ASSIGNING A SEMANTIC SCOPE TO OPERATORS 
Massimo Poesio 
University of Rochester, Department of Computer Science 
Rochester, NY 14627-0226, USA 
poesio@cs, rochester, edu 
Abstract 
I propose that the characteristics of the scope disamhiguation 
process observed in the literature can be explained in terms 
of the way in which the model of the situation described 
by a sentence is built. The model construction procedure I 
present builds an event structure by identifying the situations 
associated with the operators in the sentence and their mu- 
tual dependency relations, as well as the relations between 
these situations and other situations in the context. The pro- 
cedure takes into account lexical semantics and the result of 
various discourse interpretation procedures such as definite 
description interpretation, and does not require a complete 
disambiguation to take place. 
THE PROBLEM 
Because new ways of obtaining semantically distinct inter- 
pretations for sentences are continuously discovered, com- 
ing to grips with ambiguity is becoming more and more 
of a necessity for developers of natural language process- 
ing systems, linguists and psychologists alike \[9, 31, 7, 2\]. 
In this paper, I am concerned with the scopal ambiguity of 
operators I \[31, 33\]. 
The attention of both psycholinguists and computational 
linguists interested in ambiguity has concentrated on the 
problem of combinatorial explosion. If the number of read- 
ings of an utterance were to actually grow with the factorial 
of the number of operators, even a simple sentence like (1), 
with 4 operators (the modal 'should', tense, an indefinite and 
a definite), would have 4I = 24 scopally different readings. 
Two distinct questions thus must be answered: how can lis- 
teners (and how should machines) deal with the combinato- 
rial explosion of readings? Do we really use the brute-force 
strategy of considering all of the available readings, and then 
choose among them? And, if we do choose among several 
readings, how is that done? 
(1) We should hook up an engine to the boxcar. 
To my knowledge, three positions on the problem of com- 
binatorial explosion have been taken in the literature. Some 
have argued that there is no problem: our brains contain 
1I use here the term operator as it is used by Heim \[13\], i.e., to 
mean either quantifier or modal/tense operator. 
78 
more than enough machinery to process in parallel 4I in- 
terpretations. It's unclear, however, whether this strategy 
is feasible when larger numbers of readings are concerned. 
A classical demonstration of the number of readings one 
may have to consider is (2), which has 1 l I interpretations 
if the standard treatment of quantification and modality is 
assumed. 
(2) You can fool most people on most of the issues most 
of the time, but you can't fool everybody on every single 
issue all of the time. \[15\] 
Another position is that sentences like (1) are not semanti- 
cally ambiguous, but vague. Consider for example (3): 
(3) Every kid climbed a tree. 
Here, one of the readings (the one in which the indefinite 
takes narrow scope) is entailed by the other (in which the 
indefinite takes wide scope). The claim is that (3) is inter- 
preted in the vaguest possible way, and the strongest reading, 
if at all, is derived by pragmatic 'strengthening' \[25\]. A dif- 
ficulty with this approach is that a vaguest reading doesn't 
always exist. The two readings of (4), for example, are dis- 
tinct. 
(4) Few people speak many languages. \[27\] 
Finally, it has been proposed that the reason why listeners 
do not seem to have problems in processing utterances like 
(1) is because they do not disambiguate. They build a non- 
disambiguated representation of the sentence and leave the 
interpretation open. This strategy might be advantageous 
for some kinds of applications 2 and it has been argued that 
a complete disambiguation never takes place \[7\]. 
No matter what processing strategy is chosen, the ques- 
tion of how listeners choose one particular interpretation 
cannot be ignored. All experimental work done on the sub- 
ject of scopal ambiguity \[20, 35, 26\] indicates that subjects 
do have preferred interpretations when confronted with tasks 
which require understanding. In addition, sentences like (1), 
(5) and (6) clearly have preferred interpretations. However, 
the only answers to to this question that I have seen are based 
on heuristics) 
2E.g., machine translation \[2\]. 
3See \[17\] for an example of state-of-the-art techniques 
(5) A girl took every chemistry course. \[20\] 
(6) Each daughter of an admiral married a captain. 
I present in this paper an hypothesis about interpretation that 
accounts for facts about scope disambiguation that were pre- 
viously explained in the literature by stipulating a number of 
unmotivated principles. The proposal developed here is be- 
ing applied to develop the module of the TRAINS-93 system 
\[1\] that handles scope disambiguation and reference inter- 
pretation. The goal of the TRAINS project is to develop a 
conversationally proficient planning assistant. More details 
about the project and the work presented here can be found 
in \[29\]. 
