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\begin{document}
\noindent To appear in: Proceedings of SALT V, Cornell University, 1995\\[0.4in]

{\centering
{\large\bf The Pragmatics of Word Meaning}\\[\baselineskip]
\parbox{2.75in}{\centering\bf Alex Lascarides\\ University of Edinburgh}
\parbox{2.75in}{\centering\bf Ann Copestake\\ University of Cambridge}
}
%\vspace{\baselineskip}

\section*{Abstract}
In this paper, we explore the interaction between lexical semantics
and pragmatics.  Linguistic processing is informationally encapsulated
and utilises relatively simple `taxonomic' lexical semantic knowledge.
On this basis, defeasible
lexical generalisations deliver defeasible parts of logical form.
In contrast, pragmatics is open-ended
and involves arbitrary knowledge.
Two axioms specify
when pragmatic defaults override lexical ones.  We
demonstrate that modelling this interaction allows us to achieve a
more refined interpretation of words in a discourse context than
either the lexicon or pragmatics could do on their own.

\section{Introduction}

Much recent work on lexical semantics has been concerned with 
accounting for the flexibility of word meaning.
For example, there are many cases of regular polysemy,
which includes not only the familiar verb alternations 
and nominalisations but
also related senses of nouns such as the
mass/portion senses 
{\it beer}, {\it coffee} etc and 
the container/contents alternation found with {\it box}, {\it case} and
so on.  There is also the
phenomenon which Pustejovsky (e.g.~1991, in press) has called
{\it logical metonymy}
where additional meaning seems to arise for particular verb/noun
or adjective/noun combinations.  For example, (\ref{enjoy}a) usually
has the same interpretation as (\ref{enjoy}b):
\begin{examples}
\item  \label{enjoy}
\begin{subexamples}
\item   Mary enjoyed the book.
\item   Mary enjoyed reading the book.
\end{subexamples}
\end{examples}
Syntactic realisation and lexical semantics are
closely interrelated: it is not an arbitrary fact that {\it beer} is a
mass noun when it refers to an unbounded quantity of liquid, and a
count noun when it refers to the portion, or that {\it enjoy} can take
a nominal complement.
The challenge is to account for these processes compositionally in a
way which allows for their partly conventional nature, within a 
general framework of linguistic description that recognises the role of
pragmatics.

Briscoe \etal (1990) and Copestake
(1992) argued for an  
interaction between lexical semantics and pragmatics in which purely
linguistic processing is informationally encapsulated and 
utilises relatively simple `taxonomic' lexical semantic knowledge. 
Lexical semantic information and real world knowledge were not seen as
necessarily distinct.  Instead, linguistic processes had
limited access to world knowledge, which could therefore interact with
knowledge of language and possibly
become conventionalised in various ways.
For processes such as logical metonymy, 
linguistic processing delivered
a partly defeasible logical form, which could be overridden by 
open-ended pragmatic 
reasoning.
This work concentrated on providing an account of lexical
semantics which was integrated
with syntax and compositional semantics by
utilising a uniformly unification-based approach.  However, the account
was incomplete, because the interaction with pragmatics was left open.
Defaults were simply used to 
aid in the encoding of static lexical generalisations.  Thus 
the use of lexical defaults in syntax and morphology 
(e.g. Flickinger (1987), Evans and Gazdar (1989)) was extended
to lexical semantics.  But it
was not related to the notion of defeasibility in the
logical form, making it unclear how the unification based techniques
served to distinguish defeasible from indefeasible parts of logical form.

Here we review the earlier account and argue for a new
treatment of defaults, which allows default results
of lexical generalisations to {\em persist} as default beyond the
lexicon and thus be available 
to the interface with pragmatic reasoning.  
We will make specific proposals for the formalisation of the pragmatic
component, and illustrate how this allows us to account for alternative
interpretations of words in a discourse context.
The decision as to whether the lexical default survives
at the discourse level or not will be
modeled in a formally precise way in the nonmonotonic logic for
pragmatic reasoning.  Just two rules will be needed to encode the
communication link between
default reasoning in the lexicon on the one hand, and default
reasoning at the discourse level at the other.
By providing this link between lexical operations and discourse ones,
we will explain how words are
interpreted in discourse, in a way that neither the lexicon
nor pragmatics could achieve on their own.

\section{Generalisations with Exceptions}

Verbs such as {\it enjoy}
can be described as selecting semantically
for an event in examples such as (\ref{enjoyvp}): 
\begin{examples}
\item \label{enjoyvp} Mary enjoys playing the guitar.
\end{examples}
However {\it enjoy} can also take an NP complement, and 
in (\ref{enjoy}a) 
the complement {\it the book} denotes a physical object:
\begin{examples}
\item[\ref{enjoy}]
\begin{subexamples}
\item Mary enjoyed the book.
\item Mary enjoyed reading the book.
\end{subexamples}
\end{examples} 
Traditionally the only way to handle
this is to assume two lexical entries for {\it enjoy}
and to relate the different senses by meaning postulates.
However, quite apart from the
undesirability of proliferating senses,
this does not explain why the usual reading of (\ref{enjoy}a) is
(\ref{enjoy}b), and it misses the generalisation to other cases
where a noun phrase is interpreted as an event, such as those in
(\ref{metonymyeg}).
\begin{examples}
\item   \label{metonymyeg}
\begin{subexamples}
\item   John began a new book.
\item   John finished the beer.
\item   Bill enjoyed the film.
\item   After three glasses of champagne, John felt much happier.
\end{subexamples}
\end{examples}
It also does not allow for cases where an NP and a VP are conjoined,
such as (\ref{conjenjeg}):
\begin{examples}
\item   \label{conjenjeg}
Mary enjoys books, television and playing the guitar.
\end{examples}

