On Underspecified Processing of Dynamic Semantics 
Alexander Keller, Joachim Niehren 
University of the Saarland, Saarbriicken, Germany 
{koller@coli I niehren@ps}, uni-sb, de 
Abstract 
We propose a new inference system which oper- 
ales on underspecified semantic representations 
of scope and anaphora. This system exploits 
anaphoric accessibility conditions from dynamic 
selnantics to disambiguate scope ambiguities if 
possible. The main feature of the system is 
that it deals with underspecified descriptions di- 
rectly, i.e. without enumeratlng readings. 
1 Introduction 
A particularly appealing aspect of lmdersl)eci- 
fication (van Deemter and Peters, 1996; Reyle, 
1993; Muskens, 1995; Pinkal, 1996; Bos, 1996) 
is that it can in principle deal very efficiently 
with local ambiguities - ambiguities which are 
only due to lack of inibrmation at an interme- 
diate stage of processing and go away by the 
end of the analysis. An example for this effect 
is (1): The scope ambiguity that is perceived 
alter processing the first sentence is no longer 
present after the second one. This effect can 
be explained in a framework of dynamic selnan- 
tics (Groelmndijk and Stokhof, 1991; Kamp and 
Reyle, 1993) by the fact that a wide-scope uni- 
versal quantifier would make the indefinite inac- 
cessible for anaphoric reference from the second 
sei/tence. 
(1) Every man loves a woman. 
Her nanle is Mary. 
In this paper, we show how this particular 
type of local ambiguity can be processed effi- 
ciently. The approach we propose employs de- 
terministic inference rules that can exclude the 
readings which violate anaphoric accessibility 
conditions without enlnnerating them. These 
rules operate directly on underspecified descrip- 
tions and fully maintain underspecifiedness. We 
also show how this behaviour Call be captured 
by constraint propagation in an existing imple- 
mentation of tree descriptions using finite set 
constraints (Duchier and Niehren, 2000; Keller 
and Niehren, 2000; Duchier and Gardent, 1999). 
More specifically, we introduce DPL struc- 
tuT"cs~ extended trce structures that encode for- 
mulas of dynamic predicate logic (DPL) in much 
the same way as Egg et al.'s (1998) lambda 
structnres encode A-terms. Then we define a 
constraint  tbr the description of DPL 
structures, called CL(DPL), in analogy to Egg 
et al.'s constraint langague for lambda struc- 
tures (CLLS). We characterize those DPL struc- 
tures in which all restrictions oil anaphoric ac- 
cessibility are obeyed by talking directly about 
the syntactic structure of a DPL formula. This 
is ill contrast to the standard procedure in dy- 
nanfic semantics, where the dynamic behaviour 
is produced by the semantics of the logic; we do 
not need to (and do not) talk about interpreta- 
tion of DPL structures and model accessibility 
by purely "static" means. 
The paper is structured as follows. In Sec- 
tion 2, we introduce DPL structures and tree 
descrit)tions in the  CL(DPL). In Sec- 
tion 3, we add syntactic restrictions on admis- 
sible variable bindings to DPL structures and 
present axioms that characterize these restric- 
tions. In Section 4:, we turn these axioms into 
deterministic infhrence rules and combine them 
with deterministic inference rules known from 
an existing ilfference algorithm for dominance 
constraints. We obtain a procedure that can do 
the kind of underspccified reasoning described 
above without enmncrating readings. In Section 
5, we sketch all imtflelnentation of our inf'erence 
system based on finite set constraint prograln- 
ming. This implementation can be obtained by 
adapting an existing ilnI)lelnentation of a solver 
for dominance constraints. Finally, we conclude 
and point to further work in Section 6. 
2 Tree Descriptions 
In this section, we define the Constraint Lan- 
guage tbr DPL structures, CL(DPL), a lan- 
guage of tree descriptions which conserw~tively 
extends donfinance constraints (Marcus et al., 
1983; Rainbow et al., 1995; Keller et al., 2000) 
by variable binding constraints. CL(DPL) is 
a close relative of the Constraint Language for 
460 
Lamb(la Structures (CLLS), 1)resented in (Egg 
et al., 1998). It; is interl)reted over DPL struc- 
tures - trees extended by a variable 1)inding 
function which can be used to encode tbrmulas 
of dynamic (or static) predicate logic. We will 
define DPL structures in two steps and then the 
 to talk al)out them. 