SCOPE DISAMBIGUATION FACTORS 
Most proposals on scope disambiguation were developed to 
account for the general preference of the leftmost quantified 
phrase from taking wide scope in simple active sentences 
like (7): 
(7) Every kid climbed a tree. 
Lakoff \[27\] proposed that this preference is due to the fact 
that sentences are parsed from left to right; "every kid" takes 
scope over "a tree" because it is processed first. (Kurtzman 
and MacDonald called this the Left to Right principle.) 
Ioup \[20\] argued instead that "...in natural language, or- 
der has little to do with the determination of quantifier 
scope." (\[20\], p.37). The preferred reading of (8), for ex- 
ample, is the one in which the NP "each child" takes wide 
scope. 
(8) I saw a picture of each child. \[20\] 
According to Ioup, the relative scope of quantifiers is deter- 
mined by the interaction of two factors. First of all, quan- 
tifiers such as "each" or "the" have the inherent property of 
taking wide scope over indefinites, which, in turn are lexi- 
cally marked to take scope over plural quantifiers like "all." 
This hypothesis is motivated by contrasts such as those in 
(9), and accounts for cases such as (8). 4 
(9) a. I saw a picture of each child. 
b. I saw a picture of all the children. 
Secondly, Ioup proposed that a hierarchy exists among 
grammatical functions, such that listeners tend to attribute 
to NPs in subject position wide scope over NPs in indirect 
object position, which in turn tend to take wide scope over 
NPs in object position. The hierarchy between grammatical 
functions accounts for the preferred reading of (7). 
Ioup also observed that NPs in topic position tend to take 
wide scope, This is especially obvious in languages that 
have a specific grammatical category for topic, like Japanese 
or Korean. The Japanese sentence (10b) is ambiguous, but 
the reading in which the NP in subject position, "most stu- 
dents" takes scope over the NP in object position, "every 
language," is preferred. This preference is maintained if the 
')Van Lehn \[35\] and Hendrix \[14\] also studied the effect of 
lexical preferences, or 'strengths' as they are also called. 
79 
NP in object position is scrambled in sentence-initial posi- 
tion, as in (10c) (another counterexample to Lakoff's left- 
to-right principle). If, however, the NP is marked with the 
topic-marking suffix "wa," as in (10d), suddenly the pre- 
ferred reading of the sentence becomes the one in which 
"every language" takes wide scope. 5 
(I0) a. Most students speak every language. 
b. Hotondo-no gakusei-ga subete-no gengo-o hanasu 
most-gen student-nora every language-ace speak 
c. Subete-no gengo-o hotondo-no gakusei-ga hanasu 
every language-ace most-gen student-nora speak 
d. Subete-no gengo-wa hotondo-no gakusei-ga hanasu 
every language-TOP most-gen student-nora speak 
Several proposals attribute an important role to structural 
factors in assigning a scope to operators. Jackendoff \[21\] 
and Reinhart (\[32\], ch. 3 and 9) propose to account for the 
preferred reading of (7) by means ofa C-commandprinciple 
according to which a quantified expression is allowed to take 
scope over another quantified expression only if the latter is 
c-commanded by the former at surface structure. 
Structural explanations (in the form of constraints on syn- 
tactic movement) have also been proposed to explain the 
constraint that prevents a quantifier to take scope outside 
the clause in which it appears, first observed by May \[28\] 
and called Scope Constraint by Heim \[13\]. This constraint 
is exemplified by the contrast in (11): whereas (lla) has 
a reading in which "every department" is allowed to take 
wide scope over "a student," this reading is not available for 
(llb). 
(11) a. A student from every department was at the party. 
b. A student who was from every department was at the 
party. 
Lexical semantics and commonsense knowledge also play 
an important role in detemaining the scope of operators. The 
contrast between the preferred readings of (12a) and (12b) 
can only be explained in terms of lexical semantics: 
(12) a. A workstation serves many users. 
b. A workstation can be found in many offices. 
Kurtzman and MacDonald \[26\] set out to verify the empiri- 
cal validity of several of these principles. The most crucial 
result is that none of the principles they set to verify can 
account for all the observed effects, and actually counterex- 
amples to all of thenv--including the quantifier hierarchy-- 
can be found. No evidence for a Left-to-Right processing 
principle was found. Kurtzman and MacDonald hypothesize 
that "...processes that are not strictly dedicated to the inter- 
pretation of scope relations may nonetheless influence the 
interpretation of quantifier scope ambiguities." (\[26\], p.22). 