Pustejovsky (e.g.,~1991)
proposes that examples such as (\ref{enjoy}a) be treated as
involving {\it logical metonymy}. 
He treats nouns as having
{\it qualia structure} as part of their lexical entries
which specifies possible events associated with the entity.
For example, the telic (purpose) role of the qualia structure for {\it book}
has a value equivalent to {\it reading}.  When combined
with {\it enjoy}, a metonymic interpretation is
constructed where the particular sort of event
which is likely to be involved can be determined from the qualia
structure,
which results in an
interpretation for (\ref{enjoy}a) equivalent to (\ref{enjoy}b).
In \S\ref{truth}, we outline an account which is broadly similar to
Pustejovsky's.
In our treatment of (\ref{enjoy}a), the
verb provides the basic metonymic interpretation, which can be
glossed as (\ref{enjoy2}a) with the logical form shown in
(\ref{enjoy2}b):\footnote{Here and in the
following examples we ignore temporal information for the sake of
simplicity.} 
\begin{examples}
\item \label{enjoy2}
\begin{subexamples}
\item
Mary enjoyed some event associated with the book.
\item
$\exists y,e,e' [\mbox{{\em enjoy}}(e,\mbox{Mary},e') \wedge
\mbox{{\em object}}(e,e') \wedge 
\mbox{{\em act-on-pred}}(e',\mbox{Mary},y) \wedge
\mbox{{\em book}}(y)]$
\item $\exists y,e,e' [\mbox{{\em enjoy}}(e,\mbox{Mary},e') \wedge
\mbox{{\em object}}(e,e') \wedge \mbox{{\em read}}(e',\mbox{Mary},y) \wedge
\mbox{{\em book}}(y)]$
\end{subexamples}
\end{examples}
The constant {\it act-on-pred} is general over a 
broad class of predicates which we will not attempt to precisely delimit
here, but which includes {\it watch}, {\it eat}, {\it smoke}
and so on.
However, the noun phrase provides the specific
predicate involved, thus giving the interpretation shown in (\ref{enjoy2}c)
(which corresponds to
(\ref{enjoy}b)).
If the noun does not have a conventionalised telic role,
the sentence is odd (out of context), as in (\ref{pebble}):
\begin{examples}
\item \label{pebble}
? Mary enjoyed the pebble.
\end{examples}

\subsection{Exceptions to the generalisation}

This generalisation about the interpretation
has two classes of exceptions.  
The first case is exemplified by (\ref{dictionary}):
\begin{examples}
\item \label{dictionary}
? Mary enjoyed the dictionary.
\end{examples}
This is odd (again out of context) because dictionaries are usually
used as reference books, and so its telic role {\it referring},
which is
point-like, doesn't combine easily with {\it enjoy}, which
has to be true of an event with
significant duration.  Thus (\ref{dictionary2}) is only natural on an
iterative interpretation:
\begin{examples}
\item \label{dictionary2}
Mary enjoyed referring to the dictionary.
\end{examples}
In Briscoe \etal (1990) and Copestake (1992), such cases are allowed
for by using a default inheritance hierarchy in the lexicon.  
So, although {\it dictionary},
like {\it book}, could inherit its lexical
semantic characteristics from a 
more general class such as
{\bf literature}, the telic role of the
qualia structure specified for {\it dictionary} corresponds to
{\it refer to}, and this overrides the inherited value {\it read}.  
The use of defaults in the lexicon was taken to be strictly part of the
description language, and led to a conventional 
lexical entry expressed as a typed feature structure.
Using defaults is an
important part of our theory of lexical structure, since it allows
concise specification of lexical entries and avoids redundancy.
However, purely lexical defaults do
not extend to the second class of exceptions, 
which are triggered by context, or wider world knowledge.  
For example, 
(\ref{goat}a) means (\ref{goat}b) and not (\ref{goat}c):
\begin{examples}
\item   \label{goat}
\begin{subexamples}
\item   My goat eats anything.  He really enjoyed your book.
\item   The goat enjoyed eating your book.
\item   The goat enjoyed reading your book.
\end{subexamples}
\end{examples}
Similarly, our interpretation of {\it Mary enjoyed the book} is
different if we know that Mary is a goat and is revised if we 
subsequently learn this.

Briscoe \etal (1990) allow for the second type of
defaults by introducing a
consistency operator $M$ (cf.~Reiter 1980)
into the part of the logical form derived from
the telic role.  Thus 
the logical form of (\ref{enjoy}a) is (\ref{enjoywff}); it
can be
glossed 
as ``the event enjoyed is reading, in the absence of information
to the contrary'':
\begin{examples}
\item   \label{enjoywff}
$\exists y,e,e' [\mbox{{\em enjoy}}(e,Mary,e') \wedge
\mbox{{\em object}}(e,e') \wedge M\mbox{{\em read}}(e',Mary,y) \wedge
\mbox{{\em book}}(y)]$
\end{examples}

This account was intended as a placeholder in the absence of
a proper treatment of pragmatics.  Even so, it has some major disadvantages.  
Firstly, the assumption that goats don't read is
itself default, because of contexts such as fairy stories.
Assuming that this default is encoded
in the same logic,
it is unclear how one could ensure that the axioms on $M$ resolve the
conflict between the default logical form and the default world knowledge
in favour of the latter, especially since the
two defaults are logically unrelated.
Secondly, the
consistency operator is introduced into the grammar
as an ad-hoc stipulation.  
There is no connection between the
defeasibility of the telic role with respect to its inheritance in the
{\it dictionary} case and its defeasibility in the logical form.  
The pragmatic overriding in the goat example is due to 
the subject of {\it enjoy}.  But the object can also have this effect, 
as shown in the examples in (\ref{funnybooks}), given
that {\it book made out of marzipan} and {\it book with blank pages} 
can't be lexicalised (unlike {\it dictionary}).
\begin{examples}
\item   \label{funnybooks}
\begin{subexamples}
\item  John enjoyed the book made out of marzipan.
\item  ? John enjoyed the book with blank pages.
\end{subexamples}
\end{examples}
Intuitively, these cases are just like the dictionary one, in
that they arise because the object is an abnormal book.
In fact, we hypothesise that all cases of overriding of the logical
form arise because the context is such that the entity is being used in
an abnormal way.
Ideally, therefore, we would like the defeasibility in the logical form
to arise from the default nature of the usual purpose specification
made in the lexicon.
But, because defaults in Briscoe \etal (1990) are simply part of the
lexical description language, they could not persist
beyond the lexicon, and the defeasibility in the logical form had to be
stipulated.

