Semantic-Head Based Resolution of Scopal Ambiguities* 
BjSrn Gamb/ick 
Information and Computational Linguistics 
Language Engineering University of Helsinki 
SICS, Box 1263 P.O. Box 4 
S-164 29 Kista, Sweden SF-00014 Helsinki, Finland 
gamback@sics, se 
Johan Bos 
Computational Linguistics 
University of the Saarland 
Postfach 15 11 50 
D-66041 Saarbriicken, Germany 
bos©coli, uni- sb. de 
Abstract 
We introduce an algorithm for scope resolution in 
underspecified semantic representations. Scope pref- 
erences are suggested on the basis of semantic argu- 
ment structure. The major novelty of this approach 
is that, while maintaining an (scopally) underspec- 
ified semantic representation, we at the same time 
suggest a resolution possibility. The algorithm has 
been implemented and tested in a large-scale system 
and fared quite well: 28% of the utterances were 
ambiguous, 80% of these were correctly interpreted, 
leaving errors in only 5.7% of the utterance set. 
1 Introduction 
Scopal ambiguities are problematic for language 
processing systems; resolving them might lead 
to combinatorial explosion. In applications like 
transfer-based machine translation, resolution 
can be avoided if transfer takes place at a rep- 
resentational level encoding scopal ambiguities. 
The key idea is to have a common representa- 
tion for all the possible interpretations of an am- 
biguous expression, as in Alshawi et al. (1991). 
Scopal ambiguities in the source language can 
then carry over to the target language. Recent 
research has termed this underspecification (see 
e.g., KSnig and Reyle (1997), Pinkal (1996)). 
A problem with underspecification is, how- 
ever, that structural restrictions are not en- 
coded. Clear scope configurations (preferences) 
in the source language are easily lost: 
(1) das paflt auch nicht 
that fits also not 
'that does not fit either' 
(2) ich kanni sie nicht verstehen ~i 
I can you not understand 
'I cannot understand you' 
* This work was funded by BMBF (German Federal 
Ministry of Education, Science, Research, and Technol- 
ogy) grant 01 IV 101 R. Thanks to Christian Lieske, 
Scott McGlashan, Yoshiki Mori, Manfred Pinkal, CJ 
Rupp, and Karsten Worm for many useful discussions. 
433 
In (1) the focus particle 'auch' outscopes the 
negation 'nicht'. The preferred reading in (2) is 
the one where 'nicht' has scope over the modal 
'kann'. In both cases, the syntactic configu- 
rational information for German supports the 
preferred scoping: the operator with the widest 
scope is c-commanding the operator with nar- 
row scope. Preserving the suggested scope res- 
olution restrictions from the source language 
would be necessary for a correct interpretation. 
However, the configurational restrictions do not 
easily carry over to English; there is no verb 
movement in the English sentence of (2), so 'not' 
does not c-command 'can' in this case. 
In this paper we focus on the underspecifi- 
cation of scope introduced by quantifying noun 
phrases, adverbs, and particles. The representa- 
tions we will use resembles Underspecified Dis- 
course Representation Structures (Reyle, 1993) 
and Hole Semantics (Bos, 1996). 
Our Underspecified Semantic Representation, 
USR, is introduced in Section 2. Section 3 shows 
how USRs are built up in a compositional se- 
mantics. Section 4 is the main part of the paper. 
It introduces an algorithm in which structural 
constraints are used to resolve underspecified 
scope in USR structures. Section 5 describes an 
implementation of the algorithm and evaluates 
how well it fares on real dialogue examples. 
2 Underspecified Semantics: USR 
The representation we will use, USR, is a ter- 
tiary term containing the following pieces of se- 
mantic information: a top label, a set of labeled 
conditions, and a set of constraints. The condi- 
tions represent ordinary predicates, quantifiers, 
pronouns, operators, etc., all being uniquely la- 
beled, making it easier to refer to a particular 
condition. Scope (appearing in quantifiers and 
operators) is represented in an underspecified 
way by variables ("holes") ranging over labels. 
Labels are written as ln, holes as hn, and vari- 
ables over individuals as in. The labelling allows 
us to state meta-level constraints on the rela- 
tions between conditions. A constraint l < h is 
a relation between a label and a hole: 1 is either 
equal to or subordinated to h (the labeled con- 
dition is within the scope denoted by the hole). 
(ll , 
(top) 
{lldecl m / / } 12 : pron(il), 14 _< hi, 
13 : passen(i2,il), 15 _< hi, 
14 : auch(h2), , 18 _< hl, ) 
I~ : nicht(h3), Is _< h2, 
16 : group(12,13) 16 _< hs 
(conditions) (constraints) 
Figure 1: The USR for 'das patgt auch nicht'. 
