\documentclass{llncs}

\begin{document}

\title{Word Senses and Semantic Representations -- can we have both?\thanks
{This research has been partially supported by the Czech
Ministry of Education under the grant VS97028.}}


\author{Karel Pala}



\institute{
     Faculty of Informatics, Masaryk University Brno\\
     Botanick\'a 68a, 602\,00 Brno, Czech Republic\\[1mm]
     E-mail: \texttt{pala@fi.muni.cz}
}

\maketitle


\begin{abstract}
In the paper we offer one possible way how to bridge the gap existing
between the lexical and logical semantic analysis of natural language
expressions. We look for a link that would allow us to perform a
more adequate and integrated semantic analysis of natural language
expressions. The solution is to combine the descriptions of lexical
units as they are developed within the area of lexical semantics
e.g. WordNet) with logical analysis of sentence meanings worked out
within Transparent Intensional Logic framework.

The data structures based on both approaches may take the form of
richer dictionary entries that together would form a dictionary of
the new type -- a Lexico-Logical Dictionary (LLD).
\end{abstract}


\section{Introduction}

Present approaches to semantic analysis in NLP field typically follow
two directions which do not seem to be very well integrated.
The first direction can be briefly characterized as {\it lexicalist}
and it concentrates primarily on exploration of the word senses or
senses of selected word collocations (phrases). A good survey of
the techniques used in this direction (with regard to the word
disambiguation) can be found in \cite{IdeVeronis}.

The second direction may be labelled as {\it logical} and it
pays attention mostly to the techniques that enable us to
describe formally sentence meanings and build what is usually
characterized as {\it semantic representations} of the sentences.
Here various logical formalisms are employed, particularly, first
order logic (FOPL) is the most used one. A good example of this
approach can be found in \cite{Allen}. There have been earlier
attempts to explore word meanings within Montague Grammar framework
\cite{Dowty} where attention has been paid to the issues how
word meanings as they are treated within generative semantics by
means of decomposition analysis can be integrated into Universal
Grammar. Dowty's approach is theoretically stimulating in several
ways, mainly it shows how the things can be done, however, if one
is looking for more applicable results that could be used in experimental
NLP systems he or she will not be probably satisfied. Though some
relevant theoretical problems are addressed in \cite{Dowty},
in a sense his analysis appears to be rather narrow because he pays attention
only to English, which due to its poor morphology does not allow
to see some of the phenomena in the full extent. Take, e.g.\,verbal aspect
-- it is not a grammatical category in English (as it is the case in
Czech or Russian), or the derivational morphology and lexical rules
as discussed by Dowty certainly cannot be regarded general enough.
Also the version of the componential analysis dealt with by Dowty (and
by generative semanticists) is interesting only from the theoretical
point of view and according to our knowledge it has not been immediately
used in building any existing dictionary. Further, it will become
obvious that among logical approaches we rather prefer not Universal
Grammar but TIL formalism (see below) which, in our opinion is suited
better for the task.

\section{Lexicalist View -- Word Senses}

In this area the attention is essentially concentrated on obtaining
plausible descriptions of the word senses or the senses of word
collocations. Standardly, they are studied within the field of lexical
semantics (lexicology) and the result of this effort is the information
about senses of the individual lexical units as it can be found in various
dictionaries. The descriptions of the word senses may take different
form depending on the type and purpose of a dictionary -- starting
from the classical dictionaries using definitions based on genus
proximum and distinguishers, and ending e.g. with the machine lexical
databases like WordNet where the sense descriptions are based on
the synsets, Top Ontology (yielding a selected set of semantic labels
(features)) plus hypero/hyponymy hierarchy.

In the following we will refer to WordNet like dictionaries
since they can be regarded as good representants of the description
that employs extensively the semantic relations between words. As
the developers of Czech Wordnet, which has been built within
EuroWordNet-2 project (\cite{Pala�eve�ek2}) we also have
the positive experience with them.

Thus within EuroWordNet-1,2 framework (\cite{Vossen}) each
lexical unit is treated as a {\it synset} corresponding to the
respective word sense. Therefore, it can be seen that each lexical
unit due to its position in the respective hypero/hyponymical tree
and the links given by it can be associated with a set of semantic
features that can be regarded as a characterization (or description)
of its sense. These data now can be obtained automatically by the
Polaris database tool developed within EuroWordNet-1,2. Moreover,
in this framework it is now possible to exploit what is called
{\it Internal Language Relations (ILR)} which link together lexical
units according to the semantic relations having the nature of the
semantic cases (agent, patient, instrument, etc.).