It is implausible that these problems could be resolved by adopting a
purely lexical account, since arbitrarily complex reasoning could be
involved in deciding that the subject can't read or that the object is
unreadable.  The alternative would be to claim that the interpretation
of the event was purely pragmatic (i.e. that the logical form for 
(\ref{enjoy}a) was simply (\ref{enjoy2}b), with the interpretation of
the predicate {\it act-on-pred} 
being completely pragmatically determined).  
Such an approach is suggested by Hobbs {\em et al.} (1990) who use
weighted abduction on pragmatic knowledge to determine the value of
the underspecified predicate.  
But serious challenges to this 
line exist (see also Briscoe \etal (1990)).

First, an adequate theory has to account for the
usual interpretations.  The corpus analysis
described in Briscoe \etal (1990)
showed that for most metonymic examples 
the telic role of the noun gives an appropriate
reading.  What's more, the explicit mention of the verbal predicate is
relatively rare in such cases---that is, examples such as 
(\ref{enjoy}a) are more common than 
(\ref{enjoy}b).  On the other hand, the contexts in which the  
interpretation would not have been predicted by the qualia structure
were informationally-rich (a concept which we will be able to formalise in
\S\ref{infrich}).  A purely pragmatic theory could only account for this
data by assuming that some interpretations were privileged; for
example, one would need a rule that encapsulates that {\em enjoy
the book} by default means {\em enjoy reading the book}.  But
this would cause the same problems with prioritising defaults
which we mentioned above.  That is, one would have to impose
prioritorisations on world
knowledge that weren't
independently motivated, because the conflicting knowledge that was
pertinent to the case would be logically unrelated.
In the case of weighted abduction, it is thus unclear how one can
assign the weights that guide inference in a principled way.

Furthermore, there is some evidence which
suggests that logical metonymy is partially conventionalised and
triggered by the lexical item, rather than knowledge of the context.
For example, (\ref{doorstop})
is strange,
even if the hearer and the speaker both know that the
doorstop is a book, which would not be predicted if the purpose were
pragmatically determined by real world knowledge of the entity:
\begin{examples}
\item   \label{doorstop}
? John enjoyed the doorstop.
\end{examples}
There are also examples where the coerced form is less acceptable
than might be expected if interpretation was simply a matter of finding
a possible event: for example, (\ref{path}) seems relatively
strange, even though hiking is a common recreational activity:
\begin{examples}
\item   \label{path}
? John enjoyed the path.
\end{examples}
Godard and Jayez (1993) give some data for {\it commencer}
which leads them to suggest that the telic interpretation is only
available for objects which are being in some sense
consumed or affected by the action.  However they then have to assume
that books are affected by being read.  Since it is unlikely
that real world properties of books would 
necessarily lead to this conceptualisation, these exceptions support
the hypothesis that logical metonymy is partially conventionalised.
Conventionalised exceptions can be lexically encoded, but 
resist a purely pragmatic treatment. 

We therefore did not want to reject the hypothesis that the lexicon
proposes a partially defeasible logical form.
Instead, we make use of a new formalisation of defaults, which
allows them to persist beyond the lexicon.  The default nature of the
part of the logical form contributed by the telic role is not simply
stipulated, but arises directly from the lexical default.
The interface with pragmatics is set up so that reasoning with
real world knowledge can override the defaults proposed
lexically.
Thus we can provide an
integrated account of the interaction of lexical semantics and
pragmatics.  We describe this account in \S\ref{truth} and \S\ref{infrich}
but first we briefly review some other data which
requires this sort of treatment.

\subsection{Adjectives and compound nouns}

Some examples of adjective interpretation can be treated along the same
broad lines as {\it enjoy} and other event invoking predicates.
Pustejovsky (e.g., 1991, in press) and others have argued against
distinct lexical entries for {\em fast}, for each of its senses in
{\em fast car}, {\em fast typist}, {\em fast motorway} and so on.  Instead, it
is possible to assume just a single
lexical entry for {\em fast},
where its different `senses' arise from the process of syntagmatic
co-composition.
The lexical generalisation is much
like that for {\em enjoy}: adjectives like {\em fast}
predicate over the telic role of the artefact
(although {\it fast} can also apply to other parts of the qualia).  So
the lexical
account predicts that {\em fast car} means {\em a car
which goes fast}, and {\em fast typist} means {\em a typist who types
fast}, via the same entry for {\em fast}.

But as before, some discourse contexts trigger exceptions to this
generalisation.  In (\ref{fasttext}), {\em fast typist}
means {\em typist who runs fast}, and not {\em typist who types fast}.
\begin{examples}
\item   \label{fasttext}
\begin{subexamples}
\item
All the office personnel took part in the company sports day last
week.  
\item One of the typists was a good athlete, but the
other was struggling to finish the courses.  
\item The fast typist
came first in the 100m.
\end{subexamples}
\end{examples}
As in the {\it enjoy} examples, the pragmatic component needs to know that
the interpretation of {\em fast typist}
as {\em a typist who types fast} is a default.