Fig. 1 shows the USR for (1). The top label 11 
introduces the entire structure and points to the 
declarative sentence mood operator, outscop- 
ing all other elements. The pronoun 'das' is 
pron, marking unresolved anaphora. 'auch' and 
'nicht' are handled as operators. The verb con- 
dition (passen) and its pronoun subject are in 
the same scope unit, represented by a grouping. 
The first three constraints state that neither 
the verb, nor the two particles outscope the 
mood operator. The last two put the verb in- 
formation in the scope of the particles. (NB: no 
restrictions are placed on the particles' relative 
scope.) Fig. 2 shows the subordination relations. 
ll:decl(hl) 
14:auch(h2)~.~ <" < - " " h3) 
16: \[ 13:passen 
12:pron \] 
Figure 2: Scopal relations in the USR. 
A USR is interpreted with respect to a "plug- 
ging", a mapping from holes to labels (Bos, 
1996). The number of readings the USR encodes 
equals the number of possible pluggings. Here, 
two pluggings do not violate the _< constraints: 
/3/ }h I = 14, h2 = 15, h3 = 18 t ls, h2=le, hs 14 
The plugging in (3) resembles the reading where 
'auch' outscopes 'nicht': the label for 'nicht', 15, 
is taken to "plug" the hole for 'auch', h2, while 
'auch' (14) is plugging the top hole of the sen- 
tence, hi. In contrast, the plugging in (4) gives 
the reading where the negation has wide scope. 
434 
With a plugging, a USR can be translated 
to a Discourse Representation Structure, DRS 
(Kamp and Reyle, 1993): a pron condition in- 
troduces a discourse marker which should be 
linked to an antecedent, group is a merge be- 
tween DRSs, passen a one place predicate, etc. 
3 Construction of USRs 
In addition to underspecification, we let two 
other principles guide the semantic construc- 
tion: lexicalization (keep as much as possible of 
the semantics lexicalized) and compositionality 
(a phrase's interpretation is a function of its sub- 
phrases' interpretations). The grammar rules al- 
low for addition of already manifest information 
(e.g., from the lexicon) and three ways of pass- 
ing non-manifest information (e.g., about com- 
plements sought): trivial composition, functor- 
argument and modifier-argument application. 
Trivial composition occurs in grammar rules 
which are semantically unary branching, i.e., the 
semantics of at the most one of the daughter 
(right-hand side) nodes need to influence the in- 
terpretation of the mother (left-hand side) node. 
The application type rules appear on se- 
mantically binary branching rules: In functor- 
argument application the bulk of the semantic 
information is passed between the mother node 
and the functor (semantic head). In modifier- 
argument application the argument is the se- 
mantic head, so most information is passed up 
from that. (Most notably, the label identifying 
the entire structure will be the one of the head 
daughter. We will refer to it as the main label.) 
The difference between the two application 
types pertains to the (semantic) subcategoriza- 
tion schemes: In functor-argument application 
(5), the functor subcategorizes for the argument, 
the argument may optionally subcategorize for 
the functor, and the mother's subcategorization 
list is the functor's, minus the argument: 
Mother (5) \[ main-label 
=~ 
I. Functor (head) Argument (nonhead) 
main-label "main-label F\])\] 
In modifier-argument application (6), Modi- 
fier subcategorizes for Argument (only), while 
Argument does not subcategorize for Modifier. 
Its subcat list is passed unchanged to Mother. 
Mother 
• \[ subeat ( ) 
Modifier (nonhead) Argument (head) 
main-label Label subeat (\[i\]) \] \[main-label 
4 A Resolution Algorithm 
Previous approaches to scopal resolution have 
mainly been treating the scopal constraints sep- 
arately from the rest of the semantic structure 
and argued that contextual information must be 
taken into account for correct resolution. How- 
ever, the SRI Core Language Engine used a 
straight-forward approach (Moran and Pereira, 
1992). Variables for the unresolved scoped were 
asserted at the lexical level together with some 
constraints on the resolution. Constraints could 
also be added in grammar rules, albeit in a 
somewhat ad hoc manner. Most of the sco- 
pal resolution constraints were, though, pro- 
vided by a separate knowledge-base specifying 
the inter-relation of different scope-bearing op- 
erators. The constraints were applied in a pro- 
cess subsequent to the semantic construction. 
4.1 Lexical entries 
In contrast, we want to be able to capture 
the constraints already given by the function- 
argument structure of an utterance and provide 
a possible resolution of the scopal ambiguities. 
This resolution should be built up during the 
construction of (the rest of) the semantic repre- 
sentation. Thus we introduce a set of features 
(called holeinfo) on each grammatical category. 
