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\title{Representing Lexical Polysemy}
\author{Ann Copestake\\ Stanford University, University of
Cambridge and University of Stuttgart\thanks{The research reported in this paper was
partially funded by the ESPRIT project ACQUILEX II  
grant to Cambridge University.  
Much of it was done in collaboration with Ted Briscoe and
Alex Lascarides, but they are not responsible for the mistakes in this
paper.}\\ {\tt aac@csli.stanford.edu}}
\begin{document}
\setlength{\unitlength}{1mm}
\maketitle

\begin{abstract}
This paper gives an overview of work on a
computational approach to representing 
lexically governed polysemy.  The
framework is illustrated with an account of the interpretation of compound
nouns and with some examples of extended usages of words. 
I discuss how generative devices can be controlled to avoid an
explosion in interpretations and in the number of lexical entries.
\end{abstract}

\section{Introduction}

This work arose out of an attempt to build large lexical knowledge
bases (LKBs), during which it became apparent that existing
computational and formal approaches were inadequate with respect to the
representation of polysemy.  In particular, it is not possible to build
a satisfactory LKB based on word sense distinctions given in a
conventional dictionary, because this will not reflect the relationship
between word senses nor will it be compatible with an LKB constructed
on the basis of a different dictionary's sense distinctions.  Furthermore an
LKB must incorporate generative devices in order to cover naturally
occurring data, since it is not possible to list
all potential usages.
The current paper is based on the framework described in
Copestake and Briscoe (in press).  That paper (henceforth C+B) should be
consulted for an overview of the literature and for many of the details
of our own approach.
Here I will briefly summarise the
more important points 
and give more details about the use of probabilities to encode
semi-productivity.  I will also show that the 
representation techniques we
introduced there can be applied to the
interpretation of compound nouns.
Lascarides (this volume) gives a formal
description of the interface with pragmatics
which was assumed in C+B but not worked out there.

I am only concerned with (semi-)regular polysemy,
not homonymy (e.g.~{\it bank}\/:financial institution vs {\it bank}\/:mound
of earth) or irregular/unpredictable polysemy 
(e.g.~{\it bank}\/:tilt of plane vs {\it bank}\/:mound of earth).
I will make a distinction between {\it constructional polysemy} and
{\it sense extension}.  The former includes, for
example, logical metonymy (Pustejovsky, 1991),
while the latter term covers cases like 
{\it rabbit} meaning the animal or its meat or fur, and {\it violin}
meaning the instrument or the musician.  This distinction
will be further motivated below.

I will also make a distinction between {\it nonce}, {\it
institutionalised} and {\it lexicalised} terms, which more or less
corresponds to the terminology in Bauer (1983).  As there, I will use
{\it established} to cover both institutionalised and lexicalised.
In terms of
the computational lexicon, these terms have a precise
definition: nonce words and usages are not recorded in the lexicon at all,
but (for the cases we are interested in) can be produced/interpreted by
generative devices.  Institutionalised senses are recorded in the 
lexicon, but all that needs to be stipulated about them is the
regular process by which they were formed (e.g.~that {\it retie} is a
particular sense of {\it tie} with the prefix {\it re}).
Finally, lexicalised senses will either be unrelated to
other senses, or will have an entry in which some regularly derived
information is either augmented or overridden. 

The approach to lexical representation which I am assuming involves the
use of typed default feature structures.  Typed feature structures
should be familiar from work within HPSG.  The addition of defaults is less
well understood but here I am assuming the variant of order independent default
unification (Lascarides et al, in press) described by Lascarides and
Copestake (1995).  Luckily the technicalities of the definition will
not be important, the main point is that we assume that
defaults are not just confined to the lexicon, but have a role during
syntagmatic processing, and in the interaction with pragmatics.  This is
discussed in detail by Lascarides (this volume): here I want to give an
description of the lexical aspects of
representation of polysemy using this framework.

\section{Constructional polysemy}

In C+B we used the term constructional
polysemy to cover cases of polysemy where a
single sense assigned to a lexical entry is contextually specialised.
This can be represented using
(default) inheritance.  For example, {\it reel} was taken
to have a basic underspecified representation, which stated that it was
a container artifact with the purpose of (un)winding, where
the material wound is left largely unspecified.  
In a use such as {\it cotton reel}, the object of the
(un)winding is specialised.  We represent this using 
Pustejovsky's theory of lexical semantics (e.g.~Pustejovsky 1991).
Under this account, the representation of
nouns includes a specification of their {\em qualia structure}, which
encodes the form, constituency, agentive and telic (purpose) roles.  Thus
the telic role of the basic sense of {\it reel} would be only partially
instantiated, but could become further instantiated contextually.
However, 
physical differences between types of reel are treated as
outside the domain of lexical semantics.

