RESOLVING QUASI LOGICAL FORMS 
Hiyan Alshawi 
SRI International 
Cambridge Research Centre 
23 Millers Yard 
Cambridge CB2 1RQ 
U.K. 
The paper describes intermediate and resolved logical form representations of sentences involving referring 
expressions and a reference resolution process for mapping between these representations. The intermediate 
representation, Quasi Logical Form (or QLF), may contain unresolved terms corresponding to anaphoric 
noun phrases covering bound variable anaphora, reflexives, and definite descriptions. Implict relations arising 
in constructs such as compound nominals appear in QLF as unresolved formulae. The QLF representation is 
also neutral with respect to ambiguities corresponding to quantifier scope and the collective/distributive 
distinction, the latter being treated as quantifier resolution. Reference candidates are proposed according to 
an ordered set of "reference resolution rules" producing possible resolved logical forms to which linguistic 
and pragmatic constraints are then applied. 
1 INTRODUCTION 
This paper is concerned with the relationship between the 
linguistic analysis of sentences and their interpretation in 
context. Our model is described as implemented in the Core 
Language Engine (CLE), a domain-independent system for 
translating natural language sentences into logical form 
representations. One of the characteristics of this system is 
that it embodies an extreme form of a staged natural 
language processing architecture whereby modular process- 
ing components have the function of mapping between 
different levels of sentence representation. Representations 
at the level of quasi logical form (QLF) are the result of 
applying declarative rules for morphological, syntactic, and 
semantic analysis. These QLF representations have subex- 
pressions corresponding to unresolved referring construc- 
tions. The QLF level can be regarded as the natural level of 
sentence representation resulting from compositional seman- 
tic analysis independently of the influence of context: 
Sentence-LINGUISTIC ANALYSIS ----~ 
QLFs-QLF RESOLUTION IN CONTEXT---~LF. 
QLFs are also neutral with respect to quantifier scope, and 
the distributive/collective and referential/attributive dis- 
tinctions. Collective and attributive readings are viewed as 
resolution to suitable quantifiers in a manner explained in 
the paper. We will not be discussing the process of quanti- 
fier scoping here: a scoping mechanism for the CLE has 
already been described by Moran (1988), and a later 
version is described by Pereira in Alshawi et al. (1988). 
Formally, it may be possible to regard the resolution 
process as defining a function from (QLF,context) pairs to 
LFs. In practice, however, since the contextual information 
exploited by the CLE resolution process is incomplete, a 
particular QLF expression may correspond to several LF 
expressions. 
2 DERIVING LFs FROM QLFs 
2.1 QLF CONSTRUCTS 
The QLF language is a superset of the LF (logical form) 
language used in the CLE (Alshawi and van Eijck 1989). 
LF is itself an extension of first order logic, including 
generalized quantifiers and some higher order operators 
and relations. The additional QLF constructs relevant to 
reference resolution are a_terms (anaphoric terms), 
q_terms (quantified terms), and a_forms (anaphoric for- 
mulae). In general, the first two arise from anaphoric and 
quantified noun phrases, while a_forms arise from linguis- 
tic expressions that embody implicit relations or ellipsis. 
a_terms, q_terms and a_forms include linguistic informa- 
tion represented as a 'reference category,' a variable, and a 
restriction (a QLF formula): 
a-term(Category, Entity bar, Restriction) 
q_term(Category, Entity Var, Restriction) 
a._~\[orm(Category, Predicate Var, Restriction). 
In a_terms and q_terms the variable stands for a referent, 
or is simply the variable of an LF quantification, and the 
formula is a restriction on that variable. In a_forms the 
variable appears in predicate position in the restriction. We 
Computational Linguistics Volume 16, Number 3, September 1990 133 
Hiyan Alshawi Resolving Quasi Logical Forms 
will show categories as a list of feature-value pairs: 
(Feature I = Value 1 ..... Feature N = Value N> 
(In fact the CLE uses a different, but equivalent, notation 
for categories.) 
All three QLF constructs are introduced explicitly by the 
semantic analysis rules. For example, the sentence She met 
a friend of John has the following QLF representation in 
which the a_term is the semantic analysis for she, the 
q_term is the analysis of the quantified noun phrase a 
friend of John, and the a_form is the analysis of friend of 
John: 1 
\[meet, 
a_term(( t = ref,p = pro,l = she,n = sing, a = ( ) ), 
Y, 
\[female,Y\]), 
q_term( ( t = quant, n = sing, 1 = a ), 
X, 
a_{orm((t =prod, p = genii ), 
R, 
\[and,\[friend, X\],\[R,john,X\]\])\])\]). 
The QLF expressions corresponding to various linguistic 
phenomena are described in Section 4. 
2.2 QLF RESOLUTION 
Basically, the process of QLF resolution involves determin- 
ing possible LF terms to replace each QLF a___term or 
definite description, possible quantifiers to replace the deter- 
miners for q_terms, and possible formulae to replace each 
QLF a_form. The quantifier seeping phase determines the 
scope, or body, for each q_term producing seeped expres- 
sions that employ a four part generalized quantifier nota- 
tion (Woods 1978): 
quant (Quantifier, Variable, Restriction, Body). 
• In the example above, QLF resolution leads to the follow- 
ing LF in which the a_term is replaced by an intersenten- 
tial referent mary, the noun phrase determiner is replaced 
by the quantifier exists, and the a_form is simply replaced 
by a formula involving the relational noun predicate 
friend__of taken from the lexicon: 
quant (exists, X, 
\[and,\[friend,X\],\[{riend--of,john, X\]\], 
\[meet,mary, X\]). 
Proposing resolutions for a QLF is followed by the 
application of plausibility constraints, both linguistic and 
nonlinguistic (Section 6). The constraints are applied to a 
version of the QLF that includes proposed resolutions of 
referring expressions. This 'resolved quasi logical form,' or 
RQLF, thus implicitly represents a QLF, an LF, and the 
correspondence between them. If the proposed RQLF fails 
to obey these constraints, then reference resolution will 
generate other possibilities for resolving the QLF; if all 
such proposed RQLFs fail the tests, other QLFs for the 
sentence wilt be considered. Once an RQLF is accepted, 
the CLE updates its model of currently salient discourse 
entities used for resolving intersentential references (Sec- 
tion 5). The LF implicit in the RQLF is then extracted to 
become the final output of the reference resolution and 
plausibility phases. To summarize, we can view a QLF as 
giving a semantic analysis for an utterance, an RQLF as a 
representation of its interpretation in context, and an LF as 
a representation of its truth conditions. The process of QLF 
resolution can be viewed schematically as follows: 
QLF-scoPING AND REFERENCE ----~ 
RQLFs-CONSTRAINTS AND PLAUSIBILITY--*LF. 