On terminals, the features in this set will nor- 
mally have the values shown in (7), indicating 
that the category does not contain a hole (isa- 
hole has the value no), i.e., it is a nonscope- 
bearing element, sb-label, the semantic-head 
based resolution label, is the label of the element 
of the substructure below it having widest scope. 
In the lexicon, it is the entry's own main label. 
(7) holeinfo isa-hole no 
hole no 
Scope-bearing categories (quantifiers, parti- 
cles, etc.) introduce holes and get the feature 
setting of (8). The feature hole points to the 
hole introduced. (Finite verbs are also treated 
this way: they are assumed to introduce a hole 
for the scope of the sentence mood operator.) 
435 
(8) holeinfo isa-hole yes 
hole Hole 
4.2 Grammar rules 
When the holeinfo information is built up in the 
analysis tree, the sb°labels are passed up as the 
main labels (i.e., from the semantic head daugh- 
ter to the mother node), unless the nonhead 
daughter of a binary branching node contains 
a hole. In that case, the hole is plugged with 
the sb-label of the head daughter and the sb- 
label of the mother node is that of the nonhead 
daughter. The effect being that a scope-bearing 
nonhead daughter is given scope over the head 
daughter. On the top-most level of the gram- 
mar, the hole of the sentence mood operator is 
plugged with the sb-label of the full structure. 
Concretely, grammar rules of both application 
types pass holeinfo as follows. If the nonhead 
daughter does not contain a hole, holeinfo is 
unchanged from head daughter to mother node: 
Mother 
(9) \[ holeinfo \[\] \] =¢" 
Head Nonhead 
\[holeinfo IS-I\] \[holeinfo \[isa-hole no \]\] 
However, if the nonhead daughter does con- 
tain a hole, it is plugged with the sb-label of the 
head daughter and the mother node gets its sb- 
label from the nonhead daughter. The rest of 
the holeinfo still come from the head daughter: 
Mother 
isa-hole 
hole 
Head 
sb-label H~adLabel" 
isa-hole 
hole 
Nonhead 
isa-hole yes 
hole Hole 
The hole to be plugged is here identified by 
the hole feature of the nonhead daughter. To 
show the preferred scopal resolution, a relation 
'Hole =sb HeadLabel', a semantic-head based 
plugging, is introduced into the USR. 
4.3 Resolution Example 
We will illustrate the rules with an example. 
The utterance (1) 'das pa£t auch nicht' has the 
semantic argument structure shown in Fig. 3, 
where Node\[L, HI stands for the node Node hav- 
ing an sb-label L and hole feature value H. 
The verb passen is first applied to the subject 
'alas'. The sb-label of 'passen' is its main label 
(the grouping label 16). Its hole feature points 
to hi, the mood operator's scope unit. The pro- 
noun contains no hole (is nonscope-bearing), so 
we have the first case above, rule (9), in which 
the mother node's holeinfo is identical to that 
of the head daughter, as indicated in the figure. 
/\ 
ni cht \[15,/h3\] ~S\[16 ,hi\] 
das\[12,no~assen\[16,hl\] 
Figure 3: Semantic argument structure 
Next, the modifier 'nicht' is applied to the ver- 
bal structure, giving the case with the nonhead 
daughter containing a hole, rule (10). For this 
hole we add a 'h3 =sb 16' to the USR: The la- 
bel plugging the hole is the sb-label of the head 
daughter. The sb-label of the resulting struc- 
ture is 15, the sb-label of the modifier. The pro- 
cess is repeated for 'auch' so that its hole, h2, is 
plugged with 15, the label of its argument. We 
have reached the end of the analysis and hi, the 
remaining hole of the entire structure is plugged 
by the structure's sb-label, which is now 14. In 
total, three semantic-head based plugging con- 
straints are added to the USR in Fig. 1: 
(11) hi =sb 14, h2 =sb 15, 53 "=sb 16 
Giving a scope preference corresponding to the 
plugging (3), the reading with auch outscoping 
nicht, resulting in the correct interpretation. 
4.4 Coordination 
Sentence coordinations, discourse relation ad- 
verbs, and the like add a special case. These 
categories force the scopal elements of their sen- 
tential complements to be resolved locally, or in 
other words, introduce a new hole which should 
be above the top holes of both complements. 
They get the lexical setting 
(12) holeinfo isa-hole island 
hole Hole 
So, isa-hole indicates which type of hole a 
structure contains. The values are no, yes, 
and island, island is used to override the ar- 
gument structure to produce a plugging where 
436 
the top holes of the sentential complements get 
plugged with their own sb-labels. This compli- 
cates the implementation of rules (9) and (10) 
a bit; they must also account for the fact that a 
daughter node may carry an island type hole. 