Our use of default inheritance allows us to extend this
style of representation to examples such as {\it cloud}, which is
treated as having a basic sense with a specified formal role, but a
default constitutive role (water vapour).  In phrases such as {\it
cloud of mosquitos}, the default is overridden.
Some further examples of constructional polysemy are discussed by C+B
and Lascarides (this volume),
including adjectival interpretation ({\it fast car} versus {\it fast
typist}, 
Pustejovsky and Boguraev, 1993) and logical metonymy (Pustejovsky, 1991).
What all these cases have in common is that conventional monotonic
accounts 
can only assign a very underspecified representation, which is
assumed to be instantiated by pragmatics.
Clearly, without an account of the pragmatic component and the
interface between it and syntax/semantics, theories which make this
claim are difficult to falsify, and few formal accounts have been
attempted (although see Hobbs et al (e.g.~1990)).  
But for all these examples, a pragmatic
explanation runs into difficulties under standard assumptions about
the limitations on the type of information the pragmatic component has
access to.  This is discussed in the references above.  The alternative
approach is to assume a relatively rich lexical semantic
representation, such as qualia structure,
but this has to be done in a representational
framework which allows defaults, in order to allow pragmatics to
override the lexically instantiated defaults. 
Lascarides (this volume) explains how the lexical / pragmatic interface
may be formalised --- since she also gives the more salient details of the
C+B accounts of
logical metonymy and adjectival interpretation, 
I will not repeat them here.  

\section{Sense extension}

In previous papers we have argued for an approach to examples such as
those in \exnum{+1}{} which treats them as extensions from a base
sense.
\begin{ex}
\begin{subex}
He bought two beers.\\
comestible substance {\tt ->} conventional portion (portioning)
\end{subex}
\begin{subex}
He drank a bottle of whisky. \\
container {\tt ->} contents 
\end{subex}
\end{ex}
Sense extensions may have syntactic/grammatical effects: e.g.~portioning
\exnum{0}{a} converts mass to count.
Some sense extensions are
comparable in semantic effect to morphological processes.  The 
`container {\tt ->} contents' example in \exnum{0}{b} is paralleled by
suffixation with {\it -ful}.  The same polysemy patterns are often found
cross-linguistically, but may be accompanied by morphological effects
in one language that are not mirrored in the other.  For example, in
English the same word is often used for a plant and for its fruit
(e.g.~{\it olive}), but in Spanish there is a gender
distinction (e.g.~{\it aceituna/aceituno}).  
Sense extensions often seem to fall into families, as in the examples
in \exnum{+1}{}, where meat-grinding and fur/skin grinding can be
regarded as conventionalised special cases of grinding.
\begin{ex}
\begin{subex}
Sandy likes to eat rabbit.\\ 
animal {\tt ->} meat (meat-grinding)
\end{subex}
\begin{subex}
Sandy likes to wear rabbit.\\ 
animal {\tt ->} fur/skin (fur/skin grinding)
\end{subex}
\begin{subex}
That stuff on the tarmac looks like rabbit.\\
physical object {\tt ->} substance (grinding)
\end{subex}
\end{ex}
However languages differ in
what sense extensions are possible: for example, Nunberg and Zaenen
(1992) report that Eskimo has no conventionalised meat-grinding.
Finally, some extended senses are established while others are not, as
illustrated in \exnum{+1}{}:
\begin{ex}
\begin{subex} 
That restaurant serves ostrich.\\
animal {\tt ->} meat
\end{subex}
\begin{subex}
The ham sandwiches has paid his check.\\
physical object {\tt ->} associated person
\end{subex}
\begin{subex}
\mbox{}[Chester] serves not just country folk, but farming, suburban and city
folk too.  You'll see Armani drifting into the Grosvenor Hotel's exclusive
(but exquisite) Arkle Restaurant and C+A giggling out of its streetfront
brasserie next door. (Guardian Weekly)\\
manufacturer {\tt ->} product +\\ clothes {\tt ->} wearer
\end{subex}
\end{ex}