A general property of RQLFs is that they are formed by 
adding information to the QLFs from which they were 
derived; intuitively, this corresponds to fleshing out the 
QLFs in context. Thus referents are shown in-place in an 
RQLF, that is, the variables for resolved a_terms and 
definite descriptions are unified with their referents, and 
re,;olved a__form relations are instantiated in the a_form 
re,;triction, q_terms also remain in the RQLF, so the 
information about quantified noun phrases from the origi- 
nal (unscoped) QLF is preserved. This does mean that an 
RQLF can contain redundancies, but these will be removed 
when the final LF is extracted from it (though, for brevity, 
we will usually not show q_terms in seeped expressions). 
The RQLF interpretation leading to the LF shown above is 
quant(exists, X, 
a__form((t = pred, p =genit ), 
friend_of, 
\[and,\[friend, X\],\[friend--of, john,X\]\], 
\[meet, 
a_term((t = rel,p = pro,l = she, n = sing, a = ( ) ), 
mary, 
\[{creels,mary\]), 
q_term( ( t = quant,n = sing,l = a), 
X, 
a__form(.., friend._ol...))\]\]. 
In addition to the CLE procedures for proposing refer- 
ents, checking constraints, and updating the salience model, 
the CLE provides an interface in terms of a set of applica- 
tion definable procedures (Section 5.2) for performing 
these functions. This interface allows the context imposed 
by a natural language processing application to influence 
reference resolution and plausibility checking, while keep- 
ing the CLE itself application independent. 
3 REFERENCE RESOLUTION RULES 
The motivation for having a set of rules for reference 
resolution is that this allows the basic resolution algorithm 
to be independent of the details of how anaphoric expres- 
sions are categorized and how different approaches to their 
resolution are ordered. This is in contrast to approaches 
(e.g., Hobbs 1976; Carter 1987) in which these details are 
encoded in the algorithm, leading to different success rates 
for different algorithms depending on the type of text 
134 Computational Linguistics Volume 16, Number 3, September 1990 
Hiyan Alshawi Resolving Quasi Logical Forms 
(Walker 1989 compares the performance of two such algo- 
rithms). Our approach should make it possible to write 
different sets of resolution rules for different natural lan- 
guages, or sublanguages, without changing the mechanism 
applying these rules. 
In the CLE, an ordered set of "reference resolution 
rules" determines the order in which proposed resolved LFs 
are derived from a QLF. Unresolved QLF expressions can 
be nested, so before the rules are applied to an unresolved 
expression, they are applied recursively to its restriction. 
Each rule specifies a "resolution method" that can be used 
to suggest a referent for an unresolved expression that 
matches a QLF expression specified in the rule: 
refrule( OLF_expression, Method). 
The resolution method corresponds to a relation between 
QLF expressions, contexts, and referents. In the CLE 
implementation, a method is the name ofa Prolog predicate 
that takes an unresolved expression and returns candidate 
referents in a preference order by backtracking, so the 
method may succeed zero, one, or several times. The contex- 
tual information handed to the resolution method is in the 
form of an ordered list of discourse entities (Section 5.1) 
together with the whole QLF for the sentence being pro- 
cessed. 
Resolution rules are ordered, with each rule being tried 
in this order against each unresolved expression in the 
sentence QLF. The QLF expression appearing in a rule is a 
term that can unify with either an a_term, a q_term or an 
a_form. A rule is taken to be applicable to the resolution of 
a QLF-expression if the expression unifies with the left 
hand side of the rule. In general, it is the category in 
unresolved QLF expressions that plays the major role in 
selecting resolution methods to be applied. The information 
represented in these categories is in principle open-ended in 
the same sense that holds for categories appearing in rules 
in unification grammar formalisms. 
As well as the main reference resolution rules just de- 
scribed, the resolution process makes use of lexical declara- 
tions specifying, for example, the predicate corresponding 
to relational nouns or the quantifier cardinality predicate 
corresponding to determiners: 
reflex( WordSense, Category, Predicate). 
Examples of these "lexical reference declarations" will be 
given in Section 4. 
The implementation of our QLF resolution model in the 
CLE uses a set of rules covering a range of reference 
phenomena that occur in English, including pronouns (Sec- 
tions 4.1, 4.2, 4.3, 4.8), definite descriptions (Sections 4.4 
and 4.9), quantifiers and collective readings (Sections 4.5 
and 4.6), one-anaphora (Section 4.14), and implicit rela- 
tions (Sections 4.11 and 4.12). The set of CLE resolution 
rules can, of course, be extended or changed, and we hope 
to develop a theory of ellipsis resolution based on this 
framework. 
The possibilities available for resolving QLF expressions 
are governed by the set of reference rules and the context 
from which they propose referents. Choosing between these 
possibilities to arrive at a final LF depends on the con- 
straints applied during the plausibility phase and on heuris- 
tic factors such as rule ordering and the salience weights 
associated with discourse entities. We will not be discussing 
these heuristic factors much, but instead will focus prima- 
rily on illustrating how a wide range of semantic and 
pragmatic phenomena can be viewed as QLF resolution 
(Section 4), and secondarily on the application of con- 
straints on resolution to resulting RQLF interpretations 
(Section 6). 
One way of viewing a QLF expression is as a conditional 
interpretation in the sense of Pollack and Pereira (1988). 
To take the simplest case, we can regard an Lterm 
representing a pronoun in a QLF as an assumption that the 
variable for the a_term can be resolved by a matching 
reference rule. Our framework for QLF resolution can then 
be seen as a modular approach to representing and discharg- 
ing such assumptions in a way that does not require their 
interactions, or the constraints on resolution, to be specified 
in the semantic interpretation rules of the system. It may be 
a consequence of the resulting simplicity of description that 
we have been able to cover a wide range of English construc- 
tions in the CLE implementation. We now turn to discuss- 
ing these particular cases. 
4 REFERRING EXPRESSIONS 
Various anaphoric phenomena handled by the CLE are 
considered in separate sections for expository purposes, but 
this does not correspond to a disjoint classification; bound 
variable anaphora, for example, overlap with both refexive 
and nonreflexive pronouns. The particular features in the 
reference categories in this section are t, specifying the type 
of anaphoric expression (e.g. ref for noun phrase refer- 
ence); p, for the phrase type (e.g. pro for pronoun); 1, for 
lexical information; n, for number; and a, for specifying 
intra-sentential antecedents. 
4.1 PRONOUNS 
The QLF representation of a pronoun is an a_term. For 
example, the translation of him in Mary expected him to 
introduce himself is as follows: 
a__term( ( t = re~,p = pro,1 = him, n = sing, a = ( mary ) ), X,\[male, X\]) 
The reference category states that the a_term is for a 
nonreflexive pronoun, with surface form him, expecting a 
singular referent, and that mary is a possible referent from 
within the sentence. The logical form restriction on the 
variable X constrains the referent to be male in this case. In 
the case of there and then it ensures that the referent is a 
place or time, respectively, this information being specified 
in the sense entries for the pronoun. 
