On Inference-Based Procedures for Lexical Disambiguation 
Jiirgen Wedekind 
Institute for Natural Language Processing 
University of Stuttgart 
Azenbergstr. 12 
D-70174 Stuttgart, FRG 
j uergen(0)ims.uni-stuttgart.de 
Abstract 
In this paper we sketch a decidable 
inference-based procedure for lexical dis- 
ambiguation which operates on semantic 
representations of discourse and concep- 
tual knowledge, In contrast to other ap- 
proaches which use a classical logic for 
the disambiguating inferences and run 
into decidability problems, we argue on 
the basis of empirical evidence that the 
underlying iifference mechanism has to 
be essentially incomplete in order to be 
(cognitively) adequate. Since our con- 
ceptual knowledge can be represented 
in a rather restricted representation lan- 
guage, it is then possible to show that the 
restrictions satisfied by the conceptual 
knowledge and the inferences ensure in 
an empirically adequate ww the decid- 
ability of the problem, although a fully 
expressive language is used to represent 
discourse. 
1 Introduction 
The determination of the contextual appropriate- 
hess of a reading of a lexically ambiguous sentence 
is conlmonly called lexical disambiguation. Lexical 
disambiguation presents a particular problein for 
any sort of natural language processing, but espe- 
cially for machine translation, since the seInantic 
grids of the source and the target may diverge 
in such a way that one has to disambiguate in 
cases where it, is not required for applications of 
the source alone. 1 Resolving lexical ambiguities 
is a problematic task, since it, involves different 
sources of linguistic and nonlinguistic information: 
intbrmation about the context of a sentence in a 
discourse, about the meanings of the words and 
about the world. 
iFor the translation from German to English e.g. it; 
is necessary to disambiguate 'Uhr' (clock/watch), but 
1lot for knowledge retrieval or other 1,atural language 
processing tasks based on German alone. 
Approaches to model the lexical disambigua- 
tion process formally differ as to the degree to 
which they consider the information of tile various 
sources needed to disambiguate properly. We can 
distinguish two classes of approaches: "surface- 
oriented" approaches and "inference-based" ap- 
proaches. Surface-oriented approaches rely on 
selectional restrictions (of. e.g. McCord 1989) 
(sometimes supplied by an external type hierar- 
chy/ontology (e.g. Nirenburg 1989) or are statis- 
tical (e.g. Kameyama, Peters, and Schiitze 1993). 
Although quite useful for some purposes, the 
performance of surface-oriented approaches is in- 
herently limited in that their context sensitivity is 
always locally bounded (see e.g. Kay, Gawron, and 
Norvig 1994 for details). Since we cannot assume 
fixed finite context, boundaries within each lexical 
ambiguity can be locally resolved, inference-based 
approaches seem more promising for handling lex- 
ical disambiguation, hfference-based approaches 
assume thai; the language of a logic is used to rep- 
resent the meaning of a discourse, that the same 
language is used to store our conceptual and world 
knowledge and that resolution is achieved on the 
basis of the underlying logic by special inferences. 
The most promineut inference pattern (which 
is also the center of the discussion here) is e.g. 
the proof of a contradiction from a given read- 
ing in a given context and our conceptual and 
world knowledge which allows us to rule out that 
reading. Although these approaches can handle 
the problem of disambiguating information arbi- 
trarily far away (the whole context is available as 
a premise), without any fllrther restrictions they 
run into tractability problems which exclude a 
practical application. Since we need - as we will 
show below a representation language which is 
at least as expressive as the language of first-order 
predicate logic for an adeqm~te representation of 
discourse meanings, an inconsistency test is not 
computable anymore if a classical (sound and as 
far as possible complete) calculus is used for the 
test: the underlying problem is simply undecid- 
able. 