Another case where a default interpretation apparently
arises from the lexicon/grammar is the interpretation of compounds.
For example,
there appears to be a generalisation that when a noun that
refers to a solid substance combines with a noun that refers to a
solid artefact, the compound
refers to the
artefact made of the substance ({\em wickerwork chair},
{\em plastic toy}, {\em wrought iron table}, {\em mahogany dresser}).
On the other hand, some compounds can
only be interpreted in context.  Downing attests (\ref{applejuice}) 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{examples}
\item   \label{applejuice}      Please sit in the apple juice chair.
\end{examples}
Here {\em apple juice chair} means
``chair in front of a place setting with apple juice'', but obviously
this meaning cannot be listed in the lexicon.  

Examples like
(\ref{applejuice}) have 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).
There are, however, serious objections
to this application of the pragmatic dustbin.  Without further
elaboration it gives no explanation of the
fact that the majority of compound nouns behave in a {\em semi}-regular
manner.  But
if the above generalisation about solid
substance/artefact compounds were encoded
via a standard default inheritance
mechanism, default and non-default
information would not be distinguished in the result.  
But the ``made-of'' relationship between the nouns in
compounds like {\em wickerwork chair} can be
overridden in discourse:
\begin{examples}
\item   \label{chairtext}
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 made of red plastic, for example.
\end{examples}
These observations make noun-noun compounds a good candidate for the
use of defaults which persist beyond the lexicon, along
broadly similar lines to the discussion of logical metonymy above.


\section{Persistent Default Unification and the Lexicon}
\label{truth}

We use a typed feature structure formalism comparable to that used in
HPSG (Pollard and Sag, 1994)
to implement the grammar and
the lexicon.
The standard method of implementing default inheritance within
unification-based approaches to linguistic representation is to use
some variety of default unification (see Copestake, 1993, for a overview).
This is usually taken to be an operation in the
description language, which allows one feature structure ({\sc fs}) to incorporate
only the consistent information from another {\sc fs}.  Inconsistent
information is ignored, rather than causing failure of the operation
as in normal unification.  But since default
unification returns a normal {\sc fs}, there is no distinction
between default and non-default information in the result.  Thus, 
for example, there is no way
of specifying that the telic role for the {\bf literature} class
is defeasible.  The lexical entry for
{\it dictionary} could override it (in fact {\it
dictionary} could override any part of the information it was inheriting)
but there is no way in which it can be stated to be defeasible more
generally. 

There is another problem with using this operation as a
basis for lexical organisation.  With the exception of Young and Rounds
(1993), default unification 
is order-dependent.  This 
somewhat compromises the declarativity of the formalism, but
is not a serious problem for the
lexicon itself, because all the entries to be unified are 
in a fixed hierarchy and an inheritance order can be imposed.
But in a discourse situation, one cannot
predict which pieces of information are to be unified, {\em in
advance} of starting the discourse parsing process.  So
the interface between discourse processing and order dependent
lexical processing would have to take into account the order in which
the unification operations are done, which is impractical.

Lascarides \etal (1994) have defined an
order independent form of
default unification over typed default feature structures ({\sc tdfs}s).  
{\sc tdfs}s are typed {\sc fs}s
where default information is marked as such, and the default
unification operation is one where 
defaults in a {\sc tdfs}, if they survive at all, survive with the
marking that they are default.  So this unification operation
is one which permits defaults to {\em persist} as
default beyond
the lexicon's boundaries, in the sense 
that one can distinguish in the {\sc fs} which parts are default.
Because of this, the
operation is known as Persistent Default Unification ({\sc pdu}).

{\sc tdfs}s are {\sc tfs}s augmented
with a slash notation which demarcates the indefeasible parts from the
defeasible.  
Values to the left of the slash are indefeasible and those to
the right defeasible ({\em indefeasible/defeasible}).  We abbreviate
this to {\em /defeasible} where the indefeasible value is 
completely general, and
omit the slash when the defeasible and indefeasible values are the
same.  So, for example, the {\sc tdfs} (\ref{fseg}) states that the
value on the feature {\sc f} is by default {\sc g:}{\bf a}, although
the type of the {\sc fs} and the 
existence of the feature {\sc f} itself is non-default:
\begin{examples}
\item   \label{fseg}
{\tiny
$\avmplus{\att{t}\\
\attval{F}{/\avmplus{\attvaltyp{G}{a}}}}$}
\end{examples}
When a default value survives {\sc pdu} (notated
$\ddunify$), it does so with the slash notation.  The details of {\sc
  pdu} are given in Lascarides \etal (1994)
but two examples are given in Figure~\ref{pduegs}.
These indicate that {\sc pdu} validates defeat of Defeasible
Modus Ponens ({\sc dmp}), and unlike
Young and Rounds' definition,
it also validates Specificity (i.e., defeasible
information on more specific {\sc tdfs}s overrides conflicting defaults
on more general {\sc tdfs}s).
\begin{figure}
Where
{\bf t$'$} is more specific than ($\sqsubset$) {\bf t}:\\
{\tiny $\avmplus{\att{t}\\
        \attvaltyp{F}{a}} \mbox{\normalsize $\ddunify$} 
       \avmplus{\att{t$'$}\\
       \attvaltyp{F}{/b}} \mbox{\normalsize $=$}
\avmplus{\att{t$'$}\\
        \attvaltyp{F}{a}}$} \hfill Defeat of DMP\\
{\tiny $\avmplus{\att{t}\\
        \attvaltyp{F}{/a}} \mbox{\normalsize $\ddunify$}
 \avmplus{\att{t$'$}\\
 \attvaltyp{F}{/b}} \mbox{\normalsize $=$}
\avmplus{\att{t$'$}\\
        \attvaltyp{F}{/b}}$}
\hfill Specificity/The Penguin Principle
\caption{Some examples of PDU}
\label{pduegs}
\end{figure}