Inter-sentential reference possibilities are not included 
on the list of antecedents, since this list is built by the 
sentence-level semantic analysis rules. The list contains 
Computational Linguistics Volume 16, Number 3, September 1990 135 
Hiyan Alshawi Resolving Quasi Logical Forms 
indices to the denotations of other noun phrases in the 
sentence. In our current semantic rules, the list is built up 
by unification by accumulating it in a pair of features that 
are "threaded" through the daughters of each constituent 
in a manner similar to the threading of long distance 
dependency gaps (Pereira 1981). Consequently, a pronoun 
cannot co-refer with a nonpronomial noun phrase following 
it in the order in which antecedents are threaded, unless 
this co-reference is made through an inter-sentential refer- 
ence of the pronoun. 
The threading order can be varied for different semantic 
rules, but tends to correspond to a recursive traversal of the 
nodes in the syntax tree in the order: mother, left-daughter, 
right-daughter. For semantic analysis rules covering topi- 
calization, however, indices of noun phrases in the preposed 
constituent are threaded as though there was no topicaliza- 
tion, allowing a treatment of a common type of cataphoric 
reference. For example, in both of the sentences: 
Mary heard a dog behind her 
Behind her, Mary heard a dog 
mary is on the antecedents list for her because in the second 
case Behind her is analyzed as preposed. 
Several CLE reference rules cover pronouns, including 
the following: 
refrule(a-.term((t = ref,p = pro,1 = i ) .... ), 
hearer_speaker_ref) 
refrule(a--term((t = ref, p = pro),_,_), 
intra_sentential) 
refrule(a_.term((t =ref, p= pro) .... ), 
inter-sentential). 
The ordering of the rules shown above means that prece- 
dence is given to the method hearer_speaker__xef when 
the pronoun is "I," and that intra-sentential pronoun refer- 
ents (taken from antecedents lists) are proposed before 
inter-sentential ones (discourse entities from the context 
model). 
4.2 REFLEXIVE PRONOUNS 
Reflexive pronouns are also translated into a_terms in 
QLF, the only difference being that the phrase type feature 
is refl instead of pro, the main reference rule being 
refrule(a__term((t = re:\[,p = refl) .... ), 
intra_sentential). 
Again taking the sentence Mary expected him to introduce 
himself the a_term for himself is 
a__term((t =ref,p = refl,1 = him,n = sing,a= (-X,mary)),Y,\[male,Y\]). 
The antecedents list for this reflexive pronoun includes 
mary as well as the variable from the other pronoun 
a_term; i.e. the variable that will eventually be unified with 
the referent of him. 
"\]File QLF level of representation does not take account of 
the linguistic constraints on co-reference for reflexive and 
nonreflexive pronouns. Instead, these constraints are han- 
dled separately (Section 6), so the antecedent lists for 
reflexive and nonreflexive pronouns are the same. Another 
possible approach is for the semantic rules to maintain two 
lists, one for reflexive and one for nonreflexive pronouns, 
but 1:here are disadvantages to this: it adds considerable 
complexity to the semantic analysis rules, it is difficult to 
implement by unification (since it can involve moving items 
between the two lists), and it is also arguable that the 
consl:raints on reflexives are not purely linguistic (Section 
6). 
4.3 BOUND VARIABLE ANAPHORA 
In ~.he reference category of the example a_term just given 
in the previous section, we saw that the antecedent list for a 
pronoun may contain variables. Resolving one pronoun to 
the variable corresponding to another one ensures that they 
co-refer. In the case of Mary expected him to introduce 
himself this means that both a_terms will be replaced by 
the same constant from outside the sentence. Bound vari- 
able anaphora, on the other hand, involves replacement of 
the a_term by a variable bound by a logical form quantifier 
(Partee 1978). A simple example is Every bishop admires 
himself which has the following seeped QLF: 
quant( ( t = quant, p = dot,1 = every, n = sing ), X, 
\[bishop, X\], 
\[admire,X, 
a-term ( ( t = ref, p = refl,1 = him, n = sing, a = ( -X ) ),Y, 
male,Y\])\]). 
In the resolved LF, the a_term will have been replaced by 
the variable X giving \[admire, X, X\] as the scope of the 
quar.,tification over X. Further examples of resolving pro- 
nouns to variables are given in Sections 4.4, 4.10, and 4.13. 
In the antecedents list, the item -X indicates that the 
variable X comes from a singular noun phrase antecedent 
(it would have been +X for a plural antecedent). This 
information is included in the reference category of the 
a_term rather than in its restriction, because it is relevant, 
for intra-sentential reference, to syntactic agreement as 
opposed to constraining what the logical form variable can 
be bound to. This can be seen by comparing the sentences 
Every bishop admires himself and All bishops admire 
themselves. In both cases the logical variable ranges over 
individual bishops, while there is number agreement be- 
tween the the pronoun and the singular and plural subject 
noun phrases respectively. 2 
4.4 DEFINITE DESCRIPTIONS 
Definite descriptions are represented as q_terms in QLF, 
and as such are seeped by the CLE quantifier scoping 
mechanism in the same way as other quantified noun 
phrases. The seeping of definite descriptions is motivated 
by the possibility of their resolution to quantifiers (Section 
136 Computational Linguistics Volume 16, Number 3, September 1990 
Hiyan Alshawi Resolving Quasi Logical Forms 
4.7). The scoped QLF and unscoped QLFs for the small 
dog slept are therefore, respectively: 
\[sleep, 
q_term(( t = ref,p = def,1 = the,n = sing,a = ( ) ), 
X, 
\[and, \[dog, X\],\[small, X\]\])\]. 
quant((t =re\[,p = del,l=the, n = sing,a = ( > }, 
X, 
\[and,\[dog,X\],\[small,X\]\], 
\[sleep,X\]). 
If the referent of the definite description here is fide, say, 
then the resolution of the description is effected by replac- 
ing the above quant formula by its body after replacing 
occurrences of the variable X in the body with fide. In 
simple cases such as this, the same effect could have been 
achieved by representing the definite description by an 
a_term to be replaced by fide in the resolved LF. 
The rules for handling such referential readings of defi- 
nite descriptions include methods for proposing referents 
from the external application context as well as the CLE 
context model: 
refrule(q_term( ( t = ref, p = de~,l = the,n = sing ) .... ), 
salient--satisfying--restriction) 
refrule(q-term( ( t = ref, p = def,1 = the,n = sing ) .... ), 
reference_eandidate_applic). 
In the second rule, the resolution method is an application 
dependent method for singular definite descriptions. Typi- 
cally, such a method will attempt to check that candidates 
it proposes satisfy the restriction (though not necessarily 
the body) of the definite quantifier by simple database 
lookup or inference from a knowledge base. For example, it 
might propose a salient entity john as the referent for the 
sailor that Mary loves if it managed to prove that the LF 
\[and, \[sailor, john\], \[loves, mary, john\]\] 
holds in the knowledge base. We will return to definite 
descriptions when discussing plurals and attributive read- 
ings in the following sections. 
4.5 DETERMINERS AND QUANTIFIERS 
Resolving QLFs covers phenomena that are often handled 
by the semantic analysis and quantifier scoping compo- 
nents of language processing systems (including earlier 
versions of the CLE). Some of these, such as the correspon- 
dence between determiners and quantifiers and the deriva- 
tion of collective and attributive readings of noun phrases, 
are handled as "quantifier resolution." The basic idea will 
be given in this section; other cases are discussed in Sec- 
tions 4.6 and 4.7. 