  The presented approach deals preferrably with the word senses
or senses of collocations but as far as we know, in this approach
there is no complete way how to build representations of sentence
meanings or, in other words, their {\it semantic representations
(SR)}. Thus, the issues of reference are not adressed here.

\section{Logical View -- Sentence Meanings}
Logical analysis of the sentence meanings as in \cite{Materna}
or \cite{Dowty} offers techniques for building SR of the sentences.
Typically, this can be done by means of a selected logical formalism
such as first order logic (FOPL, \cite{Allen}) or one of the intensional
logic calculi -- we will prefer here {\it Transparent Intensional Logic (TIL)} by
\cite{Tich�} and \cite{Materna} since it does not suffer
from the shortcomings typical of FOPL. In these formalisms the individual
semantic representations may take form of logical formulae as we
know them from FOPL or from Lambda Calculus if Transparent Intensional
Logic is chosen.

  These formulae follow the compositional principle and they
yield a description of sentence meaning (its reference) in the terms
of the entities like extensions (in FOP) or extensions and intensions
(TIL). This means that sentence like\\
(1) {\it John loves his computer}. \\
can be represented as \\
(1a) $\lambda w \lambda t$ ({\bf lov}$_{wt}$ ({\bf J},
     ({\bf comp}$_{wt}$))).\\
Thus, in TIL we get a formula which represents a proposition stating
that there is a relation-in-intension between two individuals. It
should be added that TIL exploits the ramified theory of types,
therefore its expressive power in comparison with FOPL appears to
fulfill better the requirements that arise in realistic NLP systems.

In our NLP Laboratory we work on {\it Normal Translation Algorithm}
that takes (Czech) input sentences and as its output produces their
semantic representations in the form of Lambda formulae and their
corresponding semantic trees \cite{Hadacz}.

However, in this kind of analysis which is necessary for building
reasonable knowledge representations and making inferences from
them there is something missing as well. It is obvious that we lack
here the idiosyncratic lexical information that can be associated
with word senses occurring in the sentence like (1) and that is
certainly used in semantic analysis of (1) when it is performed by
humans. Thus we know that the expression {\it his computer} in
(1) denotes an individual object (having logical type {\tt iota}, which is
the type of individual) but there is no way how to associate this
information with the fact that typically a computer {\it is a machine
able to process information}. This kind of fact can be obtained from the
respective knowledge representation, however, as we have tried to show above,
at present it can be automatically retrieved from a lexical
database of the WordNet type: thus we are led to a reasonable
conclusion: it makes sense to attempt to combine the two mentioned
ways of semantic analysis and try to integrate them.

\section{The Link -- Lexico-Logical Dictionary (LLD)}
A possible solution that would allow us to intertwine both the lexical
and logical analysis of NL expressions is, in our opinion, to build
a data structure that can be implemented as a dictionary of the new
type. It can comprise in its entries both the lexical information
about lexical units (e.g. as they are now in WordNet) and the information
about the logical types that can be associated with natural language
expressions. It can be shown \cite{Podlezlov�} that if we
treat verbs as logical predicates we can assign the respective
logical types to them (mostly intensions). For example, in TIL framework
many werbs denote relation-in-intension between two individuals:
thus the verb {\it to love} from (1) above can be associated with
the following logical type: \\
(1b) $(o\iota\iota)_{\tau\omega}$. \\
The verbs denoting properties of individuals (typically intransitives),
e.g.\,{\it to read} as in \\
(2) {\it Our son reads well}.\\
can be associated with the following logical type:\\
(2a) $(o\iota)_{\tau\omega}$. \\
To give another example, take the verbs denoting propositional
attitudes such as {\it believe, know, think}. They can be associated
with the logical type \\
(3) $o(\iota, o_{\tau\omega})_{\tau\omega}$. \\
% $o(\iota, *_n)_{\tau\omega} (*_n)$ - class of constructions of order n \\
Our preliminary analysis also shows that some regular relations
can be found between semantic classes of verbs (\cite{Levin})
and the corresponding logical types, for example, the verbs denoting
relation-in-intension between two individuals will certainly constitute
well defined classes (transitives) whereas the verbs expressing
property of an individual will clearly constitute another collection
of typical verb classes (intransitives). The idea then is to explore
the semantic classes of (Czech) verbs and try to find the correspondencies
between them and the logical types as they are defined within TIL.