The essential points of our analysis are that sense extensions are
treated by lexical rules which are similar in all respects 
to rules
which encode derivational morphology
except for the change in orthography/phonology.\footnote{The term lexical rule
has come to seem something of a misnomer, but this is
rather of peripheral interest here.  I will also ignore the issues which
arise when formalising lexical rules in a constraint based
framework: for current purposes we can treat lexical rules as being similar to
non-branching phrase structure rules or schemata
(cf Riehemann's (1993) treatment of derivational morphology within HPSG).}
Sense extension rules can inherit from one another.  For example, 
the meat-grinding and fur/skin grinding rules illustrated above 
can be regarded as subtypes of the more general grinding rule.  
Because we use a
fine-grained lexical semantic representation, we can be quite specific
about the class of lexical items to which a rule is intended to apply.
We sketch the grinding and meat-grinding rules in
Figure~\ref{grinding} (see C+B for a full description). 
Note that the semantic effect of grinding is
captured by an operator which applies to the predicate, while the
specialisation of the meaning in meat-grinding is indicated in the
qualia structure.
\begin{figure}
{\centering
\tiny
{\normalsize {\bf grinding} $<$ {\bf lexical-rule}} \hfill \mbox{}\\
$\avmplus{\att{lex-count-noun}\\
                  \attval{ORTH}{\ind{0}}\\
                  \attvaltyp{SYN}{noun-cat}\\
                  \attval{SEM PRED}{\ind{3}}\\
                  \attvaltyp{QUALIA}{physical}}
\mbox{\normalsize $\rightarrow$}
\avmplus{\att{lex-uncount-noun}\\
                  \attval{ORTH}{\ind{0}}\\
                  \attvaltyp{SYN}{noun-cat}\\
                  \attvaltyp{SEM PRED}{grinding$'(\ind{3})$}\\
                  \attvaltyp{QUALIA}{physical}}
$\\[0.1in]
{\normalsize {\bf meat-grinding} $<$ {\bf grinding}} \hfill \mbox{}\\
$
\avmplus{\attvaltyp{QUALIA}{animal}}
\mbox{\normalsize $\rightarrow$}
\avmplus{\attvaltyp{QUALIA}{edible\_substance}}       
$

}
\caption{Grinding and meat-grinding}
\label{grinding} 
\end{figure}

The motivation for making the
distinction between constructional polysemy and sense extension 
is discussed extensively in C+B
and we will not repeat it here, but there are several reasons why simple
inheritance is not adequate for lexical rule representation.  
Rules can feed each other: \exnum{0}{c} appears to be a case of this, and
in 
a context such as \exnum{+1}{c}, below {\it three
rabbits} could mean three portions of rabbit meat.  
Furthermore in order
to describe the semantic effect of lexical rules it seems
necessary to postulate operators such as {\bf grinding}$'$, which
cannot be satisfactorily represented using simple inheritance, because
there is no (substantive) common core meaning to the senses which can
be specialised.
Simple inheritance is
known to be inadequate for derivational morphology, for similar
reasons, and since we would like to use the same mechanism for both
derivation and sense extension
this further argues for the use of lexical rules.

\subsection{Semi-productivity}

Lexical rules must be able to generate nonce senses to deal with
examples such as those in \exnum{0}{}.  But,
at least from a computational perspective, this leads to a considerable
problem since
lexical polysemy then becomes intractable.  It is not even clear
whether the lexicon can be regarded as finite, 
since sense extension rules can feed one another (again this is also an
issue in derivational morphology).  We described an approach to 
restricting productivity in
C+B which I want to elaborate on here.  We argued 
that in the absence of
other factors, language users utilise
frequency information to resolve indeterminacies in both generation
and interpretation. Such a strategy is compatible with and may
underlie the Gricean Maxim of Manner, in that language
will be more easily interpretable if there is a tacit agreement not to
utilise abnormal or rare means of conveying particular messages.  We
can model this aspect of language use as a conditional probability
that a word form will be used in a specific sense:
Prob(lexical-entry $\mid$ word-form).  
We assume
that probabilities are associated with all established forms,
regardless of whether they can be treated as derived from other senses,
and we make no claim that a derived sense will
necessarily be less frequent than a basic one; 
for example for {\it turkey} our intuition is that the meat 
sense is more frequent than the basic animal sense.

For example, a word form such as {\it rabbit} can be associated with
an entry like that illustrated in Figure~\ref{rabbit}, in which
meat grinding is shown to be (hypothetically) more probable than
grinding, meat grinding followed by portioning, or fur/skin
grinding. 
\begin{figure*}
{\centering
\tiny
$\avmplus{\att{lexeme}\\
          \attval{BASE}{\avmplus{
                        \attval{SIGN}{\avmplus{\att{lex-count-noun}\\
                                               \attvaltyp{ORTH}{rabbit}\\
                                               \attvaltyp{CAT}{noun-cat}\\
                                         \attvaltyp{SEM}{obj-noun-formula}}}\\
                        \attvaltyp{PROB}{0.4}}}\\
         \attval{LRS}{\left\langle
                       {\avmplus{\attvaltyp{RULE}{grinding}\\
                                 \attvaltyp{PROB}{0.05}}},
                        {\avmplus{\attvaltyp{RULE}{meat-grinding}\\
                                 \attvaltyp{PROB}{0.3}}},
                        {\avmplus{\attvaltyp{RULE}{meat-grdg+portioning}\\
                                 \attvaltyp{PROB}{0.15}}},
                        {\avmplus{\attvaltyp{RULE}{fur/skin-grdg}\\
                                 \attvaltyp{PROB}{0.1}}}\right\rangle}}$