As mentioned earlier, the QLF representation of a quan- 
tified noun phrase or definite description is a q_term for 
which the scoping algorithm proposes possible scopes (body 
expressions). This process takes into account scoping pref- 
erences, in particular those associated with the determiner 
appearing in the category of the q_term. In the resulting 
scoped QLF, there will be a quant formula for each q_term 
as follows: 
q_term( Category, Variable, Restriction) 
quant( Category, Variable, Restriction,Body) 
In earlier versions of the CLE scoping algorithm, the 
q_termwas replaced with its variable. Currently this infor- 
mation is only removed from the body when a final LF is 
extracted from an RQLF, so that it can be taken into 
account by the constraints applied to RQLF interpreta- 
tions. 
After scoping, reference resolution fixes the interpreta- 
tion of determiner categories as quantifiers, yielding 
quant ( Ouantifi'er, Variable, Restriction, Body). 
The mapping of determiner categories to quantifiers de- 
pends on lexical reference declarations. For example, the 
following two declarations allow resolution of the determin- 
ers in some dog and all dogs to exists and retell, respec- 
tively: 
reflex( some, ( t = quant, p = det, n = sing, 1 = some ), exists) 
reflex(all, ( t = quant, p = det,1 = all ), forall) 
Quantifiers (in the distributive case) are taken to be 
predicates on two cardinalities, the number of entities, R, 
satisfying the restriction, and the number of entities, I, 
satisfying the conjunction of the restriction and the body. 
Abbreviations for these predicates are used for common 
cases, so, for example, forall abbreviates XrXi.r = i, which 
^ A in our notation is R I \[eq, R,I\]. Other examples of the 
declarations for distributive quantifiers are 
reflex(several, (t = quant,p = det,n = plur,lex = several ), 
- ^ 
R I \[geq,I,3\])) 
reflex(N, ( t = quant, p = det, n = number(N),lex = N ), R ^ I ~ \[geq, I, N\]) ) 
reflex(bare, ( t = quant, n = plur,1 = bare ), forall) 
A A reflex(bare,(t=quant,n=plur, l=bare),R I \[geq, I,2\]) 
reflex(bare, ( t = quant,n = plur, 1 = bare ), most). 
The first of these is for numeral determiners, so this decla- 
ration treats 3 as at least 3 (geq is the >__ relation).3 The last 
three declarations allow "empty determiners" for bare 
plurals like dogs to be resolved as a universal, as in dogs are 
animals, or some number greater than one, as in she could 
hear dogs barking, or most as in dogs eat meat. 
4.6 COLLECTIVE READINGS 
Our treatment of quantifier resolution covers distributive/ 
collective distinctions. In the LF language, quantifiers can 
be of the form set(Q), where again Q is a predicate on two 
numbers. For example, the LF representation of the collec- 
tive reading of Two boys carried John is 4 
quant(set(R" I ^ \[geq,I,2\]), 
B, 
\[boy,B\], 
quant(exists,E,\[event,E\],\[carry,E,B,john\])) 
Computational Linguistics Volume 16, Number 3, September 1990 137 
Hiyan Alshawi Resolving Quasi Logical Forms 
The interpretation of a collective set quantification is as 
follows. Set quantification variables range over sets of 
individuals. For such a quantificatien to be true, Q must 
hold of the cardinality of the union of sets satisfying the 
restriction, and the cardinality of the maximal subset of 
this union that satisfies the body) 
The QLF for the sentence, before seeping, is 
\[carry, 
q_term((t = quant,n= sing,1 =ex),E,\[event,E\]), 
q_term( ( t = quant, p = det, n = number(2), 1 = 2 ), B,\[boy, B\[), 
john\], 
in which the determiner is resolved to the set quantifier 
according to the first of the following declarations: 
reflex(N, (t = quant,p = det,n = number(N),l = N ),set(R ^ I ^ \[geq, I,N\])) 
reflex(several, ( t = quant, p = det, n = plur, 1 = several ), 
set(R" I A \[geq,I,3\])). 
The interaction of seeping alternatives with the collective/ 
distributive readings allowed by the declarations matching 
several and 2 gives several possible LFs for a sentence like 
2 girls met several boys, of which the following involves two 
(or more) girls, a meeting event for each girl, each event 
involving three or more boys: 
quant(R ^ I" \[geq, l,2\],G,\[girl, G\], 
quant(exists,E,\[event,E\], 
quant(set(R" I A \[geq, I,3\]),B,\[boy,B\], 
\[meet,E,G,B\]))). 
4.7 ATTRIBUTIVE DESCRIPTIONS 
As well as the referential readings of definite descriptions 
discussed in Section 4.4, attributive readings expressed as 
quantified LF expressions are also proposed during QLF 
resolution. Since definite descriptions are represented in 
QLF as q_terms, the analysis of Mary met the minister 
from France is 
\[meet, 
mary, 
q_term( ( t = ref, p = dM,1 = the, n: sing, a = ( mary ) ), 
M,\[and,\[minister,M\],\[from,M, france\]\])\]. 
After seeping, determiner resolution (Section 4.5) takes 
place according to a lexical declaration: 
reflex(the, ( t = tel, p = def,1 = the, n = sing ), exists), 
producing the following LF: 
quant(exists,M, 
\[and,\[minister,M\],\[from, M,france\]\], 
\[meet, mary,M\]). 
If uniqueness of the description referent is required, for 
example, if presuppositions are being derived from the 
sentence, a more appropriate lexical declaration might be 
^ ^ 
one giving the quantifier predicate R I \[eq, I,1\] (exactly 
one). 
In the case of parametrized definite descriptions, only 
attributive readings are allowed. An example of a descrip- 
tion parameterized by a free variable can arise in the 
resolution of a sentence such as Every dog buried the bone 
that it found for which the QLF, shown here after seeping, 
is 
qu ant( ( t = quant, p = det,1 = every ), 
X,\[dog,X\], 
quant( ( t = rel,p = def,l = the,n = sing,a = ( - X) ) , Y , 
\[and,\[bone, Y\], 
\[find, 
a._term( ( t = ref, p = pro,1 = it, 
n=sing,a=(- Y,- X)), 
W,\[impersonal,W\]), 
Y\]\], 
\[bury,X,Y\]). 
One of the possibilities for resolving the pronoun it in this 
sentence is to treat it as a bound variable anaphor, i.e., to 
replace the a_term with X, the variable ranging over dogs. 
(This resolution is proposed because X is on the a_term 
antecedents list; see Section 4.1. Y is also proposed, but this 
possibility is eventually ruled out by sortal constraints). If 
this resolution is made, then the definite description vari- 
able:, Y, cannot be resolved to a constant because the 
variable X is free in its restriction. This constraint is 
checked along with other binding constraints on resolution 
(Section 6). After resolution of the pronoun, determiner 
resolution takes place, giving 
quant(forall,X,\[dog,X\], 
quant(exists,Y, 
\[and,\[bone, Y\],\[find,X,Y\]\], 
\[bury,X,Y\])). 