They conclude that "...the results leave open the question 
of whether the building and selection of representations of 
scope are mandatory processes" (\[26\], p.45). 6 
5Arguably, the closest thing to an explicit topic marker in En- 
glish are certain uses of definite descriptions and the topicalization 
construction; in both cases, the topically marked NP tends to take 
wide scope. 
6Their experiments are discussed in more detail in \[29\]. 
OVERVIEW OF THE PROPOSAL 
Scope Disambiguation as Construction of an Event 
Structure 
It is commonly assumed in the psycholinguistic literature 
on sentence interpretation that hearers interpret sentences 
by constructing a model of the situation described by the 
sentence \[10, 22\]. I propose that the scope assigned to the 
operators contained in a sentence is determined by the char- 
acteristics of the model construction procedure. The model 
being constructed, which I call event structure, consists of a 
set of situation descriptions, one for each operator, together 
with dependency relations between them. The task of the 
model construction procedure is to identify these situations 
and to establish dependency relations. The scope assigned 
by a hearer to an operator depends on the position of the 
situation associated with that operator in the event structure. 
For example, I propose that the scope assigned to quanti- 
tiers depends on how their resource situation \[3, 8\] is iden- 
tiffed. It is well-known that a sentence like (13): 
(13) Everybody is asleep. 
is not interpreted as meaning that every single human be- 
ing is asleep, but only that a certain contextually relevant 
subset is. The process of identifying the set of individuals 
over which an operator quantifies is usually called domain 
restriction. In the case of, say, (7) whether "every kid" or"a 
tree" takes wide scope depends on how the listener builds a 
model of the sentence. If she starts by first identifying a situ- 
ation containing the group of kids that"every" is quantifying 
over, and then proceeds to 'build' for each of these kids a 
situation which contains a tree the kid is climbing, then "ev- 
ery kid" will take wide scope. In other words, I propose that 
a listener has a preferred reading for a sentence if she's able 
to identify the resource situation of one or more of the oper- 
ators in that sentence ('to picture some objects in her mind'), 
and to hypothesize dependency relations between these sit- 
uations. If this process cannot take place, the sentence is 
perceived as 'ambiguous' or 'hard to understand.' 
The less context is available, the more the establishment 
of dependency relations between situations depends on the 
order in which the model is built, i.e., on the order in which 
the situations associated with the different operators and 
events are identified. This order depends in part on which 
NPs are perceived to be 'in topic,' and in part on gen- 
eral principles for building the conceptual representation of 
events (see below). In addition, some operators (e.g., defi- 
nite descriptions) impose constraints on their resource situ- 
ation. 
A Model Construction Procedure: The DRT 
Algorithm 
In order to make the intuition more concrete we need the 
details of the model construction procedure. Ideally, one 
would want to adopt an existing procedure and show that 
the desired results fall out automatically. Unfortunately, the 
model construction procedures presented in the psycholin- 
guistic literature are not very detailed; often it's not even 
clear what these researchers intend as a model. There is, 
80 
however, a discourse interpretation procedure that is speci- 
fied in detail and has some oftbe characteristics of the model 
construction procedure I have in mind; I'm thinking of the 
DRS construction algorithm \[23, 24\]. 
The DRS construction algorithm consists of a set of rules 
that map discourses belonging to the language into certain 
"interpretive structures". The output structures are called 
"Discourse Representation Structures" or "DRSs." A DRS 
is a pair consisting of a set of discourse referents and a set 
of conditions (= predicates on the discourse referents). The 
construction algorithm works by first adding the syntactic 
structure of the sentence to the 'root' DRS representing the 
discourse up to that point, then applying the rules to the syn- 
tactic structure, thus adding discourse referents and condi- 
tions to the DRS. Consider how the algorithm is applied to 
obtain an interpretation for (7): 
(14) Every kid climbed the tree. 
The initial interpretation of (14) is the tree shown in (15). 
(15) S 
NP VP 
Det N' V NP 
Det A 
Every kid climbed a tree 
The DRS construction role for definites and universal quan- 
tification are as follows: 
(Definite Descriptions)When a syntactic configuration 
containing a definite NP is met in a DRS K, 
1. Add a new discourse referent x to the root DRS, 
2. Add a new condition to the root DRS representing the 
restriction on the indefinite NP, 
3. Replace the NP with x in the syntactic configuration. 
(Universal Quantification) When a syntactic configura- 
tion containing an NP with determiner "every" is met in a 
DRS K, 
1. Add a complex condition KI ~ 1(2 to K, 
2. Add a new discourse referent x to K~, 
3. Add a new condition to K1 representing the restriction 
on the indefinite NP, 
4. Replace the NP with the discourse referent in the syn- 
tactic configuration, 
5. Move the syntactic configuration insider K2. 
Both the rule for definites and the rule for universal quantifi- 
cation are triggered by (15). Two hypotheses are obtained; 
that obtained by applying first the rule for definite descrip- 
tions is shown in (16). Both of these hypothesis contain op- 
erators whose DRS construction roles haven't been applied 
yet: this algorittun comes with a built-in notion of partial 
hypothesis--a paltial hypothesis is a DRS some of whose 
operators still have to 'interpreted' in the sense just men- 
tioned. 