Lascarides \etal (1994) show one way of encoding
the inheritance of telic roles in 
{\sc  pdu} (Figure~\ref{telic}).  So, for example,
the telic role
of {\bf literature} is {\bf read} and this is inherited
by {\bf book}, but for the subclass {\bf dictionary}
it's {\bf refer-to}.  This is superficially
similar to previous
descriptions, apart from the slash, but here
default inheritance can proceed in any order to compute the
telic roles.
\begin{figure}
{\modsmalltree{5}{
\multicolumn{5}{c}{{\node{topavm}{
{\tiny $\avmplus{\att{artefact}\\
\attvaltyp{TELIC PRED}{eventuality}}$}}}}\\
\\
\multicolumn{5}{c}{{\node{repart}{
{\tiny $\avmplus{\att{represent-art}\\ 
\attvaltyp{TELIC PRED}{/perceive}}$}}}}\\
\\
{\node{visart}{{\tiny
$\avmplus{\att{visual-rep}\\ 
\attvaltyp{TELIC PRED}{/watch}}$}}} & 
\multicolumn{4}{c}{{\node{litart}{{\tiny
$\avmplus{\att{literature}\\ 
\attvaltyp{TELIC PRED}{/read}}$}}}}\\
\\
{\node{film}{{\tiny $\avmplus{\att{film}}$}}} & \multicolumn{3}{c}{
{\node{reference}{{\tiny $\avmplus{\att{dictionary}\\ 
\attvaltyp{TELIC PRED}{/refer}}$}}}} &
{\node{book}{{\tiny $\avmplus{\att{book}}$}}}\\
%\\
%{\node{noir}{{\tiny $\avmplus{\att{film-noir}}$}}}
}
\nodeconnect{topavm}{repart}
\nodeconnect{repart}{visart}
\nodeconnect{repart}{litart}
\nodeconnect{litart}{reference}
\nodeconnect{litart}{book}
\nodeconnect{visart}{film}
%\nodeconnect{film}{noir}
}
\caption{The Telic Role of Artefacts}
\label{telic}
\end{figure}

Copestake and Briscoe (1995)
show how to state the
lexical generalisation concerning 
{\em enjoy}, that it predicates over the
telic role of the artefact as shown in 
Figure~\ref{enjoyfig}.\footnote{Unlike 
Pustejovsky (in press) and Briscoe \etal (1990), this account
assumes that the {\sc fs} for {\it enjoy} when it takes an
object which denotes an individual entity
is distinct from the form which takes an event (although both inherit
from a common underspecified form).
The `coercion' from object to event
is represented
as internal to the verb semantics.
Some of the reasons for preferring this account are given in
Copestake and Briscoe (1992, 1995) and Godard and Jayez (1993).
However the differences between this and
the alternative account
where the NP itself undergoes coercion
are largely irrelevant here.}
When {\em enjoy} takes an artefact-denoting 
object (which instantiates the {\sc cat subcat} `slot'), the event that is
enjoyed is instantiated via the telic role, as indicated by the
coindexation $\ind{P}$ in Figure~\ref{enjoyfig}.
In the figure, R is the
predicate associated with the verb itself (e.g., {\bf enjoy}) $\ind{P}$
and $\ind{n}$ indicate coindexation (we are using letters here for
readability rather than the conventional integers).
\begin{figure}%
{\tiny\centering 
$\avmplus{\att{coercing}\\
          \attvallist{CAT SUBCAT}{\avmplus{\att{np}\\
                                     \attval{SEM}{\ind{n}}\
\mbox{\normalsize $[Q(y)]$}\\
                                     \attval{QUALIA TELIC PRED}{\ind{P}}}}\\
          \attval{SEM}{\mbox{\normalsize $[e] [\mbox{R}(e,x,e') \wedge
\ind{P}\mbox{act-on-pred}(e',x,y)
\wedge \ind{n} ]$}}}
$ 
}
\caption{The generalisation for verbs like {\em enjoy}.}
\label{enjoyfig}
\end{figure}%
The instantiated form is shown in Figure~\ref{instenjoyfig}.
\begin{figure}%
{\tiny\centering 
$\avmplus{\att{coercing}\\
          \attvallist{CAT SUBCAT}{\avmplus{\att{np}\\
                           \attval{SEM}{\ind{n}}\\
                           \attval{QUALIA TELIC PRED}{\ind{P}\myvaluebold{act-on-pred/read}}}}\\
          \attval{SEM}{\mbox{\normalsize $[e] [\mbox{enjoy}(e,x,e') 
\wedge \ind{P}(e',x,y) \wedge \ind{n}\mbox{book}(y)]$}}}
$ 
}
\caption{The sign for {\it enjoy} instantiated with information from
the NP for {\it the
book} (ignoring tense and the determiner)}
\label{instenjoyfig}
\end{figure}

In these figures the logical form is shown in a linearised notation 
for readability,
rather than in its actual encoding in {\sc tdfs}s.  
It is important, however, that we use the same formalism throughout,
since it means we can use {\sc pdu} to construct the semantics, just as
normal unification is often used in {\sc fs} based frameworks.
We have
shown the path {\sc qualia telic pred} explicitly, to illustrate that
it is the predicate itself which is slashed.
The semantic representation
assumed is InL (Indexed Language, 
Zeevat \etal 1987), which has a direct equivalence to {\sc drt}.
We'll assume the use of {\sc drt} here,
since this is the semantic representation
scheme that underlies the pragmatic component {\sc dice}
(Lascarides and Asher, 1991, 1993) that we'll link
the grammar to.  We assume that {\sc drs}-conditions that arise from
elements on the {\sc rhs} of the slash notation are embedded in an 
operator * in the {\sc drs} conditions, and this
will affect their truth conditional status.  So the logical form of
(\ref{enjoy}a) derived via {\sc pdu} is (\ref{enjoy}a$'$):
\begin{examples}
\item   [\ref{enjoy}]
\begin{subexamples}
\item   [a]      John enjoyed the book.
\item   [a$'$]
{\small
\topdrs{$e,e',x,y$}{$\mbox{{\em john}}(x)$\\ $\mbox{{\em
      enjoy}}(e,x,e')$\\
$\mbox{{\em book}}(y)$ \\ 
%$hold(e,t)$ \\ 
%$t\prec \mbox{{\em now}}$ \\
% Alex, OK to add the following and lose the tense? 
$\mbox{\em act-on-pred}(e',x,y)$\\
$*\mbox{{\em read}}(e',x,y)$}
}
\end{subexamples}
\end{examples}
For brevity, we have omitted
{\sc wff}s of the form $*\phi$ when $\phi$ also holds.