4.8 PLURAL PRONOUNS 
Plural pronouns that are bound variable anaphora are 
treated in the CLE in the same way as singular cases, but 
taking number agreement into account, as was illustrated 
in Section 4.3 above with the example All bishops admire 
themselves. This gives us a collective or distributive read- 
ing depending on whether the variable replacing the a_term 
is bound by a set quantifier or a normal quantifier (Section 
4.6). 
Plural pronouns, including plural reflexives, can also be 
resolved to collections (i.e. sets of entities) taken from the 
antecedents list in reference categories or from the context 
model (Section 5.1). These referents may be proposed by 
either intra-sentential or inter-sentential resolution meth- 
ods, including application specific methods. At the QLF 
level, a plural pronoun such as they is represented as a 
q__term for quantifying over subsets S of a collection 
corresponding to an a_term: 
q._term((t = quant,1 = all ), 
S, 
\[subset,S, 
a._term( ( t = ref, p = pro,1 =they, n = plur ), 
X,\[entity,X\])\]). 
138 Computational Linguistics Volume 16, Number 3, September 1990 
Hiyan Alshawi Resolving Quasi Logical Forms 
This QLF representation covers the possibilities of a distrib- 
utive or collective interpretation depending on whether the 
q_term is resolved to a normal or set quantifier. In other 
words, the use of the two QLF constructs in the pronoun 
analysis factors out the distributivity and reference aspects 
of its interpretation. 
As an example, the QLF representation for John and 
Mary met after they graduated is 
\[and, 
\[meet, 
q_term((t=quant,n=sing,l=ex),E,\[event, E\]), 
\[john,mary}\], 
\[after, E, 
\[graduate, 
q_term( ( t = quant, n = sing,1 = ex ), F,\[event, F\]), 
q_term( ( t = quant,1 = all ), S, 
\[subset,S, 
a__term( ( t = ref,p = pro,1 = they, n = plur, 
a= ({john,mary\],mary, john) ), 
X,\[entity,X\])\])\]\]\]. 
In this example, the collection {john,mary} is the subject of 
the (collective) meeting event, and it also appears on the 
antecedents list for they. If the pronoun a_term is resolved 
to this collection and its q_term is resolved to the normal 
(distributive) forall, we get the following LF: 
quant(exists,E,\[event,E\], 
\[and, 
\[meet,E,~ohn,mary\]\], 
\[after,E, 
quant(forall,S, 
\[subset,S,\[john,mary\]\], 
quant(exists,F,\[event,F\], 
\[graduate,F,S\]))\]\]). 
Since the variable S is interpreted distributively, the restric- 
tion will bind it to singleton subsets of {john,mary}, ensuring 
that there are graduation events for each of John and 
Mary. 
4.9 PLURAL DEFINITE DESCRIPTIONS 
Plural definite descriptions are handled in a parallel fashion 
to their singular counterparts, except that the restriction 
employs subset in a similar way to plural pronouns. The 
QLF representation for a noun phrase like the three dogs is 
thus 
q_term( ( t = quant, n = plur,l = all ), 
S, 
\[subset,S, 
q_term( ( t = ref, p = def,1 = the, n = number(3) ), 
X,\[dog,X\])\]). 
If the lower q_term is resolved to an explicit set, this gives 
a referential reading. Otherwise the determiner can be 
resolved to a quantifier with the declaration: 
reflex(the, ( t = ref, p = def, n = number(N)),set(R "I ^ \[eq, I,N\])) 
giving an attributive reading. The distribution/collective 
distinction arises from the resolution of the quantifier for S 
to forall or set(forall), as explained in the case of plural 
pronouns (Section 4.8). 
The formation of discourse entities for plural referents is 
a major problem for language processing systems. This is 
reflected in the CLE in that the current coverage of English 
plural reference is far from complete. In particular, none of 
the current built-in resolution methods in the CLE pro- 
duces new collections from the set of entities present in the 
context model, which is required for handling discourses 
such as John left; Bill left; they were angry. However, the 
CLE external context interface (Section 5.2) allows collec- 
tions, such as the set of answers to a database query, to be 
included in the model. 
4.10 UNBOUND ANAPHORIC TERMS 
When an argument position in a QLF predication must 
co-refer with a pronoun or definite description, this is 
indicated as a_index(X), where X is the variable for the 
antecedent. For example, because want is a subject control 
verb, we have the following QLF for He wanted to swim: 
\[want, 
a--term((t = ref,p = pro,1 =he,n= sing,a= ( ) ),X,\[male,X\]), 
\[apply, 
Y A \[swim,Y\], 
a_index(X)\]\]. 
(The unreduced lambda application comes from the infini- 
tive; Section 6.4.) If the a_index variable is subsequently 
resolved to a quantified variable or a constant, then the 
a_index operator becomes redundant and is not included 
in the final LF. However, in special cases, such as the 
so-called "donkey sentences" (Geach 1962; Kamp 1981), 
an anaphoric term may be resolved to a quantified variable 
V outside the scope of the quantifier that binds V. An 
example is one reading of Every farmer who owns a dog 
loves it, in which the "unbound dependency" is indicated 
by retaining the a_index operator in the final structure: 
quant(forall,X, 
\[and, 
\[~armer, X\], 
quant(exists,Y, 
\[dog,Y\], 
\[own,X,Y\]), 
\[love,X,a__index(Y)\]). 
Such structures, which in some sense are not fully resolved 
LFs, cannot be given an interpretation using normal vari- 
able binding. However, an interpretation model similar to 
the one advocated by Groenendijk and Stokhof (1987) for 
their "dynamic logic" may be appropriate. The more imme- 
diate question of how we recognize that the out-of-scope 
reference is permitted is treated in our framework as a 
constraint on binding (Section 6). 
Computational Linguistics Volume 16, Number 3, September 1990 139 
Hiyan Alshawi Resolving Quasi Logical Forms 
4.11 IMPLICIT RELATI\[ONS 
English constructions like possessives, genitives, and com- 
pound nouns are translated into QLF expressions contain- 
ing uninstantiated relations introduced by the a_form 
relation binder. This binder is used in the translation of 
John's house, which says that a relation, R, introduced 
implicitly by a possessive phrase, holds between John and 
the house. Since possessive constructions are treated as 
definite descriptions, the seeped QLF for John's house 
leaks is as follows: 
quant( ( t = ref, p = def,... ),X, 
a_form( ( t = pred, p = poss ), R, 
\[and,\[house,X\],\[R,john,X\]\]), 
\[leak, X\]). 
The implicit relation R can then be determined by the 
reference resolver and instantiated, to owns or lives_in 
say, in the resolved LF. (The plausibility phase would then 
be expected to rule out incorrect candidates giving different 
relations in the two sentences Where was John's car hired 
from? and John's car broke down three days after he 
bought it.) 