}
\caption{Lexeme for {\it rabbit}}
\label{rabbit}
\end{figure*}
The attribute {\sc lrs} associated with the lexeme for {\it rabbit}
records which combinations of lexical rules have been attested with what
frequency in the experience of the language user.
If we assume that speakers choose well-attested
high-frequency forms to realise particular senses and listeners choose
well-attested high-frequency senses when faced with ambiguity, then
much of the `semi-productivity' of lexical rules is predicted. 
For instance, we would predict that in the
`null' or a neutral context\footnote{Following Lascarides (this volume) 
we can give a formal definition of what we mean by neutral context ---
it corresponds to a situation where there are no applicable pragmatic
rules which affect the interpretation of the lexical item under
consideration other than those licensed by the sentence itself.} 
\exnum{+1}{a} will be interpreted as
rabbit meat, and \exnum{+1}{b} will be interpreted as animals.
Less frequent but attested senses could be chosen
when dictated by the context, as in
\exnum{+1}{c}.
\begin{ex}
\begin{subex}
John prefers rabbit.
\end{subex}
\begin{subex}
John wants three rabbits.
\end{subex}
\begin{subex}
The diners ordered three rabbits.
\end{subex}
\end{ex}
 
Probability also plays a role in the application of lexical rules in
novel usage. 
Under the current proposal, lexical rules are somewhat
like `redundancy' rules in that they can be
used to construct appropriate signs for institutionalised
senses of a word form, which will have a non-zero
probability in the lexeme entry. However, in the situation
where an interpretation for a novel usage is called for, an assessment
of the relative probability of possible lexical rules would provide a
means for adopting the most likely `analogous' interpretation. For
instance, interpreting an examples such as \exnum{+1}{}, the listener who
had not experienced examples of any variant of the
grinding rule with 
{\it guinea pig} would choose the rule with the highest probability given the
semantic type of the noun.
\begin{ex}
John prefers guinea pig
\end{ex}
The probability of a lexical rule can be derived by comparing the
number of lexemes to which the rule could apply 
where that sense is unattested, to those for which it is
attested.  The following formulation is due to Ted Briscoe:
\[\mbox{Prob(lexical-rule)} \approx
\frac{\sum_{N} Prob(le_{0}|wf_{0})}{N} \]
(where $N$ = number of lexical entries which match the lexical rule
input and $le_{0}$ and $wf_{0}$ denote the output lexical-entry and
output word-form, respectively).

We regard our use of probabilities as being consistent with Bauer's
claim that accounting for
semi-productivity is an issue of performance, not competence
(Bauer 1983:71f).  The effect of the use of probabilities is that
unattested senses will never be assumed unless no attested sense is
possible, thus allowing interpretation of examples such as
those in \exnum{-2}{}, while
avoiding overgeneration.  This improves on the control principle 
suggested in Copestake (1992), that lexical rules should only be
applied if no interpretation was applicable which did not involve a
lexical rule, since it allows for cases such as {\it turkey} without
further stipulation.
The two other control effects 
suggested in Copestake (1992) are both also superseded by the current
proposal.
One of these was to allow for blocking, which is
discussed below.  The other 
was that more specific lexical rules should
be preferred over more general ones, e.g.~that meat-grinding should
be preferred over the general grinding rule.  We would expect that 
the probabilities derived by the formula above would 
make meat-grinding more probable than generic grinding, but the
earlier proposal would have had the undesirable consequence that a
specific sense extension rule would always be 
applied in preference to a more general one, even if it was 
attested in a much smaller number of cases.  

\subsection{Blocking}

We
are mainly interested in cases where a normally productive process does
not apply to a lexeme because of the existence of a synonym.  
This is sometimes known as {\it preemption by synonymy} and is
exemplified by \exnum{+1}{}.
\begin{ex}
\begin{subex}
?Sam ate pig (pork)
\end{subex}
\begin{subex}
?Sam likes cow (beef)
\end{subex}
\begin{subex}
There were five thousand extremely loud people on the floor eager to
tear into roast cow with both hands and wash it down with bourbon
whiskey.\\(Tom Wolfe, 1979. {\it The Right Stuff})
\end{subex}
\end{ex}
As illustrated by \exnum{0}{c}, and discussed in detail in C+B and
Briscoe et al (in press), blocked forms do sometimes occur, but
their use is highly marked and carries extra implications compared to the
unblocked form.  In \exnum{0}{c}, the use of {\it cow} rather than {\it
beef} has distinctly
negative connotations.