2.1 Tree Struetures 
For the definitions below, we assulne a signature 
Y\] = {(~12, varl0,Vl~,~ll,Al.z, manll , likel2,... } of 
node labels, each of which is equipped with a 
fixed arity n _> 0. The labels A,_~,_V,... are the. 
tirst-order commctives. Node lal)els are. ranged 
over by f, g, a, b, and the arity of a lal)el f is 
denoted by ar(./'); i.e. if J'l,~ C E then ar(f) = n. 
Let N l)e the set; of natural numbers ~. > 1. 
As usual, we write N* tbr the set of words over 
N, C for the elnl)ty word, and 7r~-' for the con- 
catellatioll of two words 7r, 7r t C N*. A wor(t 7t is 
a prefiz of 7c' (written rc _< re') if there is a word 
7r u such that 7rTr tt = 7r t. 
A node of a tree is the word rr E N* which 
addresses the node. The empty word e C N* 
is called the root node. A tree domain A is a 
nonempty, t)refixed-closed subset of N* which is 
closed under the left-sil)ling relation. 
Definition 2.1 A tree strllctilre iS a t'a\])l(: 
(A, c,) consisting of a finite, tree dmn, ain A and 
a total labeling t'unction co ° : A -+ E s'ach th, al, 
for all rr 6 A and i G N: 
c A 1 < i < 
We say that the nodes r 6 rcl,..., 7c~ m'e in the 
labeling ,'elationsh/ip 7c: J' On,..., 7r,~) ill! a (Tr) = J' 
and tbr each 1 < i < n, ~-i = ~-i. Similarly, we 
say that a node ~c properly dom, inatcs a node 
7c' and write 7r<\]+rc ' iffrr is a proper prefix of 
7c'. We take Ir and It' to be disjoint (~r J_ ~r') if 
ttley are different and neither node dominates 
the other. So any two nodes in a tree structure 
are in one of the four relations = (equality), <1 +, 
~>+ (the inverse of <1+), or _L. We shall ~lso t)e 
interested the coml)inations of these l"elatiolls by 
set operators: intersection, coml)lementation , 
union, and inversion. For instance, the dom- 
inance relation <~* is detined as the union of 
node equality and proper dominance = U<1 +. 
Finally, we detine the ternary non-intervention 
relation ~(Tr<l*Td<Frc") to hold ifl' it is not the 
case that 1)oth ~r < ~r' and ~r' < re". 
.' ~r 
var a ~ 
ma0 \lo  
var • var tr var-. 
Figm'e 1: I)PL structure tbr the meaning of (1). 
2.2 DPL structures 
Now we extend tree structures by variable 
binding and obtain DPL structures. To this 
end, we I)artition E into three sets: connee- 
tive.s Econ = {V_,A,_%...}, predicate symbols 
Epred = {man, likes,...}, and tcr'm symbols 
Ere,.,. = {var, peter, mother_of,...} which sub- 
stone, the variable symbol var and fimction sym- 
1)ols. 
Definition 2.2 A DPL structure is a triple 
(A,c&A) con.~isting of a trcc structure. (A,c,) 
and a partial varial)le t)inding flmction A : A 
A which sati.sfies for all % ~r t ~ A: 
1. the. < r.co,, u .fo,. 
all 7ci C A; 
2. < the,,,, fo,. 
all 7ci ~ A; 
I)PL structures can be used to re, present ibr- 
mulas of first-order predicate logic. For in- 
stance, the DPL structure in Fig. 1 represents 
the (unique) meaning of (1). So far, however, 
variables bound by a quantifier do not need to 
be in any special position in a DPL structure; in 
particular, not in its scope. To entbrce seeping 
as in static predicate logic, we could simpy add 
the condition ~c'<~*~r in condition 3 of Definition 
2.2. We will define an appropriate counterpart 
\]'or DPL in Section 3 (properness). 
Modeling variable binding with an explicit 
binding flmction instead of variable nmnes was 
first proposed in (Egg et al., 1998). There, bind- 
ing flmctions heJp to avoid a capturing problem 
in the context of scope underspecitication which 
t)ecomes most ~q)l)arent in the presence of ellip- 
sis. Her(; the 1)inding flmction mainly gives us a 
different t)erspective on variable binding which 
461 
R ::= <+1>+1 = I± 
I -* 
::= X:f(X\],...,X,,) (fin C E) 
I xRz 
I 
I \[ ~A~'. 