We now have the task of assigning  a semantics to
{\sc drs}-conditions of the form
$*\phi$.  This must indicate that they're
derived via defaults in the lexicon.
{\sc pdu} is formalised in a conditional logic.  So the
way defaults behave in {\sc pdu} is determined by constraints on a
function $*_{pdu}$ that's part of the model, and which takes worlds and
propositions to propositions.  $*_{pdu}$ represents assumptions about the
behaviour of defaults in the lexicon: $*_{pdu}(w,p)$
encodes what according to $w$, normally follows from $p$.  
So, let $K$ be {\sc drs}, and let $K^-$ be the {\sc drs} $K$ with all
the {\sc drs}-conditions of the 
from $*\psi$ removed.  Then we can define the semantics of $*\phi$
as follows:
\begin{itemize}
\item   $M,w\models_f *\phi$ in {\sc drs}
$K$ just in case for all $w'$ in $*_{pdu}(w,\sem{K^-})$,
there is a $g\supseteq f$ such
that $M,w'\models_g\phi$.
\end{itemize}
{\sc drs} conditions of the form $*\phi$
aren't asserted to be true in the actual world $w$, since according to
the assumptions about $*_{pdu}$ 
in {\sc pdu}, it's not necessarily the case
that $w\in *_{pdu}(w,p)$.  So in
(\ref{enjoy}a$'$), the logical semantics {\em doesn't} entail that the
event that was enjoyed was a reading; however, it does entail that an
event was enjoyed by John.  Thus we have utilised the fact that
defaults persist, by assigning the default results of {\sc pdu} a
different truth conditional status in logical semantics from the
indefeasible results.  It is now up to the pragmatic component to assess
whether {\em read} should be inferred as the appropriate event in the
discourse context.  The lexicon has proposed this,
but clues from the more open ended pragmatic reasoning may dispose of
this proposal, and replace it with another.  We'll come to this 
in the next section.

Copestake and Briscoe (1995) treat {\em fast}
in a very similar way to {\em enjoy}. 
The coindexation between the telic role of the object NP in the subcat
list and the event that {\em fast} predicates over in the semantics is
inherited via {\sc pdu} from a lexical generalisation over the class of
adjectives of which {\em fast} is a member (other members are
{\em slow}, {\em careful},
{\em long}).
In this case the telic
role of {\em typist} is $[x][\mbox{{\em /type}}(e,x)]$, where $x$ is
coindexed with the `normal' variable. But this is defeasible: it's on
the {\sc rhs} of the slash.  
The truth conditional
effects of this is are represented in the {\sc drs} (\ref{fasttypist})
for {\em fast
  typist}, where the formula $\mbox{{\em type}}(e,x)$ is within the
scope of $*$: 
\begin{examples}
\item   \label{fasttypist}
\topdrs{$x,e$}{$\mbox{{\em typist}}(x)$\\ $\mbox{{\em fast}}(e)$\\
$\mbox{\em act-pred}(e,x)$\\
$*\mbox{{\em type}}(e,x)$}
\end{examples}
So the lexicon proposes that the event {\em fast} that predicates over is
{\em type}, but this may be overridden by pragmatic information.

\section{Linking The Lexicon to Pragmatics}
\label{infrich}

\subsection{{\sc dice}}

We'll link the lexicon and grammar to a theory of pragmatics:
specifically {\sc dice} (Discourse in Commonsense Entailment,
Lascarides and Asher 1991, 1993).   This is a
model of discourse interpretation which encodes real world
knowledge like
{\em goats don't read},
and more generally, it encodes background information that's used to compute
the rhetorical links
between segments of discourse.  The representation of discourse
structure produced by {\sc dice} are segmented
{\sc drs}s ({\sc sdrs}s) (Asher 1993).  An {\sc sdrs} is a
recursively defined structure which connects {\sc drs}s together using
discourse relations like {\em Elaboration}, {\em Contrast} and so on.
These relations impose coherence constraints on the discourse.  The
details of these are in
Asher 1993, Asher and Lascarides 1995, Lascarides and Asher 1993.
We'll exploit these constraints to reason about when lexical defaults
should be overridden.  Simply put: lexical defaults will normally be 
overridden
when they lead to a bad discourse.

{\sc dice} uses the default logic Commonsense Entailment ({\sc ce})
(Asher and Morreau, 1991) to reason about pragmatic
interpretation.
This logic exploits conditions of the form: $A>B$, which
means {\em If A then normally B}.  So one could represent {\em goats
  don't read} as the schema:
\begin{itemize}
\item   {\tt Goats Don't Read:}
$\mbox{{\em goat}}(x) > \neg\mbox{{\em read}}(e,x,y)$
\end{itemize}
Furthermore, all
default rules for computing the rhetorical relation
that connects {\sc drs}s together
are of the form given in (\ref{form}).  Here
$\langle\tau,\alpha,\beta\rangle$ is the update function 
which can be glossed ``$\beta$ is
to be attached to 
$\alpha$ with a discourse relation, where $\alpha$ is part of the
discourse structure $\tau$ built so far''.  ``Some stuff'' stands
for syntactic and semantic information about $\tau$, $\alpha$ and $\beta$ and
$R$ is a particular discourse relation:
\begin{examples}
\item   \label{form}    $(\langle\tau,\alpha,\beta\rangle \wedge \mbox{
some stuff})> R(\alpha,\beta)$
\end{examples}
Details of these discourse attachment rules appear in
Lascarides and Asher (1991, 1993) and  
Asher and Lascarides (1995).