5 Implementation and Evaluation 
The resolution algorithm described in Section 4 
has been implemented in Verbmobil, a system 
which translates spoken German and Japanese 
into English (Bub et al., 1997). The under- 
specified semantic representation technique we 
have used in this paper reflects the core seman- 
tic part of the Verbmobil Interface Term, VIT 
(Bos et al., 1998). The aim of VIT is to de- 
scribe a consistent interface structure between 
the different language analysis modules within 
Verbmobil. Thus, in contrast to our USR, VIT 
is a representation that encodes all the linguistic 
information of an utterance; in addition to the 
USR semantic structure of Sectiom 2, the Verb- 
mobil Interface Term contains prosodic, syntac- 
tic, and discourse related information. 
In order to evaluate the algorithm, the results 
of the pluggings obtained for four dialogues in 
the Verbmobil test set were checked (Table 1). 
We only consider utterances for which the 
VITs contain more than two holes: The num- 
ber of scope-bearing operators is the number of 
holes minus one. Thus, a VIT with one hole only 
trivially contains the top hole of the utterance 
(i.e., the hole for the sentence mood predicate; 
introduced by the main verb). 
A VIT with two holes contains the top hole 
and the hole for one scope-taking element. How- 
ever, the mood-predicate will always have scope 
over the remaining proposition, so resolution is 
still trivial. 
Table 1: Results of evaluation 
Dial. # # Correct utt. / # holes 
Id. Utt. <2 3 4 >5 
B1 48 34 9/11 1/2 1/1 79 
B2 41 26 5/8 2/3 4/4 73 
87 48 36 7/8 0/1 3/3 83 
RHQ1 91 68 10/11 5/6 4/6 83 
Total 228 164 31/38 8/12 12/14 80 
The dialogues evaluated are identified as three of the "Blaubeuren" dialogues (B1, B2, and BT) and one of 
the "Reithinger-Herweg-Quantz" dialogues (RHQ1). 
These four together form the standard test-set for the German language modules of the Verbmobil system. 
For VITs with three or more holes, we have 
true ambiguities. Column 3 gives the number 
of utterances with no ambiguity (< 2 holes), 
the columns following look at the ambiguous 
sentences. Most commonly the utterances con- 
tained one true ambiguity (3 holes, as in Fig. 2). 
Utterances with more than two ambiguities (> 5 
holes) are rare and have been grouped together. 
Even though the algorithm is fairly straight- 
forward, resolution based on semantic argument 
structure fares quite well. Only 64 (28%) of the 
228 utterances are truely ambiguous (i.e., con- 
tain more than two holes). The default scoping 
introduced by the algorithm is the preferred one 
for 80% of the ambiguous utterances, leaving er- 
rors in just 13 (5.7%) of the utterances overall. 
Looking closer at these cases, the reasons for 
the failures divide as: the relative scope of two 
particles did not conform to the c-command 
structure assigned by syntax (one case); an in- 
definite noun phrase should have received wide 
scope (3), or narrow scope (1); an adverb should 
have had wide scope (3); combination of (a 
modal) verb movement and negated question 
(1); technical construction problem in VIT (4). 
The resolution algorithm has been imple- 
mented in Verbmobil in both the German se- 
mantic processing (Bos et al., 1996) and the 
(substantially smaller) Japanese one (Gamb~ick 
et al., 1996). Evaluating the performance of 
the resolution algorithm on the standard test 
suite for the Japanese parts of Verbmobil (the 
"RDSI" reference dialogue), we found that only 
7 of the 36 sentences in the dialogue contained 
more than two holes. All but one of the ambi- 
guities were correctly resolved by the algorithm. 
Even though the number of sentences tested cer- 
tainly is too small to draw any real conclusions 
from, the correctness rate still indicates that the 
algorithm is applicable also to Japanese. 
6 Conclusions 
We have presented an algorithm for scope res- 
olution in underspecified semantic representa- 
tions. Scope preferences are suggested on the 
basis of semantic argument structure, letting 
the nonhead daughter node outscope the head 
daughter in case both daughter nodes are scope- 
bearing. The algorithm was evaluated on four 
"real-life" dialogues and fared quite well: about 
80% of the utterances containing scopal ambi- 
guities were correctly interpreted by the sug- 
gested resolution, leaving scopal resolution er- 
rors in only 5.7% of the overall utterances. 
The algorithm is computationally cheap and 
quite straight-forward, yet its predictions are 
relatively accurate. Our results indicate that 
for a practical system, more sophisticated ap- 
proaches to scopal resolution (i.e., based on 
the relations between different scope-bearing el- 
ements and/or contextual information) will not 
add much to the overall system performance. 

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