In this respect we also have to pay an attention to the valency
frames which at the first place have to be distributed according
to the individual verb senses they belong to and only then the relations
to the corresponding logical types can be looked for. The problem,
however, is where to find the relations between the valency frames and
word senses of the respective verbs (at least for Czech). One may
hope that the explicit information of this sort might perhaps be
found in some (really good) dictionaries but unfortunately this is
not the case with the Czech ones. Thus we face the task of building
data structures for verbal lexical units that would contain the valency
frames distributed according to their respective word senses, e.g. in
the following form for the four senses of Czech verb {\it sp�t (sleep)}:\\
{\bf sp�t:1} i. {\sf setrv�vat ve sp�nku (be in sleep)}\\
valency frame: {\sf jak} {\sf (Adverb of Manner)}: {\it dob�e, tvrd� (well, hard})\\
WordNet semantic features: {\sc be asleep, rest} \\
logical type:  $(o\iota)_{\tau\omega}$ (property of individuals). \\
{\bf sp�t:2} i. {\sf nocovat, tr�vit noc (stay overnight)} \\
valency frame: {\sf kde, v �em (Place, prep.\,Locative)}: {\it v hotelu (in the hotel)} \\
WordNet semantic features: {\sc lodge + reside + occupy a position} \\
logical type: $(o\iota\iota)_{\tau\omega}$ (relation-in-intension
               between individuals)\\
{\bf sp�t:3} i. {\sf soulo�it s k�m (make love with)} \\
valency frame: {\sf s k�m (prep.\,Instrumental)} \\
WordNet semantic features: {\sc copulate + make contact + connect together} \\
logical type: $(o\iota\iota)_{\tau\omega}$ (relation-in-intension
               between individuals)\\
{\bf sp�t:4} {\sf b�t po smrti (be dead)} \\
valency frame: {\sf kde, jak (Place, Adverb of Manner, prep.\,Locative)}: {\it v hrob�, ti�e (in
the grave, quietly}\\
WordNet semantic features: {\sc be in a state + be at rest + be dead} \\
logical type:  $(o\iota)_{\tau\omega}$ (property of individuals). \\

\noindent
The work on building this kind of data structures has already started
and the first examples can be found both in Czech WordNet and other
Czech lexical resources that are being prepared in NLP Laboratory
at Faculty of Informatics, Masaryk University.
The starting list of Czech verbs with their valency frames contains
now about 15 000 items (\cite{Pala�eve�ek1}) but they are related to
the respective senses yet.

Analogous interesting relations seem to hold between the senses
of nouns, their valency frames and the logical types
and their semantic features as yielded by their positions in the
hypero/hyponymical trees in WordNet. As it can be seen from the
examples of the verb entries presented above the noun (as well as adjective and
adverb) entries comprising both the respective lexical and logical
information can be built in a similar fashion. Take, e.g. an entry
for the lexical unit {\it hlava (head)}:\\
{\bf hlava:1}  {\sf ��st t�la (part of body)}\\
valency frame: {\sf �eho, (Genitive)}: {\it hlava �lov�ka (man's head})\\
WordNet semantic features: {\sc body part + part of a natural object + entity} \\
logical type:  $\iota$ (an individual) or $(o\iota_{\tau\omega}$. \\
{\bf hlava:2}  {\sf rozum, mysl, intelekt (nous, mind, intellect)} \\
valency frame: {\sf na co (prep.Accusative)}: {\it hlava na po��ta�e (a brain in
               computers)} \\
WordNet semantic features: {\sc cognition + knowledge + psychological feature} \\
logical type: $(o\iota)_{\tau\omega}$ (property of individuals). \\
{\bf hlava:3} {\sf vedouc�, ��f (chief, boss)} \\
valency frame: {\sf �eho (Genitive)}: {\it hlava odd�len� (head of
the section}\\
WordNet semantic features: {\sc individual + being + entity + causal agency}\\
logical type:  $(o\iota)_{\tau\omega}$ (property of individuals) or $\iota_{\tau\omega}$. \\
{\bf hlava:4} {\sf horn� ��st motoru (hub, head)} \\
valency frame: {\sf �eho (Genitive)}: {\it hlava kola (head of the wheel}\\
WordNet semantic features: {\sc part + phys.object + entity} \\
logical type:  $(o\iota)_{\tau\omega}$ (property of individuals). \\
{\bf hlava:5} {\sf kapitola (chapter)} \\
valency frame: {\sf �eho (Genitive), v �em (Locative)}: {\it hlava v Bibli
 (chapter in the Bible}\\
WordNet semantic features: {\sc section + writing + communication}  \\
logical type:  $(o\iota)_{\tau\omega}$ (property of individuals). \\
{\bf hlava:6} {\sf strana mince (coin side, heads)} \\
valency frame: {\sf na �em (Locative)}: {\it hlava na desetikorun�
              (heads on the ten crown coin}\\
WordNet semantic features: {\sc side + surface + artefact + phys.object + entity} \\
logical type:  $(o\iota)_{\tau\omega}$ (property of individuals). \\