The nonmonotonic validity of {\sc ce} ($\csmodel$) has
several nice properties.  There are three that are relevant here.
First, it validates {\sc dmp}: if one default
applies and its consequent is consistent with the {\sc kb}, then it's
nonmonotonically inferred.  Second, it validates the
Specificity Principle: if conflicting defaults have their antecedents
verified, then the consequent of the default with the most specific
antecedent is preferred.  Finally, for each deduction $A\csmodel B$
there is a corresponding embedded default in the object language (that
is, a formula in which one $>$ occurs
within the scope of another) which links boolean combinations of the
formulae $A$ and $B$, and which is verified to be true.  We gloss
this embedded default formula as
$\emb(A,B)$.  So $\emb(A,B)$ means $A\csmodel B$.  This amounts to a
weak deduction theorem.  The object language formula $\emb(A,B)$ means
that $A$ nonmonotonically yields $B$ in the metalanguage.

\subsection{Linking {\sc pdu} and {\sc dice}}

To link the {\sc pdu} treatment of lexical productivity to 
pragmatic knowledge, we add two axioms to
{\sc dice}.  First, Defaults Survive captures the intuition that
defaults in the lexicon normally survive at the discourse level:
\begin{itemize}
\item   {\tt Defaults Survive:} $*\phi > \phi$
\end{itemize}
Second, we need an axiom that ensures that when the consequents of
discourse processing and lexical processing conflict, the discourse
processing wins.  This is what happens in (\ref{sentencegoat}), for
example, where
the {\sc pdu} prediction, that the event enjoyed was a reading, is
overridden by the conflicting pragmatic information stipulated in the
$>$-rule Goats Don't Read.
\begin{examples}
\item   \label{sentencegoat}    The goat enjoyed the book.
\end{examples}
Let $KB_h$ be obtained
from the knowledge base $KB$, by removing all the {\sc drs}
conditions of the form $*\phi$ ($h$ stands for
``hard information'').  Then Discourse Wins states: when this {\sc kb}
yields a nonmonotonic conclusion $\psi$, then normally this
survives the {\sc kb} with conditions like $*\phi$ added to it:
\begin{itemize}
\item   {\tt Discourse Wins:} $(*\phi \wedge
  \emb(KB_h,\psi)) > \psi$
\end{itemize}
This rule is called  Discourse Wins, because by the Specificity
Principle with Defaults Survive, 
if $\psi$ conflicts with $\phi$, then
$\psi$ is nonmonotonically inferred and $\phi$ is not, even if $*\phi$
was in the {\sc kb}.  In other words, the clues from
discourse context, if there are any, override 
conflicting results of {\sc pdu}.  On the other hand, if $\phi$ and
$\psi$ are compatible, they will both be inferred by {\sc dmp}.  So
Discourse Wins also serves to model how discourse information can
further refine the information about meaning obtained from the lexicon.

Let's now investigate how this affects the interpretation of the above
examples.  First, consider (\ref{enjoy}a), whose logical form expressed in 
{\sc drt} is
(\ref{enjoy}a$'$): 
\begin{examples}
\item   [\ref{enjoy}] 
\begin{subexamples}
\item   [a] John enjoyed the book.
\item   [a$'$]
{\small
\topdrs{$e,e',x,y$}{$\mbox{{\em john}}(x)$\\ $\mbox{{\em
      enjoy}}(e,x,e')$\\
$\mbox{{\em book}}(y)$ \\ 
%$hold(e,t)$ \\ $t\prec \mbox{{\em now}}$ \\
$\mbox{{\em act-on-pred}}(e',x,y)$\\
$*\mbox{{\em read}}(e',x,y)$}
}
\end{subexamples}
\end{examples}
There are no $>$-rules
which give information about the kinds of things that John enjoys.
Moreover, Defaults Survive applies
with the following instantiation of the
schema: $*\mbox{{\em read}}(e',x,y) > \mbox{{\em
read}}(e',x,y)$.  So by {\sc dmp} on this rule, one infers that John
enjoyed reading the book.

Now compare this with (\ref{sentencegoat}), whose logical form is
similar to (\ref{enjoy}a$'$):
\begin{examples}
\item   [\ref{sentencegoat}] The goat enjoyed the book.
\item   [\ref{sentencegoat}$'$]
{\small
\topdrs{$e,e',x,y$}{$\mbox{{\em goat}}(x)$\\ $\mbox{{\em
      enjoy}}(e,x,e')$\\
$\mbox{{\em book}}(y)$ \\ 
%$hold(e,t)$ \\ $t\prec \mbox{{\em now}}$ \\
$\mbox{{\em act-on-pred}}(e',x,y)$\\
$*\mbox{{\em read}}(e',x,y)$}
}
\end{examples}
First consider the nonmonotonic consequences on $KB_h$.  Goat's
Don't Read applies, but Defaults Survive doesn't with respect
to $KB_h$, because $KB_h$
contains no conditions of the form $*\phi$.  So by {\sc dmp} on Goats 
Don't Read,
$\neg\mbox{{\em read}}(e',x,y)$ follows nonmonotonically from $KB_h$.
That is, $\beth(KB_h,\neg\mbox{{\em read}}(e',x,y))$ holds.  In the KB
as a whole,
the instantiation of Defaults Survive given in
(\ref{goatds}) applies just as
before.  But in contrast to (\ref{enjoy}a), so does
the instantiation of the schema Discourse Wins given in
(\ref{goatdw}):
\begin{examples}
\item   \label{goatds}  $*\mbox{{\em read}}(e',x,y) > \mbox{{\em
read}}(e',x,y)$ 
\item   \label{goatdw} 
$(*\mbox{{\em read}}(e',x,y) \wedge \beth(KB_h,\neg\mbox{{\em
read}}(e',x,y))) > \neg\mbox{{\em read}}(e',x,y)$.
\end{examples}
So by the Specificity Principle on (\ref{goatds}) and (\ref{goatdw}),
$\neg\mbox{{\em read}}(e',x,y)$ is inferred.