Figure 2: Syntax of CL(DPL) 
is useflfl for defining properness of DPL struc- 
tures. 
2.3 The Constraint Language CL(DPL) 
The syntax of CL(DPL) is defined in Fig- 
ure 2. It provides constraints tbr all the 
relations discussed above. There are label- 
ing constraints X:.f(X~,...,Xr~), expressive 
combinations XRY of dominance constraints 
'with set operators (Dtu:hier and Niehren, 
200(}; Cornell, 1994), non-intervention con- 
straints ~( X <1* Y <~* Z), and binding constraints 
a(X)=Z. 
CL(DPL) is interpreted over DPL structures. 
A variable assignment into a DPL structure 54 
is a total flmction fi'om the set of variables of a 
constraint to the domain of 54. A pair (54, oz) 
of a DPL structure 54 and a variable assign- 
ment (t into 54 satisfies a constraint qo ifl' it 
satisfies all of its atomic constraints; that is, if 
the relation with the same sylnbol holds of the 
nodes assigned to their arguments. We also call 
the pair (54, oz) a solution and Ad a model of ~o. 
Only some of the atonfic constraints in 
CL(DPL) are used in mlderspecified descrip- 
tions in t)articular, labeling, dominance, and 
binding constraints; the other constraints are 
helpful in processing the others. These three 
types of constraints can be transparently dis- 
played in constraint graphs. For instance, the 
constraint graph ill Fig. 3 represents a con- 
straint describing the readings of example (1) 
including the scope ambiguity. The nodes of 
the graph stand for variables in tile constraint; 
labels and solid edges represent labeling COl> 
straints, dotted edges, donlinance constraints, 
and dashed arrows, binding constraints, hi ad- 
dition, the constraint graph represents an in- 
equality constraint X-~=Y between each two 
variables whose nodes carry a label. A con- 
straint with the latter property is called overlap- 
free. The intuition is that the solid-edge tree 
fragments in the constraint graph must never 
overlap properly in a solution. 
3 Dynamic Semantics in CL(DPL) 
The semantics of DPL is built in a way that 
allows quantifiers to bind only variables in cer- 
tain positions: inside their scopes and, if it is an 
existential quantifier, from the left-hand sides 
of conjunctions and implications into the right- 
hand sides. In CL(DPL), we model this as a 
purely syntactic restriction on the accessibility 
of binders which we define as a structural prop- 
erty of DPL structures. DPL structures which 
have this property will be called proper. 
A useflll auxiliary concept tbr the definition 
is that of an infimum of two nodes with respect 
to the dominance relation q*, which constitutes 
a lower senfilattice because of the underlying 
treeness of DPL structures. Furthermore, we 
will use the standard DPL notions of internally 
v@" = {A,~} and ex- dynamic COlUlectives ~con 
ternalh d, static connectives ~con'~stat = {2, V, __=::k, _V}. 
The semantics definition of DPL gives these two 
groups special relevance tbr variable binding. 
Now we can define pTvper \])PL structures as 
tbllows. 
Definition 3.1 A DPL structure 54 is called 
proper '~f for each, node ~r of 54 on which ~ is 
defined, one of th, e following cases holds true 
wh, ere p, is the i'nfimum of rc and A(TC). 
1. ff = ;~(~), or 
2. )@r) is labeled 'with ~_, ttl<l*.~(Tr), p,2q*% I t 
is labeled with art internally dynamic con- 
nective, and no node between ttl and A(Tc), 
inclusively, is labeled with an externally 
static connective. 
Intuitively, the first branch of the definitiou 
corresponds to usual binding of variables inside 
tile scope of a quanfifer. In the second branch, 
the positions of the variable and the (existen- 
tial) quantifier in the DPL structure are dis- 
.joint, and the quantifier is dominated by tile 
left child of the infimum. Then the infimum 
must be labeled with an internally dynamic con- 
nective, and there must be no externally static 
connective between this node and the quantifier. 
This restriction is what we are going to exploit 
462 
,..-'' 
r, 
/ 
• / 
womb2',1% ..)...':'- 
\ ,,' \ 
vat 
Figure 3: Constraint graph for (1). 
to capture the influence 055 scope. There is 51o 
such restriction for the lmth 1)etwcen the inti- 
mmn and the w~riM)le. 