Preemption by synonymy could
be explained simply by assuming that speakers will use higher
frequency forms to convey a given meaning.  Thus an extended meaning
will not become conventionalised if a common synonym exists.
This means that we do not have to stipulate a separate blocking
principle in interpretation, since the blocked senses will not be
attested or will have a very low frequency.  Blocked forms can be
interpreted however, when forced by context.
And in generation,
we assume that higher probability forms are preferred as a way of
conveying a given meaning.  
However, this is not the complete story, since we have not accounted
formally for the extra implicatures that the use of a blocked form conveys, nor
have we allowed for the generation of blocked forms (apart from in the
circumstances where the generator's lexicon omits the synonym).
Both these problems require an account of the interface with
pragmatics, though the latter is perhaps not serious for computational
applications, since we are unlikely to want to generate blocked
forms.  However, I will leave this open here, since it is not
primarily a lexical issue.


\section{Compound nouns}
\label{compounds}

The approach to compound noun interpretation proposed here draws
on representation techniques we have used in other cases of
constructional polysemy, but combines them with some of the machinery
of the previous section, to allow for the establishment of compounds.
It is well known that although many noun-noun compounds seem to fall
into a limited number of classes (e.g.~Levi, 1978), there are cases
which can only be interpreted in context.  Downing 
attests \exnum{+1}{} in a context where there was
a table already set with a glass of orange juice
by three places and apple juice by the fourth:
\begin{ex}
Please sit in the apple juice chair.
\end{ex}
Here {\it apple juice chair} has a meaning which can be glossed as
`chair in front of a place setting with apple juice', but obviously
this meaning cannot be listed in the lexicon.
Even if a compound has
an established interpretation, in context there may be another possibility.
In \exnum{+1}{}, taken from Bauer (1983:86), 
{\it garbage man} can be taken to mean `a man made out of
garbage' by analogy with snowman:
\begin{quote}
In the back street where I grew up, everybody was poor.  We were so
poor that we never went on holiday.  Our only toys were the garbage
cans.  We never built sandcastles, only garbage men.
\end{quote}
This has led to the suggestion that noun-noun compounds should be
assigned a representation where the relationship between the 
two halves of the compound is left completely unspecified and
further interpretation should
be left to the pragmatic component
(e.g.~Bauer, 1983; Hobbs et al, 1990).
There are however serious objections to
this application of the pragmatic dustbin.  Without further elaboration
it gives no explanation of the observed classes, and the fact that the
majority of compound nouns do behave in a semi-regular manner.
Some compounds which should be possible on pragmatic
grounds do not occur: for example {*\it
blacksmith hammer}, {*\it dentist chair} and other such compounds
appear unacceptable with the interpretation that the instrument is 
normally used by the someone with that occupation.  The
possessive construction is used instead ({\it blacksmith's hammer}, {\it
dentist's chair}), although in German noun-noun compounds are possible
for equivalent examples.  
Thus there are some 
linguistic constraints on compound interpretation, which
have to be represented. 
 
Even with a pragmatic account,
some compounds, such as {\it garbage man}, must be
explicitly listed as established, because in the `null-context' the
established interpretation is the only possible one.  So either the
pragmatic component has to contain lexical information\footnote{Note
that it is unlikely that it is the combination of denotations 
with the underspecified predicate that has
an established interpretation, 
since in BrE {\it rubbish} is the normal
term rather than {\it garbage}, but {\it rubbish man} is not
established.} or the lexicon has to contain some compounds with their
established meaning.  Sentences containing such compounds would be
ambiguous because the corresponding
productively generated underspecified compound would still have to be
available.  And if established compounds are listed in the lexicon,
then any generalisation about the behaviour of classes of compounds
should also be accessible to the lexicon, since many established
compounds have an interpretation that belongs to one of the standard
patterns.  

