, 7 ≥ 8
VPr
bracketleftBig
B
bracketleftbig
MINS l4bracketrightbig
bracketrightBig
VPf
bracketleftBig
B
bracketleftbig
MINS 11
bracketrightbigbracketrightBig


bracketleftBigg
NP
bracketleftBigg
B
bracketleftbigg
MINS 8
NEXT l2
bracketrightbiggbracketrightBiggbracketrightBigg bracketleftBigg
NP
bracketleftBigg
B
bracketleftbigg
MINS 12
NEXT 12
bracketrightbiggbracketrightBiggbracketrightBigg
Figure 9: Analysis of dass [jedes Buch]1 irgendeiner t1 liest
l1 : read( 1 , 2 )






VP
bracketleftBig
B
bracketleftbig
MINS 5
bracketrightbigbracketrightBig
NP1
bracketleftBigg
T
bracketleftbigg
MINS 4
NEXT 5
bracketrightbiggbracketrightBigg
NP2
bracketleftBigg
T
bracketleftbigg
MINS l1
NEXT 4
bracketrightbiggbracketrightBigg






vp np1 np2
l4 : some(x, 9 , 10 )
l5 : book(x)
9 ≥ l5, 10 ≥ 11
l2 : every(x, 6 , 7 )
l3 : person(x)
6 ≥ l3, 7 ≥ 8bracketleftbigg
VPr
bracketleftBig
B
bracketleftbig
MINS l4bracketrightbig
bracketrightBigbracketrightbigg bracketleftBigg
NP
bracketleftBigg
B
bracketleftbigg
MINS 8
NEXT l2
bracketrightbiggbracketrightBiggbracketrightBigg bracketleftBigg
NP
bracketleftBigg
B
bracketleftbigg
MINS 11
NEXT 11
bracketrightbiggbracketrightBiggbracketrightBigg
Figure 10: Semantic analysis of dass [irgendein Buch]1 jeder t1 liest
pirically justified.
5 Long-distance scrambling and
quantifier scope
So far we have examined cases where local scram-
bling affects quantifier scope order. In this section,
we will demonstrate how our analysis carries over
to long-distance scrambling.
(9) . . . dass [irgendein Lied]1 Maria
. . . that some songacc Marianom
[fast jedem]2 [ t1 zu singen]
almost everybodydat to sing
versprochen hat
promised has
‘that Maria has promised almost everybody to sing
some song’
Q1 > Q2, Q2 > Q1
In (9) both scope orders are possible.
Fig. 11 shows the syntactic analysis for (9). Ac-
cording to the treatment of weak quantifiers pro-
posed above, the minimal nuclear scope of irgen-
dein Lied is determined by the position of the
trace; it is therefore the proposition of singen. As
for fast jedem, its minimal nuclear scope is re-
quired to include the proposition of versprochen
hat. Nothing else is required, and consequently
irgendein can scope over or under fast jedem.
A problematic configuration that can occur with
scrambling concerns cases where two weak quan-
tifiers Q2 and Q3 have been moved with a third
quantifier Q1 preceding them where Q1 is either a
strong quantifier or a weak quantifier in base posi-
tion. Then Q1 has scope over Q2 and Q3 but the
scope order between Q2 and Q3 is unspecified. An
example is (10):
78









VP
NP VP∗
irgendein Lied
NP
ǫ









VP
NP VP
NP VP
VP∗ V
versprochen hat
NP
Maria
NP
fast jedem
VP
PRO VP
NP V
zu singenFigure 11: Derivation for (9)
(10) ... dass [jeder Mitarbeiter]1
... that [every colleague]
[vielen Besuchern]2 [mindestens ein Bild]3
[many visitors]dat [at least one picture]acc
gerne [t2 t3 zu zeigen] bereit war
with pleasure to show willing was
’... that every colleague is happy to show at
least one picture to many visitors.’
Q1 > Q2 > Q3, Q1 > Q3 > Q2
The syntactic derivation is shown in Fig. 12.
Such examples are problematic for our analysis:
our approach predicts that Q2 and Q3 have the
same minimal scope, namely the zeigen proposi-
tion, and that the minimal scope of Q1 is the quan-
tifier it precedes, namely Q2. But nothing in the
analysis prevents Q3 from having scope over Q1,
contrary to fact.
This example indicates that the generalization
(i) in section 4 -that the minimal scope of a strong
quantifier is the proposition of the next quantifier
in surface order- needs to be refined. More accu-
rately, the minimal scope of a strong quantifier is
the highest proposition following in surface order.
We propose to model this using the feature NEXT
also in VP nodes. Here NEXT stands for the max-
imal scope of all quantifiers following in surface
order. An attaching weak quantifier has to do two
things: 1. equate the current NEXT feature with
the new MINS that provides the minimal scope for
higher strong quantifiers, and 2. state that NEXT
is its own maximal scope. The corresponding re-
vised lexical entry for moved weak quantifiers is
shown in Fig. 13.
Fig. 14 shows the way the minimal scope for
the unmoved quantifier in (10) is computed from
combining the auxiliary trees of the moved weak
quantifiers with bereit. (The adverb is left aside.)
In the tree of a verb and also in the auxiliary trees
of moved strong quantifiers, an additional feature