Although it ,nay turn out that the disambigua- 
tion problem is in fact undecidable if world knowl- 
980 
edge is also used for disambiguating inferences, 
we assmrm~ that resolut;ion restricted to concep- 
tual knowle.dge constitutes an important subprob- 
lem froln a cognitive point of view, which is solv- 
able in eonl:rast to the general problem. Thai; all 
known approaches which are confined to concep- 
tual knowledge nevertheless rtm into probletns is 
due to an empirically false estimation: they do 
not take into account that humans are able. to 
disalntfiguate even without a fllll understmMing 
of the discourse} Lexical disambiguation works 
even very well in most of those cases where tile 
discourse is inconsistent; or its consistency ix not 
known, and the inconsistency test wouht either fail 
or ltot necessarily terminate. Thus, the kind of 
reasoning which is involved ill lexieal disambigua- 
lion has to be. essentially incoml)lete. Since our 
conceptual knowledge, on the other hand, can be 
ret)resenl;e.d in a rift;her restricted ret)resentation 
language, it is possible to restrict infere.n(:ing in 
an emt)irically adequate way which ensures decid- 
ahility of tile problem all;hough a flflly expressive, 
language in used to represent discourse. 
2 The Idea of Inference-Based 
Lexical Disambiguation 
Lexical disambiguation is a procedm'e determin- 
in~ r for a (le.xically) amhiguous sentence within a 
discourse which reading of the selttellce is contex- 
tually api)ropriate. Iq'om a logicM point of view, 
the resolution of a lexical amtfiguity is usually re- 
constructed by an inference process which rules 
out a reading if our concet)tual knowledge contra- 
dicts this readiug in the given ('ontext. '~ In order 
to illustrate this type of inference-based resolution 
t)rocedure let us consider the German sentence (1) 
(1) Einige Arzte haben eine Schwester. 
which contains the ambiguous lexical item 
'Sehwester'. Let us consider the two readings 
of (1) which have to be expressed in English by 
(2a,b) .4 
(2) (a) Some physicians haw; a sister. 
(b) Some physicians have a nurse. 
These two readings are represented by the two 
(oversimplified) predicate-calculus forinulas given 
in (3). '5 
(a) (a) 3~:( S'h>~i,.i~4~;) A ~:j( si.,.t~r.(:/, :,:))) 
(I,) ~:( l'h>~i,:i,,~(~.) ^ ~:,j(m,,,.~e(,))) 
2Approaehes which employ worhl knowledge in a 
nontrivial way m'e not; known, by the way. 
SAn overview on the, different methods is given in 
Kay, Oawron, and Norvig 1994. 
4Sentence (1) has, of course, more readings. But 
we abstract away fl'oln the others R)r the sake of 
simplicity. 
SSince we are primarily interested in the process, 
we abstract fi'om furtl,er details, like temporal aspects. 
ll,esolution of an ambiguity as in (1) is possible 
if it; is embedded in a discourse which provides 
disambiguating information. If the discourse were 
continued as in (4) 
(4) Einige Arzte haben eine Schwester, mit der sic 
verheiratet sind. 
we could rule out the mMesired reading given in (5). 
(5) 3a:(Pi~ys.(x) A 3y(Sister(y, x) A Married(x, y))) 
This reading which is expre, ssed in English by (6) 
(6) Some physicians have a sister to whom they are 
married. 
can he ruled out, since according to our concep- 
tual system nobody can be married to his sister. 
Since this part of our conceptual knowledge can 
be formalized, as in (7) 
(7) VxVy( Xistc.r(y, x) -~ -Married(x, y) ) 
the inapl)roprial:eness of reading (5) can be ex- 
plicated front a logical point of view by the fact 
that we can deriw; a contradiction fl'Oln that read- 
ing of (4) and our conceptual knowledge (meaning 
postulates).a 
3 The Intractability Problem 
Our inference-based reconstruction of the disam- 
biguation process given in the previous section re- 
quires oil the one hand that the meaning of the 
text is adequately represented in an apt)ropriate 
(formal) representation language, which allows the 
encoding of conceptuM knowledge as well. By re- 
quiring on l;he other hand the underlying logic to 
be sound and as far as possible complete, we run, 
of course, into well-known decidability prot)lems. 