These observations make noun-noun compounds a good candidate for the
use of defaults which persist beyond the lexicon, where a lexically
instantiated default interpretation can be overridden by subsequent
pragmatic processing, along broadly similar lines to the treatment of logical
metonymy in C+B and Lascarides (this volume).   
A general schema for endocentric compound
interpretation is shown in Figure~\ref{compschema}, 
with an underspecified predicate, $R$, relating the indices of
the constituents.
Most compounds will instantiate one or more of the subschemata 
which inherit from this schema
with the predicate relating the parts of the compound marked as
persistently default.
An example of a more specific schema is shown in 
Figure~\ref{subschema}.
The slash notation indicates a default value, i.e. the schema
defeasibly specifies that the compounding predicate 
is {\bf made-of-substance}.  
\begin{figure*}
{\centering
\tiny
{\normalsize {\bf compound-noun} $<$ {\bf binary-rule}} \hfill \mbox{}\\
$\avmplus{\att{lex-noun}\\
                  \attval{ORTH}{\ind{1}, \ind{2}}\\
                  \attvaltyp{SYN}{noun-cat}\\
                  \attval{SEM}{\ind{3} \wedge \ind{5} \wedge R(\ind{6},\ind{4})}\\
                  \attval{QUALIA}{\ind{7} \ \ \myvaluebold{nomqualia}}}
\mbox{\normalsize $\rightarrow$}
\avmplus{\att{lex-noun}\\
                  \attval{ORTH}{\ind{1}}\\
                  \attvaltyp{SYN}{noun-cat}\\
                  \attval{SEM}{\ind{3}\ \ P(\ind{4})}\\
                  \attvaltyp{QUALIA}{nomqualia}},
\avmplus{\att{lex-noun}\\
                  \attval{ORTH}{\ind{2}}\\
                  \attvaltyp{SYN}{noun-cat}\\
                  \attval{SEM}{\ind{5}\ \ Q(\ind{6})}\\
                  \attval{QUALIA}{\ind{7}}}
$
}
\caption{General schema for endocentric noun-noun compounds}
\label{compschema}
\vspace{0.1in}
{\centering
\tiny
{\normalsize {\bf made-of-substance-schema} $<$ {\bf compound-noun}} \hfill \mbox{}\\
$\avmplus{\att{lex-count-noun}\\
                  \attval{SEM}{\ind{3} \wedge \ind{5} \wedge 
/\mbox{made-of-substance}(\ind{6},\ind{4})}\\
                  \attvaltyp{QUALIA}{artefact}}
\mbox{\normalsize $\rightarrow$}
\avmplus{\att{lex-uncount-noun}\\
                  \attval{SEM}{\ind{3}\ \ P(\ind{4})}\\
                  \attvaltyp{QUALIA}{substance}},
\avmplus{\att{lex-count-noun}\\
                  \attval{SEM}{\ind{5}\ \ Q(\ind{6})}\\
                  \attvaltyp{QUALIA}{artefact}}
$
}
\caption{A compound noun subschema}
\label{subschema}
\end{figure*}


It should be apparent that under
this account it does not make sense to claim that compounds have 
some fixed number of
possible interpretations, since some predicates are supertypes of
more specific predicates, and there is not necessarily any limit
on specialisation of schemata.  Multiple schemata may apply to a
particular instance of a compound.  The account of semi-productivity of
lexical rules described in the previous section, can be extended to
compound interpretation, however, so massive ambiguity is avoided.

In Figure~\ref{chair}, I tabulate some examples of compounds taken from
a newspaper corpus to illustrate this approach.\footnote{Not all of
these examples are necessarily noun-noun compounds, but for the sake of
this example I have included all the possible cases.}%
\begin{figure*}
\begin{tabular}{lll}
Examples & Type of x & Interpretation  \\ \hline\hline\\
armchair, wheelchair  & artefact\_physical\_object & $P(x) \wedge
/\mbox{has-physical-part} (y,x)$\\\hline

deckchair, camp chair & location & $P(x) \wedge /\mbox{used-in-loc} (y,x)$\\
dining room chair, hospital armchair & & \\ \hline

folding chair, rocking chair & event &  $P(e) \wedge /\mbox{p-pat}(e,y)$\\ 
push-chair & & \\ \hline

cane chair, rattan chair  & substance & $P(x) \wedge /\mbox{made-of-substance} (y,x)$\\
wickerwork chair, wrought-iron chair & & \\ \hline

Mackintosh chair & human & $P(x) \wedge /\mbox{designed-by} (y,x)$\\ \hline

Mastermind chair & abstract & $P(x) \wedge R(y, x)$
\end{tabular}
\caption{Some examples of compounds involving {\it chair}}
\label{chair}
\end{figure*}%
The sample was just collected for illustrative purposes and is much 
too small (about 100 tokens) to
draw any firm conclusions, but it is worth
noticing that the only example which I found that 
should probably be given a completely underspecified
interpretation was {\it Mastermind
chair}.\footnote{Mastermind is a long-running quiz show on BBC
television, where contestants are individually questioned 
while sitting in a particular black chair.  The context in which the
compound occurred was a discussion
of bad TV reception and the full sentence was:
\begin{ex}
It's surprising how many people put up with ``snow'', blips 
and two people sitting in the Mastermind chair.
\end{ex}
This usage could be regarded as treating the TV program as a location,
but this considerably weakens the notion of location, so it
seems preferable to regard this example as one that should be
pragmatically resolved, like {\it apple juice chair}.}
Most of the other examples are established, but nevertheless fall into
some general classes.  
Some of the established examples are lexicalised, that is they
would have lexical entries which would
augment or override the productive interpretation: {\it deckchair}, for
example, is no longer particularly associated with a ship's deck.