Sohll;ions of & constraint thnt violate the (ly- 
nmnie accessibility conditions are now excluded 
silnply by restricting the, class of ~utmissible so- 
lutions to i)roper ones. As exl)ected from the 
linguistic intuition, only one sohd;ion of the nm- 
ning exmnple (1) is proper: the one where "a 
woman" is assigned wide scope (Fig. 1). Tit(; 
other solution is not prot)er because the path 
Kern the infimum ((lellol;cd by Z0 in Fig. 3) to 
the antecedent contains ;~ mfiversal qu~mtiticl". 
Prot)erness of ;~ I)PI, sl;ruct;u5"(' ('t~sl I)(; ~txioln- 
atized synta,ctically: A \])PL sl;rucl;urc is 1)rot)er 
iff the CI~(I)I'I~)~xioms (l)y,,\])to (l)yn4)in 
Fig. 4 ~re, wflid over it. The rule (Dynl) threes 
universM qmmtifiers to bind only variM)les in 
their scopes, and the rules (l)yn2) to (Dyn4) 
enforce properness of binding when a wtrial)le 
is not in the scope of its binder. 
4 Underspecified Reasoning 
We next present a procedure for mMorspeci- 
tied reasoning with dynmnic semmltics. Th(' 
goal is to narrow an mMerst)ecified (les(;rit)tion 
such that improi)er DPL-structure, s are removed 
flom the solution set. Narrowing should apply 
as soon as possible, so unde, rspeciliedness (:~m be 
5naintmned and readings need not t)e enmner- 
ated. We present ml intb, rence procedure tlmt 
can do this and go through two exmnples. 
4.1 Inference Procedure 
This infi;rence procedure ,s'atuvatt,.s a, constrMnt 
ttccording to the rules in Figures 4 and 5; that 
is, whenever a constraint conttdns the lefl;-hmM 
side of a rule,, it adds il;s right-hand side, until 
no new conjuncts ca, n 1)e ndded. Fig. 4 contains 
simply the prot)erness axioms from the, l)revi- 
ous sections, turned into deterministic proof 
rules. The rules in Pig. 5 are t)ropagation rules 
t'ronl Algorithm DO in (Duchier and Niehren, 
2000), plus new rules for non-intervention con- 
strainl;s. Algorithm DO contains some ~Mdi- 
tional rules, in I)ari;iculm' distribution rules that 
perform case distinctions, because DO is a com- 
plete solver tbr dominance constraints with set 
operators, wlfich improves on (Duchier and Oar- 
dent, 1999; Keller et M., 1998). We have omit- 
ted the (listril)ution rules here l)e,(;ause we do 
'not wmlt to perform case distinctions; l)y ndding 
1;\]1(;115 ~tg~l, ill~ WC COll\]d ellll511era, I;e all proper so- 
lutions, ~:ls Schiehlen (1997) does tbr UDI1T. 
The new rules (NonI1) ~md (NonI2) Mlow 
to derive dominan(:e infbrmation from non- 
intervention constraints. As we will see, the 
most interesting rule in Fig. 4 is (l)yn2), 
which derives explicit non-intervention int'orma- 
lion fi'om the structurM t)roperLies of dynamic 
1)inding. Note that while the rules in Fig. 5 
are sound over ;my DPL strucl;ure, those in Fig. 
4 are only serum eve5" proper DPL structures. 
This is intended: Application of a prot)erness 
rule is s'upposcd to exclude (improper) solutions. 
4.2 Examples 
The inii;rence rules go a long w:ty towards mak- 
ink tile eft'cot of dynamic seminal;its on scope 
e, xt)lieit. Let us consider |;15(; running example 
in Figure 3 to see how this works; we show how 
to derive Y3<I*X, which specifies the relative 
quantifier scope. 
First of all, we need to make the information 
463 
(Dynl) 
(Dyn2) 
(Dyn3) 
(Dyn4) 
a(x)=Y A Y:V(z') Y<*X 
Z(X)=Y A Z:f(Zl, Z2) A ZI<1*Y A Z2<\]*X A W:g(W1,..., Wn) ~dyn ~st~tt 
(fe or,, e 
~(X)=Y A Z:f(Z1,..., Zn) A Zi<:1*X A Zj<:\]*Y --+ false 
A(X)=Y A Z:f(Z1,...,Zn) A Zi<l*X A &<1*Y -~ false 
Figure 4: Properness axioms. 