(16) 
x 
TREE(X) 
S 
NP VP 
Det N' V x 
Every kid climbed 
The two partial hypotheses are made into complete hypothe- 
ses by applying the remaining rules; the complete hypothesis 
with the definite taking wide scope is shown in (17). 
(17) 
x 
TREE(X) 
YID(y) \[ ever~y> 
CLIMBED(y, X) 
Modifying the DRS Construction Algorithm 
Because the DRS construction rules depend on syntactic pat- 
terns, the role of structural factors in disambiguatiou can be 
taken into account--and a lot of data about disambiguation 
preferences can be explained without any further machin- 
ery. The Scope Constraint, for example, is embedded in 
the very semantics of DRT; and one can 'build in' the con- 
struction rules principles such as the c-command principle. 
(Kamp and Reyle do just that in \[24\].) The limitations of 
this approach are shown by examples in which the choice 
of an interpretation does not depend on the structure, like 
(12). Also, the rule for definites as just formulated is too re- 
strictive: in cases like (18), for example, predicts the correct 
reading for the definite NP''the meeting," but the wrong one 
for "the principal," that, intuitively, takes narrow scope with 
respect to "every school:" 
(18) Every school sent the principal to the meeting. 
I propose that the role of lexical semantics, as well as the 
data accounted for in the literature by introducing principles 
such as the grammatical function hierarchy, the topic prin- 
ciple, and the quantifier hierarchy, can be accounted for by 
making the activation of the DRS construction rules depend 
on factors other than the syntactic structure of the sentence. 
The factors I propose to incorporate are (i) the semantics of 
lexical items, (ii) the results of the interpretation of opera- 
tors in context, and (iii) the way the representation of events 
is built in memory. 
In order to achieve this goal, I propose two main modi- 
fications to the standard DRS construction algorithm. First 
of all, I propose that the input to the algorithm is a logi- 
calform--a structure isomorphic to the s-structure, that car- 
ties however information about the semantic interpretation 
of lexical items. In this way, the role of semantic factors 
in interpretation can be taken into account; in addition, a 
semantic value can be assigned to a representation contain- 
ing unresolved conditions or partial hypotheses. Secondly, 
I propose to make the application of the DRS construction 
rules depend on the identification of certain contextually de- 
pendent elements of the interpretation. The ingredients of 
the account thus include: a proposal about the input to the 
model construction procedure; a notion of what an event 
structure is; and an account of discourse interpretation. I 
discuss these issues in turn in the next sections. 
THE LOGICAL FORM 
As said above, the first difference between the interpretation 
procedure proposed here and the DRS construction algorithm 
illustrated above is that the rules I propose rely on semantical 
and contextual factors. I propose to do this by adding to 
standard DRT a new class of conditions, that I call 'logical 
forms.' Logical forms include semantic information about 
the lexical items occurring in the sentence. The logical form 
representation is the interface between the parser and the 
model construction algorithm, and can be compositionally 
obtained by a GPSG parser \[11, 18\] that couples a context- 
free grammar with rules of semantic interpretation. I first 
describe the language used to characterize the semantics of 
lexical items, SEL (for Simple Episodic Logic), then the 
syntax and interpretation of logical forms. 
81 
Lexical Semantics in Simple Episodic Logic 
I introduce SEL by presenting the truth conditions I propose 
to assign to (18), repeated here for convenience: 
(18) Every school sent the principal to the meeting. 
The truth conditions usually assigned to (18) in a language 
with restricted quantification, and ignoring tense, are shown 
in (19); I propose instead to assign to (18) the interpretation 
specified by (20). 