Without any flu'ther restrictions on tile expres- 
sive power of 1;he representation language and/or 
the underlying logic the inconsistency of the repre- 
sentation of an arbitrary text and our conceptual 
knowledge is not decidable. Thus a natural lan- 
guage system whose re.solver is based on such an 
inference system is not very useflfl, since an at- 
tempt to resolve an ambiguity is not guaranteed 
to terminate. 
Since the field of AI which deals with knowl- 
edge represenl;ation and rel, rievM has heen worry- 
ing about the same problem for quite a hmg time, 
it is not surprising that approaches to eope with 
~>Phere is, of course, another procedure which is 
dual to the given one. The. dtml variant allows us to 
rule out a reading if this reading of the discourse con- 
rains redundant intbrmation, i.e., inlbrmation which 
already follows fl'om the meaning postulates. This 
procedure would exchlde e.g. for 'Einige Arzte habe.n 
eine Schwester, rail; der sie nicht w'xheiratet sind' the 
Sister" reading which is expressed in English by 'Some 
physicians have a sister to whom they are not mar- 
ried', since (7) implies for physicians who 1,aw~ a sister 
that they are not married to her. 
981 
this problem within lexical disambiguation were 
directly adopted from knowledge representation. 
According to the subject of the restriction used to 
ensure the traetabilty of the problem, we have to 
distinguish three main approaches. 
The simplest way to guarantee tractability of 
the disambiguation problem is by restricted com- 
putations. If the underlying logic of a resolver is 
known to be undecidable (e.g. the inference ma- 
chine used in LILOG (Bollinger, Lorenz, and Ple- 
tat 1991)) the only chance to ensure termination 
is by stopping the computation after a limited 
amount of resources (inference length, computa- 
tion time, etc.) is consumed. Since the termi- 
nation behavior of such a system is without any 
further empirical evidence not in any way corre- 
lated with our cognitive capabilities and without 
any further formal evidence not in any way cor- 
related with the behavior which we would expect, 
if the disambiguation problem were nevertheless 
decidable, we have to rule out these approaches 
from a scientific point of view. 
The second class of approaches achieves 
tractability by restricted representation languages. 
These restrictions allow one to base retrieval on a 
tractable logic which is sound and complete. In or- 
der to support the distinction between terminolog- 
ical and assertional knowledge, most formalisms of 
this class provide two different (restricted) repre- 
sentation languages: the terminological language 
and the assertional language. 
To use one of these knowledge representation 
formalisms (especially the tractable descendants 
of KL-ONE) for lexical disambiguation leads to 
problems which disqualify language restrictions as 
the only means to ensure tractability of the dis- 
ambiguation problem. On the one hand it is, of 
course, possible to find examples of meaning pos- 
tulates which are inexpressible in the restricted 
terminological languages (see e.g. the list given in 
Doyle and Patil 1991). But these counterexam- 
ples do not provide conclusive arguments, since 
the expressive power needed in order to formulate 
these eounterexamples is still rather weak, and one 
could counter by moving a little bit of expressive 
power around. Much more crucial for disambigua- 
tion are the restrictions imposed on the assertional 
language. 
In BACK (Hoppe et al. 1993), for example, which 
is used by Quantz and Schmitz 1993 for disam- 
biguation by storing the text representation in the 
ABox (assertional knowledge base) and the mean- 
ing postulates in the TBox (terminological knowl- 
edge base) it is e.g. not possible to represent (4) 
in an adequate way. We can only find represen- 
tations whose models include the models of (5), 
but not a representation with exactly the same 
models. In order to see this, consider the set- 
theoretic versions of the satisfiability conditions 
of (5) and (7) (for a model with interpretation 
flmction Z) given in (8) and (9). 7 
(8) (~Phys.\]ZN{x I ~y((y, x)e ~Sist.\]Zn~Marr.\]Z)}) # 0 
(9) \[Sister\] z n \[Married\] z = 
According to these conditions the BACK expres- 
sions (10) and (11) were adequate representations 
of" (5) and (7). 