(Trans) 
(Lab.Dom) 
(NegDisj) 
(Lab.Disj) 
(Inter) 
(Inv) 
(Child.down) 
(NegDom) 
(NonI1) 
(NonI2) 
X <a* Y A Y <q* Z -+ X <1* Z 
x:f(...,z,...) x<+y 
X <1* Z A Y <F Z --+ X~ -L Y 
,xs,...) 
XR1Y A XR2Y -+ XRY 
XRY -+ YR-1X 
-+ -~(Z~ <*W<a*Y) 
v~dY'1 i ¢ j) (.fl,, ~ Econ - ,-,co,,, 
(.fl,, e E, i < j) 
Xi ± Xj where i < j 
if RINR2 C R 
X<:\]+Y A X:f(Xl,... ,Xn) A 
X-~ ± Y A X J_Z -+ Z-~<a*Y 
-~(X<*Y<1*Z) A X<*Y --+ Y~<*Z 
~(X<\]*Y<I*Z) A Y<*Z --," X-~<1*Y 
---> X i <F Y 
Figure 5: Propagation rules for dominance and non-intervention constr~dnts. 
Z2<1*Za explicit by application of (Lab.Dom) 
and (Inter). In this instance, (Inter) is used as 
a rule of weakening. 
(Lab.Dom) Zg:A(Za, Z4) -~ Z,~<1+ Za 
(Inter) Z.~<Y'- Za --+ Z2<F Z3 
Now we can apply the rule (Dyn2) to the vari- 
able binding constraint A(Za) = Y (drawn in 
boldface in the graph) and the V labeling con- 
straint to derive a non-intervention constraint. 
(Dyn2) Z0:A(Z:j, Z2) A ZI<1*X1 A X:V_(X1) 
A Z2<q*Za A A(Z3) = 1/ 
All that is left to do is to make the positive 
dominance intbrmation contained in the new 
non-intervention constraint explicit. As the 
constraint also contains Zo<1*X, we can apply 
(NonI1) on the new non-intervention constraint 
and derive X~<FY. 
(NonIl) =(Zo<1*X<1*Y) A Zo<1*X --+ X~<1*Y 
On the other hand, we can derive non- 
disjointness of X and Y because (Trans), 
(Lab.Dom), and (Inter) allow the deriw~tion of 
X<FW and Y<1*W: 
(NegDisj) X<*W A Y<I*W ~ X= £ Y 
We can now combiue all of our constraints tbr 
X and Y with the intersection rule and obtain 
Y<1*X, which basically determines the order of 
the two quantifiers: 
(Inter) X~<*Y A X-~ £ Y ~ Y<*X 
By exploiting the fact that the constraint is 
overlap-ti'ee (i.e. contains an inequality cost- 
straint for each two labeled variables), we (:an 
even derive Y3<I*X by repeated application of 
the rules (Child.down), (Lab.Disj), (NegDisj), 
and (NegDom). This means that we have flflly 
disambiguated the scope ambiguity by saturn- 
tion with deterministic inference rules. 
Now let us consider a more complicated ex- 
ample. Fig. 6 is the underspecified description 
of the semantics of 
(2) Every visitor of a company saw one of its 
departments. 
The constraint graph has five solntions, three 
of which are proper. Unfortunately, the con- 
straint  is not expressive enough to 
describe these three solutions ill a single con- 
straint: Both X and Z can be either above or 
below Y, even in a proper solution, but if X is 
below Y, Z must be too, and ifX is above Y, Z 
must be anywhere below X (but; may be above 
464 
• IX V ,, Y """-- q ,,,Z 
company ." " - 
x ". ." i ". ," " var " researcher i ". / of~----~ depar.tmen-gh'~ ; , 
"~". var \~! .." ' Var ~ var'~ .""" var ~"." • i .." " 
", ". L" i . " / 
var'~ vat ~ ....... 
Figure 6: Constraint graph for (2). 
YI). In other words, this constraint is an exam- 
pie where the inference procedure is not strong 
enough to narrow the description. In this case, 
we must still resort to pertbrming nondetermin- 
istic case distinctions; at worst, the rules will 
apply on solved forms of CL(1)PL) constraints. 
constraints over these set variables; examples 
for set constraints are V C V' and V = 
V~ U V.2. The new non-intervention constraint 
~(X<1*Y<1*Z) can be encoded as 
Y e <+(x) u _L(Z) u >+(Z). 