(19) (the m MEETING(m) 
(V S SCHOOL(S) 
(the p PRINCIPAL(p,s)\] 
sE~rr(s,pan)))) 
(20) (the m \[s'l ~= MEL~NG(m)\] ^ sHARl~(spkr,hearerW0 
(V S \[S'2 ~ SCHOOL(s)\] 
(too p IS3 ~ pP.n~cw~(p,s)\] 
^ SHARED(spkr,hearer ,.¢3) 
SENT(s,p,m)))) 
(20) reads: there exists a unique m that is a meeting in a con- 
textually specified resource situation s'l, and for all s's that 
are schools in a contextually specified resource situation ~2 
the unique p such that p is the principal of s participates to m. 
The intent of the expression used for the quantifier restric- 
tions in (20) is to make it explicit that the situations from 
which the quantified dements are 'picked up' need not be 
the complete set of objects and relations at which the truth of 
(20) is evaluated. This is accomplished by introducing into 
the language an explicit relation ~ ('supports') to represent 
'truth at a situation' \[8\]. A statement of the form 
Is1 MEWrING(X)\] 
evaluates to true in a situation s if the object--say, m-- 
assigned to the variable x is a meeting in the situation s 1. 
A situation is a set of objects and facts about these objects 
\[8, 18\]. I assume a language which allows us to make state- 
ments about situations, and an ontology in which situations 
are objects in the universe. Episodic Logic provides such a 
language and such an ontology \[19, 18\]; where not otherwise 
noted, the reader should assume that an expression of SEL 
has the semantics of the identical expression in Episodic 
Logic. 
The restriction of the existential quantifier in (20) con- 
tains a parameter ~. Parameters are used in SEL to trans- 
late anaphoric expressions of English. A parameter behaves 
semantically as an open variable, a value for which has to 
be provided by context. 7 
I have assumed the following translations for the lexical 
items "every," "meeting," and "sent" (I have again ignored 
tense): 
"every" -,-+ )~ P 3. Q (V x \[s'i ~ P(x)\] Q(x)) 
"meeting" -,-+ MEETING 
"sent" --~ SENT 
The semantics assigned to definite descriptions needs a bit 
of an explanation. According to the location theory \[12, 
4\] the major uses of definite NP's, as well as the contrast 
between definites, indefinites, and demonstratives, can be 
accounted for by stipulating that a speaker, when using a 
definite article, 
1. instructs the hearer to locate the referent in some shared 
set of objects, and 
2. refers to the totality of the objects/mass within this set that 
satisfy the restriction. 
I formalize this idea in \[301 by associating to definite de- 
scriptions the translation below. A situation is 'shared' be- 
tween x and y if every fact • supported by that situation is 
mutually believed by x and y (see \[301 for details). 
"the meeting" -,~ )~ P (the x: (\[S ~ MEETING(X)\] A 
SHARED (spkr,hearer,S)) P(x)) 
Syntax and Interpretation of the Logical Form 
The translations seen above, together with the obvious 
context-free roles, result in the following LF for (18) (I have 
7See \[29\] for details. The idea is to add to the parameters of 
evaluation an anchoring function a that provides the values for 
parameters, thus plays the role of 'context' in Helm's proposal. The 
reader should be aware that while the notation and terminology I 
have adopted is borrowed from Situation Theory, parameters have 
a different semantic interpretation there \[8\]. 
82 
used here, and elsewhere in the paper, a linear notation to 
save space): 
(21) \[CP \[IP \[NP '~, Q (V s \[s'2 ~ SCHOOL(s)\] Q(s))\] 
\[vP \[vP \[v' 'SENT \[NP 'Z Q (the p \[s'3 ~ PRINCIPAI~,~)\] 
^ SHARED(spkr,hearer $3) 
Q(P))\]\]\] 
\[pp 'TO 
\[NP 'Z Q (the m \[s'l ~ MEmOs(m)\] 
^ SHARED(spkr,hearer ,,q 0 
Q(m))llll\] 
I propose that expressions like (21) can appear as conditions 
of DRSs. The syntax of LFs is as follows. Each internal 
node of (21) is labeled with a phrase category; the leaves 
are labeled with expressions of the form 'a, where a is an 
expression of SEL (and has therefore a 'standard' model the- 
oretic denotation). I use the phrase structure system largely 
adopted in the Government and Binding literature, accord- 
ing to which the sentence is the maximal projection of an Infl 
node and is therefore labeled IP \[34\]. I also assume the exis- 
tence of a maximal projection of complementizer CP above 
IP. Because I don't discuss relatives here, I use the following 
simplified notation for NPs with determiners, such as "every 
school": 
\[NP '~- Q (V x \[Sl ~ SCHOOL(x)\] Q(x))\] 
LFs like (21) are usually treated in the natural language 
processing literature as uninterpreted data structures from 
which to 'extract' the readings \[16, 17\]. However, it has 
been recently proposed \[31, 2, 33\] that it is possible (and 
indeed desirable) to assign a denotation to expressions like 
(21). The reason is that in this way one can define a no- 
tion of sound inference --that is, one can specify what can 
and cannot properly be inferred from an expression like (21) 
prior to disambiguation; and therefore, a notion of 'mono- 
tone disambiguation.' I do not assume disambiguation to 
work monotonically, but I want to be able to treat expres- 
sions like (21) as full-fledged conditions so that a DRS con- 
taining a condition of this kind can be interpreted, and I need 
to be able to characterize a disambiguation step as compati- 
ble in the sense that it does not introduce any new readings. 