The structure below shows the result of instantiating the schema in
Figure~\ref{subschema} with {\it wickerwork chair} 
(ignoring the substructure in {\it wickerwork}).\\ 
{\centering
\tiny
$\avmplus{\att{lex-count-noun}\\
                  \attval{SEM}{\mbox{\bf wickerwork}(\ind{4})
 \wedge \mbox{\bf chair}\ind{6} \wedge /\mbox{\bf made-of-substance}(\ind{6},\ind{4})}\\
                  \attvaltyp{QUALIA}{artefact}}
$
}
In normal
contexts, this interpretation will stand.  However, since it is
defeasible, it can be pragmatically overridden along the same lines as
the examples discussed by Lascarides.
Thus in a context such as \exnum{+1}{},
an alternative interpretation would be found, since the default
interpretation is contradicted by the context.
\begin{ex}
At school, everyone worked on crafts in groups
round a big table, sitting on brightly coloured chairs.  
To make sure everyone could reach the materials, the groups used
particular chairs: the wickerwork chairs were red plastic, for example.
\end{ex}

There are many elaborations that could be made to this sketch.
As it stands {\it apple juice chair} would be given the default
interpretation 
\[ \mbox{chair}(y) \wedge \mbox{apple-juice}(x) \wedge 
\mbox{made-of-substance}(y,x) \]  
This would be
overridden by pragmatics, 
but it could be lexically
excluded since physical entities are subcategorised according to
physical state, so the rule could be set up to exclude solid entities
being made of liquids, for example.  
But I make no claim for the adequacy
of this particular classification of compounds since  
my aim here is just to illustrate that
the use of the persistent default mechanism makes a classification
possible in principle. 

\section{Conclusion}

In this paper, I have described an approach to representing polysemy,
which appears to have considerable promise for building LKBs, since by
using these techniques we can get away from the `dictionary' notion of
a fixed number of discrete word senses.  
Our use of default inheritance and lexical rules gives the lexicon some
generative capacity with which to interpret novel usages.
The approach to defaults described here has been implemented in the
ACQUILEX LKB system.
From a computational perspective, the main difficulty in applying the
approach to semi-productivity is collecting the probabilities, since 
this requires disambiguation of usages in corpora.  This might be
feasible, despite the 
rather disappointing results of most reported work
on sense disambiguation 
since probabilities do not
need to be exact, and the sense distinctions we are interested in are
quite coarse grained compared to those made in most learners'
dictionaries.  Furthermore Harley~(1994) suggests that better sense
disambiguation is possible, given a good lexical database. 
However, this remains as future work.  Further work would also be
required to provide a computational account of the lexical / pragmatic
interface, and a tractable implementation of the pragmatic component.