Relations implicit in (nonlexicalized) compound nouns, 
possessives, and have constructions can often only be deter- 
mined from detailed knowledge of the domain of discourse 
(Alshawi 1987). Since this knowledge is not available to 
the CLE, the CLE depends on application-specific rules 
such as: 
refrule(a_..form( ( t = pred,p = nn ) .... ), 
relation_candidate_applic) 
for proposing resolutions for these constructions. 
4.12 LEXICALIZED RELATIONS 
These are treated as a special case of implicit relations and 
are applicable to relational nouns and lexicalized com- 
pound nouns with rules such as: 
refrule(a__forra( ( t = pred,p = poss ) .... ), 
relational_sense) 
refrule(a__form((t = pred, p = nn) .... ), 
lexiealized._compound). 
At the QLF level, the representation of John's mother has 
an a_form that is exactly parallel to the one for John's 
house: 
a__form( (t = pred,p = poss ),R,\[and,\[mother,X\],\[R,john,X\]\]). 
Lexical reference declarations associated with noun senses 
in the CLE lexicon can specify a relation to be used to 
resolve the a_form analysis of a noun phrase with a rela- 
tional noun head. The declarations give the phrase type 
(e.g. poss for possessive constructions and genii for the 
genitive of construction) for which resolution to the rela- 
tional sense is applicable. Given such a declaration, 
reflex(mother, (p = poss ),mother_of), 
the resolution method relationaL_sense will propose a 
resolution of the above a_form in which R is instantiated to 
the predicate mother_of: 
\[and.,\[mother, X\],\[mother_of,john,X\]\]. 
Lexicalized compound nominals like boat train are treated 
similarly in that the method lexicalized__compound in the 
resolution rule given above proposes predicates specified in 
lexical declarations for the relevant noun senses. 
4.13 POSSESSIVE PRONOUNS 
Noun phrases with possessive pronouns acting as determin- 
ers are covered by the rules for pronouns, implicit relations, 
and definite descriptions. For example, the noun phrase his 
mother is analyzed in QLF using a combination of an 
a__term for the pronoun, a definite description quantifier 
for the whole noun phrase, and an a_form for the relation 
between the noun phrase referent and the pronoun. The 
seeped QLF representation for John met his mother is 
quant( ( t = ref,p = def, l = the, n = sing, a = ( john ) ), X, 
a_form( ( t = pred, p = poss ), R, 
\[and,\[mother,X\], 
\[R, 
a_term( ( t = ref, p = pro, 1 = he, n = sing, a = ( john ) ),Y, 
\[male, Y\]), 
X\]\]), 
\[meet,john, X\]). 
Since resolution proceeds recursively, the a_term is re- 
solved first, to john say, then the a form to the relational 
noun predicate mother_of, and finally the definite descrip- 
tion is resolved to janet, say, giving \[meet,john,janet\]. If no 
appropriate referent corresponding to John's mother is 
proposed, then an attributive reading will be produced by 
resolving the definite description to an existential quantifi- 
cation (Section 4.7) giving the following LF: 
qaant(exists,X, 
\[and,\[mother,X\],\[mother_of, john,X\]\], 
\[meet,john,X\]). 
4.14 ONE-ANAPHORA 
The so-called "one-anaphora" (Webber 1979), which can 
be complete noun phrases, as in Mary knitted one, or 
modified nominals, as in John knitted a grey one, are taken 
to refer to restrictions from a preceding noun phrase, for 
example X A \[jumper,X\] (i.e. Xx.Jumper(x)) from the sen- 
tence Is it easy to knit a jumper? It is therefore appropriate 
to :represent such an anaphor in QLF with an a__form 
rather than an a_term, so that it matches the rule: 
ferrule(a-.form( ( t = pred, p = one ) .... ), 
previous_description). 
Unlike the relation variables used in the representation of 
implicit relations, the variable bound by the a_form has 
the type of a one-place predicate. For example, the seeped 
140 Comp~tational Linguistics Volume 16, Number 3, September 1990 
Hiyan Aishawi Resolving Quasi Logical Forms 
QLF for John knitted a grey one is 
quant( ( t = quant, p = dot,1 = a, n = sing ), X, 
\[and,a-:\[orm(( t = pred, p = one),P,\[P,X\]), 
\[grey,X\]\], 
\[knit,john,X\]). 
The resolution process involves replacing the body of the 
a_form with a resolved conjunct, in this case the one 
obtained by instantiating P to jumper, giving the following 
LF for the sentence: 
quant(exists,X, 
\[and,\[jumper,X\],\[grey, X\]\], 
\[knit,john,X\]). 
In the more general case, the resolution must be made to 
some but not all conjuncts of the preceding noun phrase 
restriction. For example, after a sentence like John found a 
female cat, the resolved restriction in Mary wanted a male 
one cannot include the contradictory conjunct \[female,X\]. 
The resolution method previous_description proposes each 
of the predicates X \[and,\[cat,X\],\[female, X\]\], X \[cat, X\], 
and X ^ \[female, X\] as resolution candidates, but only the 
second of these results in an LF satisfying sortal con- 
straints. 
The current CLE one-anaphora resolution method only 
proposes restrictions present in the context model that were 
derived from noun phrases in previous sentences. However, 
it would be possible to extend the treatment to handling 
intra-sentential cases by including another method that 
proposed restrictions of noun phrases whose variables are 
threaded as possible pronoun antecedents. 
5 CONTEXT MODEL 
5.1 DISCOURSE ENTITIES AND SALIENCE 
The CLE maintains a simple model of context, consisting 
of a set of entities with associated salience weights. These 
entities, ordered by salience, are then passed to any refer- 
ence resolution methods called; methods may or may not 
make use of this information when proposing referents. 
Entities in the salience model are represented as LF expres- 
sions. They are typically constants corresponding to individ- 
uals or collections, but they also include descriptions (pred- 
icates on one argument represented as a lambda abstraction) 
that are used in one-anaphora resolution. RQLFs corre- 
sponding to the interpretation of previous sentences are also 
included in the context model for the purpose of ellipsis 
resolution. 
Updating the context model involves changing the set of 
items in the model and updating their salience weights. 
New items enter the model when an RQLF expression that 
is taken to be the correct interpretation of a sentence is 
derived. The addition of items to the context model in 
response to producing an RQLF interpretation is in many 
respects a simplification of Webber's approach to the intro- 
duction of discourse entities (Webber 1979), so we will not 
discuss it further here. One difference is that our treatment 
of bound variable anaphora operates directly on QLFs, so 
we avoid the need to generate temporary descriptions of 
entities for resolving such anaphora. 
Updating salience weights is very simple in the CLE, 
weights being decremented as new sentences are processed. 
It is possible to extend the salience weight mechanism so 
that it can take into account the influence of syntactic, 
semantic, and nonlinguistic factors contributing to contex- 
tual salience as shown in Alshawi (1987), where it is also 
argued that notions of global and local focus (Grosz 1977; 
Sidner 1979) can be viewed as corresponding to salience 
thresholds. 