To do this I need LFs to have an interpretation. 
Were it not for the problem that more than one interpre- 
tation can be associated to a single LF, one could easily de- 
fine a recursive mapping EXT from logical forms to truth- 
theoretical denotations (functions from situations to lluth 
values) in temxs of the usual \[\[ \[\[ function, as follows: 
= Ilall 
EXT(\[ v, a\]) = EXT(a) 
EXT(\[vp a\]) = EXT(a) 
EXT(\[ N, a\]) = EXT(a) 
EXT(tNP a 131) = EXT(a)(EXT(~)) 
EXT(tIP a \]~l) = EXT(a)(EXT(~)) 
if TYPE(EXT(a)) = (t~,t~) 
and TYPE(EXT(fl)) = tl; 
EXT(/~)(EXT(a)) otherwise. 
Once this is done, one can reformulate the semantics of 
DRS in terms of situations and situations extensions instead 
of embeddings and embedding extensions, and interpret all 
conditions as functions from situations to truth values. (See 
\[29\] for details.) 
Matters get more complicated when expressions with 
more than one reading like (21) are considered. Different 
ways for assigning a denotation to expressions with more 
than one interpretation have been proposed \[2, 31\]; my pro- 
posal derives from \[31\]. I use a Cooper storage mechanism 
\[5\] to define EXT in such a way as to allow for an LF to have 
more than one 'indirect interpretation.' Briefly, Cooper's 
idea is to have a syntactic tree denote a set of sequences, 
each sequence representing a distinct 'order of application' 
in computing the interpretation of the sentence. For exam- 
ple, because in interpreting (22) one can either apply the 
translation of tense immediately or walt, EXT maps (22) in 
a set of two sequences, shown in (23). 
(22) \[V" 'P \[NP '~. Q (det x R(x)) Q(x)\] \] 
EXT((22)) = {(~ x (det x R(x))P(x) ), 
(23) (P,)~ Q (det x R(x)) Q(x) )} 
I omit here the definition of the EXT function implement- 
ing Cooper storage, that is rather complex. For the current 
purposes, it is enough to understand that EXT associates to 
(21) a set of functions from situations to truth values, as in 
(24). 
(24) EXT((21)) = 
{the function denoted by 
II (the m \[s'~ p ~L~tNG(m)\] ^ SnARED(spkr,hearer,g0 
(V S \[~"2 \[= SCHOOL(s)\] 
(the p \[g3 ~ PRINCIPAL(p,s)\] 
^ SHARED(spkr,hearer ,g3) 
s~,rr(s,p,x)))) II, 
the function denoted by 
II (v s \[~2 h scnooL~s)\] 
(the m \[~¢x ~ MEElqNG(m)\] ^ SI/ARED(spkr,hearer,~l) 
(the p \[~3 P PRn~Cn'AL(p,s)\] 
^ SrlARED(spkr,hearer ,g3) 
s~cr(s,p,x)))) II, et~ } 
Having done this, we can say that a DRS condition like (21) 
is verifies the current situation s if one of the functions de- 
noted by (21) maps s into 1. 
BUILDING EVENT STRUCTURES 
Not all assertions in a narrative or conversation are going 
to be about the same situation. In the conversations with 
the TRAINS system, for example, the participants can dis- 
cuss both the state of the world and the state of the plan 
being developed. Maintaining this separation is crucial for 
the proper interpretation of definite descriptions, for exam- 
ple. The separation between the situations that are the topic 
of different sentences is achieved by translating sentences as 
situation descriptions. A situation description is a condition 
of the form: 
\[-""--'3 
s :l~ \[ (25) 
i -- I 
83 
whose intuitive interpretation is that • provides a partial 
characterization of the situation s. The semantics of situa- 
tion descriptions is defined as follows, using a semantics of 
DRSs in terms of situation extensions, as discussed in the 
previous section, and interpreting discourse markers as con- 
stituents of situations: 
The condition s:K is satisfied wrt the situation s' iffK 
is satisfied wrt the value assigned to s in s '. 