\section*{References}
% first argument - i.e. #1 is always author
% #2 is title
% last is date
% agreed author format is, for example
% Alshawi, H., D. Carter, M. Rayner and B. Gamb\"ack
% 
% the only formatting commands that should appear in fields
% are those to mark idiosyncratic information like accents
\newcommand{\book}[4]{\item #1 (#4) {\it #2,} #3.}
% #3 is publisher
\newcommand{\unpub}[4]{\item #1 (#4) `#2', #3.}
% for tech reports etc
% #3 is information about institution etc
\newcommand{\bookart}[7]{\item #1 (#7) `#2' in #5 (ed.), {\it #4,} #6, pp.~#3.}
% published book article (old \barticle)
% #3 is page numbers 
% #4 book title
% #5 editors
% #6 publishers
\newcommand{\bookartnoed}[6]{\item #1 (#6) `#2' in {\it #4,} #5, pp.~#3.}
% book article where editors are unknown
% #3 is page numbers 
% #4 book title
% #5 publishers
\newcommand{\bookartnopp}[6]{\item #1 (#6) `#2' in #4 (ed.), {\it
#3,} #5.}
% book article where page numbers are unknown
% #3 book title
% #4 editors
% #5 publishers
\newcommand{\forthart}[6]{\item #1 (#6, forthcoming) `#2' in #4 (ed.), {\it #3,} #5.}
% article in forthcoming book (old \farticle}
% #3 book title
% #4 editors
% #5 publishers
\newcommand{\forthjournart}[4]{\item #1 (#4) `#2', {\it #3,}}
\newcommand{\journart}[6]{\item #1 (#6) `#2', {\it #3,} {\bf #4},
#5.}
% article in journal (old \jarticle)
% #3 name of journal
% #4 volume
% #5 pages
\newcommand{\journartnopp}[5]{\item #1 (#5) `#2', {\it #3,} 
{\bf #4}.}
% article in journal no page numbers
% #3 name of journal
% #4 volume
\newcommand{\procart}[6]{\item #1 (#6) `#2', {\it Proceedings of the
#3,} #4, pp.~#5.}
% article in proceedings (old \particle)
% #3 name of conference
% #4 venue
% #5 pages
\newcommand{\pubprocart}[7]{\item #1 (#7) `#2', {\it Proceedings of the
#3,} #4, ,#5, pp.~#6.}
% #3 name of conference
% #4 venue
% #5 publishers
% #6 pages
\newcommand{\procartnopp}[5]{\item #1 (#5) `#2', {\it Proceedings of the
#3,} #4.}
% article in proceedings without known page numbers
% #3 name of conference
% #4 venue
\newcommand{\pubprocartnopp}[6]{\item #1 (#6) `#2', {\it Proceedings of the
#3,} #4, #5.}
% article in proceedings without known page numbers
% #3 name of conference
% #4 venue
% #5 publishers
\newcommand{\procartnoppnoplace}[4]{\item #1 (#4) `#2', {\it Proceedings of the
#3}.}
% article in proceedings without known page numbers without place
% where meeting happened
% #3 name of conference
\newcommand{\procartnoplace}[5]{\item #1 (#5) `#2', {\it Proceedings of the
#3,} pp.~#4.}
% article in proceedings where the venue is not known
% #3 name of conference
% #4 pages
%\newcommand{\acqwp}{ESPRIT BRA-3030 ACQUILEX WP NO.}
%\newcommand{\aunpub}[5]{\item #1 (#4) {\it #2.}\\ \acqwp #3}


\begin{list}{}
   {\leftmargin 1.6em
    \itemindent -\leftmargin
    \itemsep 0pt plus 1pt
    \parsep 0pt plus 1pt}

\book{Bauer, L.}
     {English word-formation}
     {Cambridge University Press, Cambridge, England}
     {1983}

\bookartnopp{Briscoe, E.J., A.~Copestake and A.~Lascarides}
            {Blocking}
            {Computational Lexical Semantics}
            {P.~St.~Dizier and E.~Viegas}            
            {Cambridge University Press}
            {in press}

\unpub{Copestake, A.}
{The representation of lexical semantic information}
{Doctoral dissertation, University of Sussex,
Cognitive Science Research Paper CSRP 280}
{1992}


\forthjournart{Copestake, A. and E.J.~Briscoe}
        {Semi-Productive Polysemy and Sense Extension}
        {Journal of Semantics}
        {in press}

\unpub{Harley, A.}
   {Cambridge Language Survey: Semantic Tagger}
   {ACQUILEX-II working paper No 39: available from {\tt
cide@cup.cam.ac.uk}}
   {1994}

\unpub{Hobbs, J.R., M.~Stickel, D.~Appelt and P.~Martin}
   {Interpretation as Abduction}
   {Technical Note No.~499, Artificial Intelligence Centre, SRI
International, Menlo Park, CA}
   {1990}


\forthjournart{Lascarides, A., E.J.~Briscoe, N.~Asher and A.~Copestake}
      {Order Independent and Persistent Typed Default Unification}
{Linguistics and Philosophy}
{in press}

\unpub{Lascarides, A. and Copestake, A.}
        {A Logic for Order Independent Typed Default Unification}
        {ACQUILEX-II working paper}
        {1995}

\book{Levi, J.}
     {The syntax and semantics of complex nominals}
     {Academic Press, New York}
     {1978}


\unpub{Nunberg, G.D. and A. Zaenen}
      {Systematic polysemy in lexicology and lexicography}
      {Proceedings of Euralex92, Tampere, Finland}
      {1992}


\journart{Pustejovsky, J.}
    {The generative lexicon}
    {Computational Linguistics}
    {17(4)}
    {409--441}
    {1991}

\journart{Pustejovsky, J. and B.~Boguraev}
      {Lexical knowledge representation and natural language processing}
      {Artificial Intelligence}
      {63}
      {193--223}
      {1993}

\unpub{Riehemann, S.}
    {Word formation in lexical type hierarchies}
    {M.Phil thesis, University of T\"{u}bingen, Germany}
    {1993}

\end{list}
\end{document}