VP
NP VP∗ NP
ǫ













l6 : quant(x, 15 , 16 )
l7 : restriction(x)
15 ≥ l7,
17 ≥ 16 , 16 ≥ 18
bracketleftBigg
NP
bracketleftBigg
B
bracketleftbigg
MINS 18
NEXT 18
bracketrightbiggbracketrightBiggbracketrightBigg



VPr
bracketleftBigg
B
bracketleftbigg
MINS 17
NEXT 17
bracketrightbiggbracketrightBigg
VPf
bracketleftBig
T
bracketleftbig
NEXT 17
bracketrightbigbracketrightBig



Figure 13: Moved weak quantifiers (revised)
NEXT is added, linked to the bottom of VP nodes.
The value of this feature is required to be higher
than the value of the bottom MINS at that position.
Whenever a moved strong quantifier adjoins, noth-
ing happens with this NEXT feature. Moved weak
quantifiers take the NEXT feature as their maximal
scope and pass it as the new MINS. This is how
in Fig. 14, the final MINS at the top of the root
of the leftmost moved weak quantifier contains all
moved quantifiers and is passed to the NP node
as new MINS limit. A (weak or strong) quantifier
substituting into the NP slot takes this new MINS
as its minimal scope. Consequently, it scopes over
both moved weak quantifiers.
6 Conclusion
It has been shown that, although quantifier scope
is usually read off surface word order in German,
ambiguities can arise from movement of weak
quantifiers. We have developed an MCTAG anal-
ysis using traces. In our approach, the scope pos-
sibilities of a quantifier are characterized in terms
of its minimal scope. In contrast to English, MINS
in German is not global but depends on the po-
79
NP
jeder Mitarbeiter
VP
gerne VP∗
VP
NP VP
VP∗ V
bereit war
VP
PRO VP
NP VP
NP V
zu zeigen


VP
NP VP∗
mindestens ein Bild
NP
ǫ






VP
NP VP∗
vielen Besuchern
NP
ǫ



Figure 12: Derivation for (10)
l1 : willing( 1 , 2 )
4 ≥ 3 , 7 ≥ 6









VPr
bracketleftBigg
B
bracketleftbigg
MINS 3
NEXT 4
bracketrightbiggbracketrightBigg
NP1
bracketleftBigg
T
bracketleftbigg
MINS 5
NEXT 3
bracketrightbiggbracketrightBigg
VP

T
bracketleftbig
MINS 5
bracketrightbig
B
bracketleftbigg
MINS 6
NEXT 7
bracketrightbigg


VPf
bracketleftbig
T . . .bracketrightbig









vp
l2 : q3(x, 9 , 10 )
l3 : picture(x)
9 ≥ l3,
12 ≥ 10 , 10 ≥ 11



VPr
bracketleftBigg
B
bracketleftbigg
MINS 12
NEXT 12
bracketrightbiggbracketrightBigg
VPf
bracketleftBig
T
bracketleftbig
NEXT 12
bracketrightbigbracketrightBig



vpr
l4 : q2(y, 13 , 14 )
l5 : visitor(y)
13 ≥ l5,
16 ≥ 14 , 14 ≥ 15



VPr
bracketleftBigg
B
bracketleftbigg
MINS 16
NEXT 16
bracketrightbiggbracketrightBigg
VPf
bracketleftBig
T
bracketleftbig
NEXT 16
bracketrightbigbracketrightBig



q2 = many, q3 = at_least_one
Figure 14: Attaching the moved weak quantifiers
in (10)
sition of the quantifier. The minimal scope of
weak and strong quantifiers is determined differ-
ently: The minimal scope of a moved weak quan-
tifier depends on its trace; the minimal scope of a
moved strong quantifier depends on the position of
the moved material.
Acknowledgments
For fruitful discussions of the work presented in
this paper, we want to thank Timm Lichte and
Wolfgang Maier. Furthermore, we are grateful to
three anonymous reviewers for helpful comments.

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