I also propose the following constraint on the model con- 
struction rules: 
Constraint on Interpretation : with the exception of the 
discourse markers interpreted over situations and of the 
situation descriptions, every discourse marker and condi- 
tion has to be part of a situation descriptions. 
Situation descriptions are added to the model by rules trig- 
gered by an LF whose root is a CP node. The rules (now 
shown for lack of space) delete the complementizer and its 
whole projection, and introduce a situation structure. The 
result is shown in (26). 
S 
(26) s: /~ 
The conslraint on discourse interpretation proposed above is 
implemented by forcing the rules that build situation struc- 
tures to be triggered before any other rule; this is done by 
having every other rule being triggered by LFs whose root 
node is an IP. The result of this constraint is that a discourse 
model consists of a set of situation descriptions: 
(27) s:~-~ 
The DRSs produced by the standard DRT algorithm are se- 
mantically equivalent to the special case of a set of situation 
descriptions all describing the same situation s. 
Models like the one in (27) enable the formalization of 
processes of resource situation identification like that de- 
scribed in \[30\]. I illustrate how my rules for interpreting 
operators differ from those of standard DRT, and how the in- 
teraction between model construction rules and discourse in- 
terpretation works, by means of the model construction rule 
for definites. The rule MCR-DD is triggered by the config- 
uration in (28), and results in the configuration in (29). The 
notation used for the pattern indicates that this mle applies 
to a definite NP in any position within a syntactic tree whose 
maximal projection is an IP node, without any intervening 
IP node. 
(28 
IP 
XX '~. Q (the y \[3 I = P(y)\] Q(y)) YY 
ANCHOR(% S') 
(29) s: 
!y 
s': P(y) 
IP 
XX y YY 
ANCHOR(% S') 
The key observation is that the application of this rule, as 
well as of any other NP rule, depends on the hearer's pre- 
vious identification of a resource situation for the definite 
description. The statement ANCHOR('~, s') constraining the 
interpretation of & is added to the situation structure by the 
processes that identify the referent of the definite descrip- 
tion; I describe these processes in detail in \[30\]. 8 
Finally, I propose that, when context is missing, a default 
model construction procedure operates. It has been sug- 
gested \[6\] that the conceptualization of events follows an 
order reflected in the thematic hierarchy AGENT < LOCA- 
TION, SOURCE, GOAL < THEME proposed to account for 
phenomena like passivization \[21\]. Briefly, the idea is that 
'the normal procedure for building an event description' is 
to follow the order in the hierarchy: first identify the agent, 
then the location, then the theme. This proposal can be for- 
malized in the current framework by having rules that oper- 
ate in case no other rule has, and that modify the model by 
introducing a resource situation for an operator and estab- 
lishing anchoring connections. These rules depend both on 
the semantics of the verb and on the syntactic configuration. 
The rule that identifies the AGENT, for example, is triggered 
by the configuration in (30), and results in the configuration 
in (31), that allows for the rule for the NP to operate in that 
the resource situation of the operator has been anchored: 
8A more conventional situation-theoretic framework is used 
there, but the analysis carries over to the framework in this paper. 
84 
(30) 
IP 
NP VP 
w 
v YP 
'3. P (det x \[~ ~ (2\] "3. x3. y v(x)(y) 
P(x)) ^ AGENT(x) 
(31 
IP 
NP VP 
V YP A 
'X P (det x \[t ~ Q\] '3. x3. y P(x)(y) 
P(x)) ^ AGENT(x) 
ANCHOR(%~, S') 
These roles can of course originate conflicts with the re- 
suits of other discourse interpretation processes. I assume 
the following conflict resolution rule: when two rules pro- 
duce conflicting hypothesis, assume the result of the more 
specific rule. In general, the discourse interpretation rules 
are more specific than the default rules for constructing 
events representations, so they will be preferred. 
Although lack of space prevents me from giving exam- 
pies, rules relating the construction of the model to lexical 
semantics, such as those accounting for data like (12), can 
also be formulated. 
AN EXAMPLE 
We can now discuss in more detail the process of disam- 
biguation of (18). I have presented the logical form for (18) 
above, as (21). 
(18) Every school sent the principal to the meeting. 
After identifying the situation descriptions, various interpre- 
tation processes take place, like those performing definite 
description interpretation described in \[30\]. These processes 
generate hypotheses about the anchoring of resource situa- 
tions. Without entering into details, I assume that the con- 
text for (18) is provided by (32), that introduces into the 
model the situation description in (33), containing a group 
of schools and a meeting. 