Note that several logical types can be associated with a given noun but which
type will be selected depends on the local context in which the noun can
take placed. In our view, it would be necessary to work not only with
single nouns but the typical collocations like {\it head of the department}.

\section{Conclusions}
In the presented contribution we payed our attention to the gap
existing presently between the present approaches to the lexical
and logical semantic analysis of natural language expressions. We are
trying to find a link that would allow us to perform a more integrated
semantic analysis of NL expressions.

 In our opinion,
it is necessary to combine the descriptions of the lexical units
as they are developed within the area of lexical semantics with
the logical analysis of sentence meanings as worked out within TIL framework.
The data structures that are based on both approaches may take, as
we tried to show, the form of the richer dictionary entries that
together would form a dictionary of the new type -- a Lexico-Logical
Dictionary (LLD).

\begin{thebibliography}{99}
\bibitem{Allen}
  {\sf Allen, J.}, Natural Language Understanding, Benjamin/Cummins,
      Redwood City, CA, 1995.
\bibitem{Dowty}
  {\sf Dowty, D., R.}, Word Meaning and Montague Grammar, Kluwer,
      Dordrecht, Second edition, 1991, esp.\,p.27-36.
\bibitem{Hadacz}
  {\sf Hadacz, L.}, Semantic Inference in Human-Machine Communication,
      Proceedings of Text, Speech, Dialogue'99 Conference, Springer
      Verl., p.353-356, MarienBad 1999.
\bibitem{IdeVeronis}
  {\sf Ide, N., Veronis, J.}, Word Sense Disambiguation: The State
      of Art, Computational Linguistics, Vol.24, No.1, March 1998,
      p.1-40.
\bibitem{Levin}
{\sf Levin, B.}, English Verb Classes and Alternations, The
      University of Chicago Press, 1993.
\bibitem{Materna}
  {\sf Materna, P.}, Concepts and Objects, Acta Philosophica Fennica,
      vol.63, Helsinki 1998.
\bibitem{Pala}
  {\sf Pala, K.}, O s�mantick�ch reprezentac�ch (On Semantic
      Representations), SP FFBU (Proceedings of Faculty of Arts,
      Brno University), A 32, p.24-35, Brno 1984.
\bibitem{PalaRychl�Smr�}
  {\sf Pala, K., Rychl�, P., Smr�, P.}, DESAM -- An Annotated Corpus
      for Czech, Proceedings of SOFSEM'98, Springer, 1998.
\bibitem{Pala�eve�ek1}
 {\sf Pala, K., �eve�ek, P.}, Valence �esk�ch sloves (Valency
      Frames of Czech Verbs), SP FFBU (Proceedings of Faculty of
      Arts, Masaryk University), A 45, p.41-54, Brno 1997.
\bibitem{Pala�eve�ek2}
 {\sf Pala, K., �eve�ek, P.}, �esk� lexik�ln� datab�ze typu WordNet
      (Czech Lexical Database of WordNet Type), SP FFBU (Proceedings
      of Faculty of Arts, Masaryk University), A 47, p.51-64, Brno 1999.
\bibitem{Podlezlov�}
  {\sf Podlezlov�-Ko�elouhov�, B.}, S�manticky orientovan� generativn�
      �esk�ch sloves nep�echodn�ch (Semantically Oriented Generative
      Description of the Czech Intransitive Verbs), Diploma Thesis,
      Faculty of Arts, Masaryk University, Brno 1974.
\bibitem{Tich�} {\sf Tich�, P.}, The Foundations of Frege's Logic, De Gruyter,
      1988.
\bibitem{Vossen} {\sf Vossen, P., et al.}, Set of Common Base Concepts in EuroWordNet-2,
      Final Report, 2D001, Amsterdam, October 1998.
 \end{thebibliography}

\end{document}