(10) X :: Phys. and some(Sister and Married) 
(11) Sister and Married :< nothing 
Although (10) contradicts the TBox representa- 
tion (11) of (7), it is not possible to use BACK 
to establish this inconsistency (incoherence), since 
BACK does not allow the conjunction of roles in 
the ABox (cf. Hoppe et al. 1993, p. 5{)) which is 
of course needed in (10) (the conjunction of the 
roles Sister and Married). 
Example (10) is, of course, just beyond the bor- 
der of the permitted expressions, since it is in 
principle expressible but not allowed, and much 
more problematic (e.g. for 'donkey' sentences) is 
certainly the fact that variables are not explicitly 
available in these representation languages. But 
it should indicate the lack in expressive power at 
least inasmuch as it is possible without a more 
general formal proof (which we cannot give here 
for lack of space). Since the correct disambiguat- 
ing inferences cannot be performed anymore if the 
truth conditions of a discourse are boiled down in 
a way that allows to represent it (somehow) in 
such a restricted assertional language, approaches 
which model lexical disambiguation on the basis of 
these knowledge representation formalisms must 
fail. 
Since an extension of the expressive power of 
the assertional languages would lead immediately 
to our original tractability problem, we have to 
give up the implicit assumption that lexical dis- 
ambiguation presupposes the consistency of the 
discourse, if we don't want to give up lexical dis- 
ambiguation at all. Thus, we end up in the third 
class of approaches which provide us with fully ex- 
pressive languages to represent discourse and en- 
sure tractability by limited inferences. In order 
to see whether the requirements of soundness and 
completeness can be adequately weakend wehave 
to study the inferences involved in lexical disam- 
biguation more carefully. 
4 Towards Tractable Lexical 
Disambiguation 
To limit inference is a well-known strategy em- 
ployed for knowledge retrieval (e.g. Frisch and 
Allen 1982). By using incomplete theorem provers 
it is certainly possible to ensure tractability, but 
incompleteness is always a compromise which can 
7We assume Married to be a symmetric relation. 
982 
be a(:cet)ted as long as the prover computes the de- 
sired inferences completely (which is in fact hard 
to show). 
In contrast to knowledge retrieval where incom- 
pleteness is assumed for utility reasons, inference 
systems used for lexieal disambiguation have to be 
essentially incomplete. Otherwise we wouht get 
wrong results. In order to motivate our restric- 
tions we proceed in three steps. In the first step 
we show that we need an incomplete (but souIld) 
inli?rence mechanism for lcxical disambiguation, 
since a complete mechanisin leads to wrong re- 
sults. We st)ecify a class of inconsistency l)rooN 
which contains the disamt)iguating inferences as a 
subclass. In the second step, we separate out those 
prooN which are in fact disamt)iguating and illus- 
trate in the last step tidal the discourse structure 
imposes further restrictions on the accessibility of 
premises. 
4.1 The Incompleteness and Decidability 
of Lexieally Disambiguating 
Inference Mechanisms 
in order ~o develop our approach to lexical dis- 
ambiguation, we work successively through some. 
adequacy conditions which have to be. satisfied by 
an adequate procedure. According to the discus- 
sion in section 3 we have to assume a fully exl)res- 
sive language for the representation of discourse. 
Assuml)tion (I) is therefore as follows: 
(I) We have to assume a fully expressive lan- 
guage for the representation of texts. Se- 
mantic representations of natural language 
texts in this language do in general not sat- 
isfy conditions which make them de<-idable 
(see e.g. Rabin 1977 for standard condi- 
tions). 