(32) There was a meeting of the schools in the district. 
s 
x S 
(33) MEETING(X) 
S: SCHOOL* (S) 
PARTICIPATE(S, X) 
Given this context, the discourse interpretation processes 
identify s as the resource situation for the NPs "every school" 
and "the meeting." However, no unique principal can be 
identified in s. The activation of the model construction 
rules for universal quantification and definite descriptions 
results in the partial model in (34), in which ~1 and s'2 have 
been identified: 
(34) 
$ $1 
$1: 
i 
: ~_emaNG(,v) 
ANCHOR(y, X) 
$2 
s2: ~:z E S 
s2 _C THIS_SITUATION 
S3 
IP 
NP VP 
s3: VP PP 
'SENT "the principal" 'TO y 
S 2 E S 3 
Th, model construction role applied to the universal "ev- 
ery school" introduces a complex condition K1 ---> I(2 as 
usual, but both the restriction and the nuclear scope include 
situation descriptions. The situation description in the re- 
striction, s2, is a subsituation of the situation at which the 
restriction is evaluated (denoted by the indexical constant 
THIS_SITUATION). The situation description in the nu- 
clear scope, s3, is an extension of s2. 
85 
Now that a situation description for the resource situation 
of the universal and a discourse marker for the school have 
been introduced (s2 and z, respectively), the roles for resolv- 
ing the parametric component Jc of the interpretation of"the 
principal" can apply. The result is that z is chosen as an- 
tecedent of ±, and s2 is chosen as the resource situation for 
"the principal." The model construction role updates s3 ac- 
cordingly; the resulting event structure is equivalent to the 
interpretation of (21) specified by (20). 
ACCOUNTING FOR THE 
DISAMBIGUATION DATA 
I briefly retum here the disambiguation principles, to show 
how the proposal just presented accounts for them. First of 
all, I'll note that, under simple assumptions about the map- 
ping between grammatical functions and theta-roles, there 
is a striking resemblance between the grammatical function 
hierarchy proposed by Ioup and the thematic hierarchy pro- 
posed by Jackendoff to account for facts about passives and 
reflexives. The facts accounted for by the grammatical func- 
tion hierarchy principle can also be explained if we assurm 
that the description of an event is constructed by identify- 
ing the filler of each thematic role in the order specified by 
Jackendoff's thematic hierarchy. 
Consider now the case of the other disambiguation fac- 
tor proposed by Ioup, the lexically encoded preference for 
certain operators to take wide scope. Definite descriptions 
are the paradigmatic case of an operator that tends to take 
wide scope. This preference can be explained in terms of 
the model construction hypothesis as follows. The choice 
of a resource situation for definite descriptions is restricted 
by the constraint that this resource situation be either shared 
among the conversational participants, or related to shared 
knowledge by shared relations \[12, 4\]. In our dialogues, for 
example, definite descriptions are usually interpreted with 
respect to the 'situation' corresponding to the current visual 
scene, which is independent from other situations. It follows 
that a definite description will be assigned narrow scope rel- 
ative to another operator only if (i) the resource situation 
of the definite is perceived to depend on this other resource 
situation, and (ii) this dependency relation is known to be 
shared. 
As for the tendency for NPs in topic to take wide scope, 
an element of a sentence is said to be in topic if it is consid- 
ered to be part of the background information on which the 
new information in the sentence depends. As the interpre- 
tation of the 'new' infonnation in the sentence depends on 
the background information, it is plausible to assume that, 
in constructing a model for the sentence, the listener begins 
by applying the model construction roles for the operators 
perceived to be in topic (or explicitly marked as being in 
topic, in the case of Japanese). The interpretation of the 
operators not in topic, when determined at all, will depend 
on the interpretation of the operators in topic, resulting in 
the dependency relations between the related situations that 
I have assumed to be the way scope is represented. 
Finally, I'll note that, in the absence of contextual clues, 
whether a completely disambiguated event structure is actu- 
ally constructed depends on how strong the model construc- 
tion roles are supposed to be; it's perfectly possible that the 
activation of these rules is controlled by additional factors, 
such as the specific needs of a task to be performed. 
ACKNOWLEDGMENTS 
I wish to thank my advisor Len Schubert and James Allen, 
Howard Kurtzman, Peter Lasersohn, and Uwe Reyle for sev- 
eral suggestions, technical help, and constructive criticism. 
This work was supported by the US Air Force - Rome Lab- 
oratory Research Contract no. F30602-91-C-0010. 

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