5.2 EXTERNAL CONTEXT INTERFACE 
When the CLE is used as an interface to application 
software, the application becomes part of the context within 
which the interpretation of user utterances takes place. In 
order that the application may influence the interpretation 
process, the CLE provides facilities for interfacing the 
application to CLE processing during the pragmatics phases; 
that is, reference resolution and plausibility checking. This 
is done through sortal restrictions (Section 6.2) and through 
the use of "interface procedures." 
CLE interface procedures relevant to reference resolu- 
tion and plausibility are concerned with proposing referents 
for noun phrase anaphora and implicit relations and for 
checking the plausibility of interpretations in the applica- 
tion context. It is easy to add reference rules with applica- 
tion-specific methods. For example, a rule could be added 
matching the a__term for the deictic pronoun here, the 
method in the rule being a procedure that returned the 
coordinates of a pointing device. This approach allows 
simpler or more comprehensive interfaces to CLE pragmat- 
ics, according to the effort available for application develop- 
ment. 
The CLE external context interface also allows applica- 
tions to send back constants, such as answers or sets of 
answers to database queries, for inclusion in the model 
after logical form evaluation has taken place. This makes it 
possible for the user to refer to such entities with anaphoric 
expressions in later exchanges. Sortal information for the 
new constants can also be provided through this interface. 
6 CONSTRAINTS ON RESOLVED LFs 
6.1 APPLYING THE CONSTRAINTS 
Resolved logical forms proposed by the reference resolution 
component are passed to the plausibility checking compo- 
nent. The main role of this component is to apply pragmatic 
constraints on plausibility in the form of sortal restrictions, 
and any application-specific constraints defined through 
the external context interface. Linguistic constraints on 
reference are also applied during this phase, because they 
also act as filters on the output of the reference resolution 
component. 
Computational Linguistics Volume 16, Number 3, September 1990 141 
Hiyan Alshawi Resolving Quasi Logical Forms 
Linguistically motivated preferences, encoded implicitly 
in the CLE by ordering lexical entries and rules, and 
explicitly as quantifier scoping rules, are reflected in the 
order in which logical forms are passed to the plausibility 
component. The normal mode of operation of the CLE is 
therefore to assume that the first proposed logical form to 
pass the plausibility constraints is the intended interpreta- 
tion. In future developments of our model, we hope that the 
plausibility component will produce numerical (e.g. proba- 
bilistic) estimates of plausibility. In the meantime, the 
interface between the plausibility component and an appli- 
cation system is such that it is possible for the application to 
compare the first five candidate interpretations, say, against 
each other, selecting one of them. 
As explained in Section 2.2, the RQLF passed to the 
plausibility phase includes the set of resolutions made, 
enabling the plausibility of these resolutions to be evalu- 
ated, rather than simply the plausibility of the correspond- 
ing final LF. This is particularly relevant to applying the 
linguistic constraints on pronoun reference, but it also gives 
the application a chance to veto resolutions proposed by the 
CLE. In general, the reason for passing the RQLF to the 
plausibility component is that plausibility, as we view it, is 
really a function of the interpretation of an utterance in 
context rather than simply a function of its truth condi- 
tions, as illustrated in the rest of this section. 
6.2 SORTAL CONSTRAINTS 
The sortal restriction mechanism used in the CLE associ- 
ates sorts with objects, properties, and relations according 
to a declaratively specified sort hierarchy (Atshawi et al. 
1988) that can be extended or redefined in order to reflect 
constraints that are specific to a particular domain of 
discourse. Sorts are coded into terms that unify if and only 
if they do not violate the restrictions (cf. Mellish 1988), 
giving an efficient way of applying plausibility constraints 
on domain predicates. The coding technique used is by now 
well known, so we will not discuss it further. In the CLE, 
checking the sortal constraints involves unifying logical 
form variables with sorted variables of the form V;S, where 
S is a coded sort term. 
It should be possible to extend the sortal restriction 
mechanism to cover constraints on whether predicates cor- 
responding to word senses take individuals or collections as 
their arguments in order to rule out distributive or collec- 
tive readings proposed during QLF resolution, but this has 
not yet been tried in the context of the CLE. 
As with the other constraints, sortal constraints are 
applied to the RQLF rather than the final LF. This is 
necessary because QLF subexpressions that do not appear 
in the final LF, such as expressions for relative clauses in 
referential definite descriptions, need to be taken into ac- 
count, and also because reference resolution introduces new 
predicates and arguments as referents. Applying the sortal 
check to the RQLF ensures that the constraints arising 
from the QLF expressions and the resolutions are checked 
for compatibility. 
6.3 BINDING CONSTRAINTS 
Var!iable binding constraints on resolved logical forms have 
already been mentioned in the discussion of definite descrip- 
tions and unbound anaphoric terms. Three constraints on 
variable binding are applied: 
1. All variables, other than a index variables, must occur 
vdthin the scope of their binders. 
2. A definite description whose restriction includes a vari- 
able bound outside the restriction must be resolved as a 
quantified expression. 
3. An a_index variable must be "accessible" from a QLF 
q__term for the variable. 
The first of these is the familiar constraint that disallows 
free variables (Montague 1973; May 1985) and covers 
variables bound by lambda abstraction as well as quanti- 
tiers. The second constraint was discussed with an example 
in Section 4.7. Clearly this constraint must be applied to an 
RQLF before its conversion into an LF, as the restriction of 
the definite description may not appear in the final LF 
representation. 
"\['he third constraint is the one relevant to unbound 
anaphoric terms (Section 4.10). Various characterizations 
of the required accessibility conditions relevant to this 
constraint have been studied, especially in terms of subordi- 
natio:a of discourse representation structures in DRT (Kamp 
1981). The accessibility condition in the CLE is rather 
simplistic and is currently restricted to making variables 
from an indefinite noun phrase in the restriction of a 
quantification accessible from its body (or one in the ante- 
cedent of an implication accessible in its consequent). This 
predicts the following for the acceptability of resolving the 
pronoun in the examples below to the dog variable (assum- 
ing narrow scoping of this variable): 
Every farmer who owns a dog loves it 
*Every farmer who owns no dog loves it 
*Every farmer who owns it loves a dog 
If a farmer owns a dog then s/he loves its 
6.4 CONFIGURATIONAL CONSTRAINTS 
The eonfigurational constraints we consider here are basi- 
cally linguistic constraints on the co-reference of reflexive 
and aonreflexive pronouns with other noun phrases in a 
sentence. In the CLE, the constraints are expressed at the 
RQL, F level in contrast to some approaches in the linguis- 
tics literature (Lasnik 1976; Reinhart 1983), where they 
are expressed at the level of syntax trees. 