To illustrate which kind of iimoinpleteness we 
need, we assume that the meaning postulates and 
the discourse can be e, xt)ressed in a first-order lan- 
guage without flmction symbols and identity. Al- 
though we think that one needs a more expressive 
language for an adequate representation of dis- 
course, and that very ofl;en nonmonotonic reason- 
ing is involved, the. first,-order case seems neverthe- 
less representative, since we have to (teal with the 
decidability problem. Moreover, we expect that 
dm methodology we used can be applied to more 
expressive discourse rel)resentadon hmguages in a 
similar way. 
For our conceptual knowledge on the other hand 
we make the much stronger assumption (1I). 
(H) Conceptual knowledge is represented by a fi- 
nite consistent and decidable set of meaning 
postulates MP that does not contain logi- 
<:ally valid subsets of formulas, s 
8Since this condition is certainly not satisfed by 
our world knowledge, its integration in the disam- 
biguation process would he a much harder prohlem. 
Decidability of MP, i.e. the decidability of MP ~- (/~ 
for a given formula (/~, results fi'oIn the fact that 
MP does not make any absolute existential claim 
on the entities in the world, especially on the, Jr 
cardinality. 9 
In order to be able to specify the incompleteness 
of our inference machinery in terms of a resolution 
logic, let us in the following assume that MP and 
the discourse is given in Skolem conjunctive form 
(SCF). I.e., as two uniw~'rsally quantified formulas 
whose matrices are in conjunctive normal form. 
Let us fllrthermore assume that we wouhl know 
that the given discourse is consistent (we abstract 
here first fi'orn the i)rohlem that this t)roperty is 
undecidable). We were then able to determine 
the m, satisfiahility of the discourse and MP by 
resolution. 
Let us take, for example, the set of clauses ob- 
tained fi'om the SCFs of the memfiilg postulate (7) 
aim the discourse (5) by the standard preparation 
pro<:edures. If we abbreviate Physician by P, Sis- 
ter by S and Married by M and use clause set no- 
tation (each conjunct of the matrix is represented 
as dm set of its disjunctively connected litenJs) 
tt~e unsatisfiability of (5) and (7) can be shown, 
since there is a resolution refiltation depicted as a 
refills<ion tree in (l 2). 
(12) {P(a)}{S(b, a)} {2kl(a, 1,)} {~S(V , a:),~M(:r, y)}.. 
,a)} 
\[\] 
The whole problem is now that despite of the de- 
(-idability of MP the lexical disamtfiguation prob- 
lem would still be undecidable if it wouhl pre- 
SUl)pose a consistent discourse. Decidability of 
the lexical disamhiguation problem results nev- 
ertheless from the fact that lexical disambigua- 
don does not involve a complete understanding of 
the discom'se. In order to illustrate that, let us 
'aBy checking several examples we found out that 
this t)rot)erty can I)e characterized model-theoretically 
as follows. There is a finite set of (up to isomorphism 
unique) tinite models {M1, ..,Mu} of MP such that 
each other finite model M~ of MP can successively be 
reduced to a model M G \[Mk\] by a chain of models 
M = M E -< M~ -< .. ~ M~. ~ of MP such that for each pair of models /VI~ = (lal',%:i), M~ +1 = (L/i+1,53 :I+1} 
dmre is a (partial) isomorphism f from l, ti+l\bli in 
la # such that ,9~(R) is the set of tuples (at,.., a,,~) 
with (bl, .., b,,~) 6 c3:{+1 (R), and al = bl if bt C b¢ i, and 
at = f(bt) if bt G U~+~\U ~, for every relation symbol 
R. Since the infinite models of MP correspond to 
unions of infinite chains of such models (i.e. MP is a 
rather restricted W-theory), we can reduce the test of 
M~. p q~ tbr each model M~. of Me to a test of Mk ~ (b. 