5 Processing with Finite Set 
Constraints 
This inferen('e procedure fits nicely with all im- 
ph;mentation of (lominance constraints t)ased on 
constraint programming (Marriott and Stuckey, 
1.998; Koller and Niehren, 2000) with tinite 
set constraints (Miiller, 1999). Constraint pro- 
gramlning is a technology for solving combina- 
toric puzzles eificiently. The main idea is to 
replace "generate and test" by "propagate and 
distrilmt(f'. Constraint prot~agation t)eribrms 
deterministic inferences which prune the search 
space, whereas distribution tmrfonns (nondeter- 
rain|st|c) case distinctions. 
Duchier and Niehren (2000) show how to 
implenmnt a (lominance constraint solver by 
encoding donfinance constraints as finite set 
constraints and disjunctive propagators. This 
solver does not handle non-intervention con- 
strain|s, lint we show here that they can tm 
added very naturally. The (Dyn) rules still have 
to be implemented as saturation rules. 
The idea of this implementation is to encode 
a solution (Ad, ~) of a donfinance constraints by 
introducing for each variable X in the constraint 
and each relation symbol R C {<1 +, t> +, =, J_ } 
a finite set variable R(X). This w~riable is sup- 
posed to denote the set of all variables denoting 
nodes that are in tile relation R to ~(X): 
l~,(X) = {Y e W(~o)I (M, ~) b- YI~.X} 
Dominance constr~fints can now be stated as 
The bull|in t)rot)agation tbr set constraints au- 
tomatically implenmnts the rules (NonI1) and 
(NonI2). For instance, assume that X<1*Y t)e- 
longs to ~; then there will 1)e a set constraint 
Y ¢ <1 +(X), so set constraint propagation will 
derive Y ~ ~_(Z) U t>+(Z). This is the |mined|- 
at(; encoding of Y_L U t>+Z, which is equiwdent 
to Y~<1* Z. 
6 Conclusion 
In this paper, we have shown how a sl)ecific type 
of local anti)|gully, which is produced by the in- 
teraction of intersentential anaphora and scope 
ambiguities, can l)e processed ell|clearly ill the 
framework of underspecification. We h~ve de- 
fined \])PL structures, which can be used to 
model fonmflas of DPL, and proper DPL struc- 
tures, ill which w~riable binding must obey the 
accessibility conditions of DPL. Finally, we have 
shown how an underspecified description can be 
narrowed to a description of its proper solutions, 
sometimes without even partial enumeration of 
readings, and integrated this operation into all 
implelnentation of dominance constraints which 
is based on tin|re set constraints. 
Se, en from the perspective of DPL, our defini- 
tion of tlrot)ern(;ss is tmrely syntactic and tech- 
nically has nothing to do with dynamic seman- 
tics. We could state such a definition t/ecause 
the expli(;it variable binding flmctions gave us a 
structure-in(let)endear handle on variable bind- 
ing that excluded all tbnns of capturing. This 
deviates from the standard perspective of indef- 
465 
inites changing the context, but has the advan- 
tage of being extremely modular in that the ac- 
cessibility conditions are factorized out explic- 
itly. For instance, it is simple to represent the 
meaning of "Bach-Peters sentences" by relaxing 
these conditions; it should also be easy to adapt 
our tbrmalism to other frameworks of dynamic 
semantics. Of course, the question of how to 
interpret a DPL structure remains open. 
Another open question is how the approach 
presented here can be extended to higher-order 
systems of dynamic semantics (e.g. Dynanfic 
Lambda Calculus (Kuschert, 1999)). In this 
context, it could be worthwhile to restore tim 
distinction of variable binding and anaphoric 
linking from CLLS. 
Finally, it should be interesting to find other 
classes of local ambiguity that lend themselves 
to a treatment as presented here. So far, there 
are not many related examples; one is lexical 
ambiguity in parsing of dependency grammar, 
as presented in (Duchier, 1999). However, we 
believe that the work presented here provides 
further illustration that underspecified process- 
ing can go a long way towards efficient process- 
ing of local ambiguities. 
Acknowledgments. This work was sup- 
ported by the l)eutsche Forschungsgemeinschaft 
in the SFB 378. As always, we thank all mem- 
bers of the SFB 378 project CHORUS at the 
University of the Saarland. We are also grateful 
to the participants at the Dagstuhl workshop on 
Dynamic Semantics in February 1999 for com- 
ments and discussions on an earlier version of 
this paper. 

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