Some constraints are implicit in the way semantic analy- 
sis rules thread items on the antecedents list for pronouns 
(Section 4.1). In this section we will describe the constraint 
that applies to the distribution of reflexive and nonreflexive 
pronouns. A simplified version of the constraint is explained 
first: a reflexive pronoun whose a_term is an argument to a 
logical form predicate must co-refer with another argu- 
ment of that predicate, whereas a nonreflexive pronoun 
cannot co-refer with such an argument. This rules out the 
142 Computational Linguistics Volume 16, Number 3, September 1990 
Hiyan Alshawi Resolving Quasi Logical Forms 
starred sentences below, under the resolutions shown in 
parentheses, while accepting the others: 
Mary shot her (Janet) 
Mary shot her (Mary)* 
Mary shot herself (Janet)* 
Mary shot herself (Mary) 
Every bishop admires him (John) 
Every bishop admires him (that same bishop)* 
John's father loves himself (John)* 
Bill said that he (Bill) had shot him (John) 
Bill said that he (John) had shot himself (John) 
Bill said that he (John) had shot himself (Bill)* 
Other possible resolutions of these sentences are also 
accepted or rejected by the constraint as expected. When 
applying the constraint, only the RQLF needs to be exam- 
ined, since this will include the predicate-argument struc- 
ture, the reference category for kterms showing p=pro 
or p=refl, and the proposed resolutions. In the first and 
last of the above sentences, the constraint applies to the 
argument sets of the predicates shoot, and say and shoot 
respectively: 
\[shoot, 
mary, 
a_term( ( t = ref, p = pro,1 = her, n = sing, a = ( mary ) ), janet, 
\[female,janet\])\] 
\[say, 
bill, 
\[shoot, 
a_term( ( t = ref, p = pro,1 = he, n = sing, a = ( bill ) ), 
john,\[male,john\]), 
a_term( ( t = ref, p = refl,1 = him, 
n=sing, a= ( - john,bill) ), 
biU,\[male, bill\])\]\]. 
The constraint gives also the expected behavior for com- 
paratives such as: 
John is taller than him (Bill) 
John is as tall as him (John)* 
because it applies to the arguments of a predicate more 
used in the LF representation of comparative constructions 
(Alshawi and van Eijck 1989), the final LF for the first of 
the examples above being 
\[more, E" F" \[tall--degree,E,FLjohn,bill\]. 
The actual constraint that is applied is slightly more 
complicated than the one stated above because it takes into 
account (and was part of the motivation for) propositional 
arguments that are unreduced lambda applications. These 
are used in the representation of infinitival complements, 
so, for example, John expected him (Bill) to shoot himself 
(Bill) has the following resolved LF: 
\[expect, 
john, 
\[apply, 
X "lshoot, X, bill\], 
bill\]\]. 
The full constraint is as stated before except that it de- 
mands that when a predicate P has a lambda application 
argument 
\[P ..... \[apply, X A Body, AL...\], 
then the argument A for the application is treated as 
though it were also an argument of P, and furthermore, the 
constraint is enforced on the lambda body after performing 
the reduction with a resolved argument. Informally then, 
the full constraint says how the simpler one should be 
applied at both clause levels. It accepts or rejects resolu- 
tions as shown for the following sentences: 
John expected to shoot himself (John) 
John expected to shoot himself (Bill)* 
John believed him (Bill) to be nice 
John expected him (Bill) to shoot himself (Bill) 
John expected him (John) to shoot himself (Bill)* 
John expected him (Bill) to shoot himself (John)* 
John expected him (Bill) to shoot him (Bill)* 
John expected him (Bill) to shoot him (John) 
Since the constraint is applied at the level of logical form, 
it can cover sentences with "picture nouns" to give 
John saw a picture of himself (John) 
John saw a friend of himself (John)* 
The implementation requires declarations specifying that 
relations such as picture_of are "representational," and 
then treats the meaning of the noun phrase a picture of 
himself as though it were co-referential with John for the 
purposes of checking the reflexive constraint. 
One weakness in the way the constraint on reflexives is 
currently applied in the CLE is that it is sensitive to 
whether prepositional phrase modifiers have been subcate- 
gorized for or whether they are optional. Optional argu- 
ments do not appear in the predication for the verb, but 
rather as additional predications involving the event vari- 
able. This means that John spoke to himself for example, 
will be rejected by the constraint as implemented unless the 
to prepositional phrase is subcategorized for. Fortunately, 
for cases like Mary wrapped a jumper round herself there 
is a strong argument that the prepositional phrase is not 
optional: Mary wrapped a jumper means something quite 
different. 
7 FURTHER RESEARCH 
We are currently developing our model for QLF resolution 
within the framework of a combined language processing 
and contextual reasoning system called CLARE, of which 
the CLE is the language component. This includes work on 
the treatment of ellipsis as QLF resolution. Some simple 
cases are already handled, such as the representation of an 
utterance consisting solely of a noun phrase as a form 
(...,P,\[P,NP\]) and resolving it by substituting the noun 
phrase meaning into the RQLF for a preceding sentence. 
We hope to extend this treatment to comparatives and 
Computational Linguistics Volume 16, Number 3, September 1990 143 
Hiyan Alshawi Resolving Quasi Logical Forms 
other elliptical expressions whose resolutions are partially 
governed by syntax. Another signif.cant aspect of QLF 
resolution that we have not yet addressed is determining 
the temporal indices implicit in QLF tense and aspect 
operators. 
Perhaps the most challenging problem in automatic lan- 
guage processing, that of simulating the role of plausibility 
in understanding, remains the most difficult part of QLF 
resolution. Our framework isolates this problem into the 
more concrete one of assigning plausibility ratings to RQLF 
interpretations. We will be looking at ways of exploiting 
inferential and probabilistic reasoning with domain knowl- 
edge in developing solutions to this problem. 
ACKNOWLEDGMENTS 
The research reported in this paper was carried out as part of the CLE 
development effort to which the following people have also contributed: 
David Carter, Jan van Eijck, Bob Moore, Doug Moran, Barney Pell, 
Fernando Pereira, Steve Pulman, and Arnold Smith. Development of the 
CLE was funded by an Alvey grant and by members of the NATTIE 
consortium (British Aerospace, British Telecom, Hewlett Packard, ICL, 
Olivetti, Philips, Shell Research, and SRI International). Steve Pulman, 
David Carter, and Jan van Eijck provided helpful comments on drafts of 
the text. 
NOTES 
1. C.LE logical forms use square brackets for the application of predi- 
cates and operators to their arguments. For expository purposes, most 
formulae are shown simplified in this paper. In particular, we will 
often omit the tense operators and Davidsonian style event variables 
that appear in CLE sentence representations. 
2. It would perhaps be more consistent with our overall framework not to 
represent this agreement information on antecedents lists, but to 
apply an agreement constraint together with the other constraints on 
pronomial reference to be discussed later. 
3. Another possibility is to treat 3 as exactly 3. We take the contextual 
dependence of the plausibility of these interpretation possibilities to 
support the "quantifier resolution" approach. 
4. In discussing collective and distributive readings, we explicitly show 
the quantification over event variables to make clear the number of 
events involved. 
5. Strictly speaking, all LF variables are interpreted as ranging over 
sets, with those for normal quantifiers ranging over individuals which 
are singleton sets. (cf. Scha 1981). 
144 Computational Linguistics Volume 16, Number 3, September 1990 

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