Thus, we can decide MP L- ~/) by checking M \[=- q5 for 
all models M E {M1, .., Mn}. But note that this does 
not allow us to test whether q5 is valid or not. 
983 
consider the inconsistent lexically ambiguous sen- 
tences (13a,c) whose Sister" readings are expressed 
in English by (13b,d). 
(13) (a) Es gibt keine Sehwestern, aber einige Arzte 
haben eine, mit der sic nieht verheiratet 
sind. 
(b) There are no sisters at all, but some physi- 
cians have one to whom they are not mar- 
ried. 
(c) Es gibt keine Schwestern, aber einige Arzte 
haben eine, mitder sie verheiratet sind. 
(d) There are no sisters at all, but some physi- 
cians have one to whom they are married. 
Although it is possible to derive from the semantic 
representations of (13a,c) a contradiction, these 
proofs are by no means disambiguating inferences, 
since the meaning postulates are not involved. In 
order to be able to explain by inconsistency proofs 
why the Sister reading is excluded for (13c) but 
not for (13a) one has to assume an incomplete in- 
ference system} ° Otherwise the system would not 
work correctly and would, of course, not necessar- 
ily terminate. Thus, our third assumption is: 
(III) Lexical disambiguation is very often possible 
although the discourse is inconsistent or its 
consistency is not known. 
What we are in fact looking for is a procedure 
which tests whether there is a consistent set of 
information pieces of the discourse which contra- 
dicts MP. In order to isolate tile consistent in- 
formation pieces provided by a (possibly inconsis- 
tent) discourse we use a discourse representation 
(and meaning postulates) in clause form. Since 
each single clause of such a representation must 
be satisfiable, we can identify the set of consistent 
information pieces provided by a discourse with 
the set of clauses of the discourse in SCF. On the 
basis of this set we can then test whether there is a 
consistent subset of these pieces which contradicts 
MP. Take as an example the clause representation 
of (13a) and our meaning postulate (7) depicted 
in (14a,b). 
(14) (a) {-,S(u,v)} {P(a)} {S(b,a)} {~M(a,b)} 
(b) {~S(y,x),-~M(x,y)} .. 
That the Sister reading is not excluded for (laa) 
is then explicable by the fact that there is no 
consistent subset of clauses of (14a) which is in- 
consistent with MP. What is consistently said in 
the (inconsistent) discourse does not violate tile 
mFor the sake of simplicity we were confined to 
short and simple examples and could therefore not 
avoid stone artificiality. Moreover, an additional test 
based on the procedure sketched in footnote 6 would 
certainly exclude the Sister reading for (laa). But it 
is, of course, easy to construct more realistic examples 
where the inconsistency is much more hidden and does 
not affect the disambiguation. 
meaning postulates in this case. In order to test 
this kind of incompatibility we have to demand 
that each resolution deduction starts with a clause 
from MP. This restriction prevents the attempt to 
prove the inconsistency of the discourse alone (at 
least if MP does not contain logically valid sub- 
sets of formulas that we assume and are able to 
decide). It prevents us Dora proving the unsatis- 
fiability of (14a,b), but we can still show the in- 
consistency of the clause representation of (13c) 
and (14tl) as in (12). 
4.2 Disambiguating Inferences 
The restriction introduced above is by no means 
sufficient, since the proof procedure is not yet sen- 
sitive to the predicates representing the readings 
of an ambiguous lexical item. In order to illus- 
trate this insufficiency let us consider the English 
translation of tile Sister" reading of (4), repeated 
in (15). 
(15) Some physicians have a sister to whom they are 
married. 
If we also assume (7) for English then a contradic- 
tion would result although we did not regard 'sis- 
ter' as ambiguous (at least in our oversimplified 
language domain), ttence, if (15) were embedded 
in a larger discourse we would have no chance to 
disambiguate other ambiguous lexical items, since 
we would get a contradiction for every reading of 
these items. That disambiguation is nevertheless 
possible in many of those cases can be made ob- 
vious e.g. by continuing (15) as in (16). 
(16) Some physicians have a sister to whom they 
are mm'ried. Some of these sisters admire stars 
who got an Oscar. 
The disambiguation of the ambiguous item 'star' 
should make no problems, given we had the right; 
meaning postulates. Thus, we have to assume: 
(IV) Lexical disambiguation is very often possi- 
ble although the discourse contradicts our 
conceptual knowledge. 
In order to disambiguate properly we have t6 
consider only those consistent sets of information 
pieces which contain at least one occurrence of 
the predicate that represents one reading of t, he 
ambiguous lexical item. Therefore we have to de- 
mand in addition that each resolution deduction 
starts with a pair of clauses A E MP and B from 
the discourse representation where B contains an 
occurrence of the predicate representing one read- 
ing of the ambiguous lexical item. This prevents 
disambiguating inferences for cases where there is 
no choice with respect to the interpretation of tile 
discourse ('sister' has to be interpreted as Sister 
although there is a contradiction). 
4.3 Reflecting Discourse Structure 
For lexical disambiguation we assumed so far that 
the underlying inference machinery operates on 
984 
the set of consistent information pieces t)rovided 
by the discourse. This set was crucially dependent 
on what is said and not on what follows, since 
we were (especially in case of inconsistencies) not 
interested in the set of all logical consequences of 
a discourse. Hence, our procedure already reflects 
in a very weak sense the discourse structure, since 
we did not allow all conversions preserving logical 
equivalence, but only those needed to construct 
an SCF froln the discourse. 
By converting the whole discourse into SCF we 
made all consistent information pieces provided 
by the discourse accessible for lexical disambigua- 
tion. Whether we need this entire set or just 
a rather limited subset of pieces which can be 
made accessible by locally restricted conversions 
into SCF, is for a first-order discourse an empir- 
ical trot no formal problem. But if we consider 
discourse representations in more expressive lan- 
guages (e.g. the language of an intensional logic) 
it becomes cleat" that we have to make only those 
consistent pieces accessible which result froln tlrst- 
order consequences of the discourse representa- 
tion. Information in the scope of the intensional 
verb in (17a) whose Sister reading is expressed in 
English by (17b) is, for example, not accessible for 
lexical disambiguation.J 1 
(17) (a) Einige .Arzte versuchten ihre Schwestern zu 
heiraten. 
(b) Some physicians tried to marry their sis- 
ters. 
Since we cannot get an SCF of the first-order con- 
sequences of a (possibly inconsistent) discourse 
represented in a more expressive representation 
language, it is necessary to find exactly those logi- 
cal equivalence preserving conversions which allow 
us to convert the discourse representation in such 
a way that the adequate set of consistent infor- 
mation pieces can be made accessible for the dis- 
ambiguation by locally restricted conversions into 
SCF. But we must, of course, admit l;hat further 
study is needed in order to be able to determine 
these conversions. 
5 Conclusion 
Lexical disambiguation is a procedure which 
works according to the communicative convention 
to interpret the discourse as consistent as possible, 
if there is a choice. It allows us to decide for two 
alternative readings of the discourse which one is 
less contradictory to what is said consistently in 
the discourse and to our conceptual knowledge. 
As the analysis of the examples in this paper has 
shown, there is a striking similarity between lexi- 
cal disambiguation and anaphoric resohltion. Not 
nMore complex examples can be found e.g. in 
Kalnp 1992, Kamp and Rofldeutseher 1994a,b. 
a complete understanding of the discourse is re- 
quired, but only an incomplete one that is re- 
stricted to a set of accessible consistent informa- 
tion pieces. The only difference is that; lexical dis- 
ambiguation requires a little bit more understand- 
ing. 
Acknowledgments 
Thanks to Ede Zimmerinann an(l Hans Kamp for 
useflll discussions and to the anonymous reviewers 
for (;oinulel/ts. 
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