\subsection{Discourse Context}

We would need more $>$-rules to infer that the event enjoyed is an
eating in (\ref{sentencegoat}).  But in (\ref{goat1}), we could infer that the
goat enjoyed eating the book via the rhetorical structure of the
discourse and the existing
{\sc dice} rules which compute that rhetorical structure
(Asher and Lascarides, 1995).  
\begin{examples}
\item   \label{goat1}
My goat ate the whole library.  \hfill $\alpha$\\
He really enjoyed your book.\hfill $\beta$
\end{examples}
The relevant rules for discourse attachment, which are taken from
Asher and Lascarides (1995), are given below:
\begin{itemize}
\item   {\tt Narration:} $\langle\tau,\alpha,\beta\rangle > \mbox{{\em
Narration}}(\alpha,\beta)$ 
\item   {\tt Axiom on Narration:} $\Box(\mbox{{\em
Narration}}(\alpha,\beta) \rightarrow e_\alpha\prec e_\beta)$
\item   {\tt Distinct Common Topic:}\\
$\Box(\mbox{{\em Narration}}(\alpha,\beta)\rightarrow \exists
\gamma(\gamma\Downarrow\alpha \wedge \gamma\Downarrow\beta \wedge
\neg(\alpha\Downarrow\beta) \wedge\neg(\beta\Downarrow\alpha)))$
\item   {\tt Subtype:}\\
$\Box((\theta_i(\mbox{{\em e-condn}}_\alpha,\alpha,\gamma_1) \wedge
\theta_i(\mbox{{\em e-condn}}_\beta,\beta,\gamma_2) \wedge \\
\hspace*{0.2in}\mbox{{\em
    e-condn}}_\beta\sqsubseteq \mbox{{\em e-condn}}_\alpha \wedge
\gamma_2\sqsubset \gamma_1)\rightarrow \mbox{{\em Subtype}}(\alpha,\beta))$
\item   {\tt Elaboration:}
$\langle\tau,\alpha,\beta\rangle \wedge \mbox{{\em
    Subtype}}(\alpha,\beta) > \mbox{{\em Elaboration}}(\alpha,\beta)$
\item   {\tt Axiom on Elaboration:}
$\Box(\mbox{{\em Elaboration}}(\alpha,\beta)
\rightarrow\alpha\Downarrow\beta)$ 
\end{itemize}
Narration together
with its Axiom capture the intuition that normally the
textual order of events match their temporal order.  
Distinct Common
Topic acts as a coherence constraint: it stipulates that a
narrative must have a distinct common topic ($\gamma\Downarrow\alpha$
means $\gamma$ is a topic for $\alpha$).
Elaboration states that if $\beta$ is to be attached to
$\alpha$ and $\beta$ is a subtype of $\alpha$, then normally
$\mbox{{\em Elaboration}}(\alpha,\beta)$ holds; its Axiom 
says that $\alpha$ must be a topic of $\beta$.
$\mbox{{\em
Subtype}}(\alpha,\beta)$ can be inferred via the monotonic rule
Subtype, which states: if (a) the
{\sc drs}s $\gamma_1$ and $\gamma_2$ respectively
identify the thematic role $\theta_i$ in $\alpha$ and $\beta$, with
respect to the event conditions
$\mbox{{\em e-condn}}_\alpha$ and $\mbox{{\em e-condn}}_\beta$, and
(b) $\mbox{{\em e-condn}}_\beta$ is a subtype
of $\mbox{{\em e-condn}}_\alpha$
(for example, {\em The goat ate $x$}
is a subtype of {\em The goat enjoyed eating $x$}), and
(c) $\gamma_2$ is part of
$\gamma_1$ (e.g., {\em book} is part of what makes up
{\em library}), then (d) $\beta$ is a subtype of $\alpha$.  

Consider how these rules apply in (\ref{goat}a).
The {\sc drs} $\beta$ representing the
second sentence in (\ref{goat}a) must be attached to the {\sc drs} $\alpha$
representing the first.
The anaphor {\em he} must be identified with an accessible
antecedent, and the {\sc sdrt} constraints on accessibility restrict
this to being the goat.  Now, if the metonymy in $\beta$ is resolved
to {\em enjoy reading a book}, then the only candidate discourse
relation according to the 
above rules for discourse attachment is {\em
Narration}.  By Distinct Common Topic, this relation requires a
distinct common topic, which in {\sc sdrt} is obtained by generalising
the propositions in the narrative to produce a single predicate
argument
structure.  But the resulting
topic is too general to really
establish anything better than
weak coherence: it's something like {\em the goat did things}.
Indeed, resolving 
metonymy to anything of the form {\em enjoy VP-ing your
book}, where VP is not related to eating, results in a similar
interpretation of the discourse i.e., the coherence is weak.

In {\sc dice}, pragmatic interpretations
of sentences that lead to weak discourse coherence are avoided if possible,
via the Interpretation Constraint below
(Lascarides \etal 1995):
\begin{itemize}
\item   {\tt Interpretation Constraint}\\
\begin{tabular}[t]{l l}
(a) & $(\langle\tau,\alpha,\beta\rangle \wedge \mbox{{\em
    Info}}(\alpha,\beta)$ \\
(b) & $\beth_{KB}(\beta', \mbox{{\em
weak}}(\tau\cup\beta))) $\\
(c) & \hspace*{0.1in}$> \neg\beta'$
\end{tabular}
\end{itemize}
In this schema, $\mbox{{\em Info}}(\alpha,\beta)$ is a gloss for all
monotonic information about $\alpha$ and $\beta$, and $\emb_{KB}(A,B)$
means $\emb(KB\wedge A,B)$ and $\neg(KB,B)$ (that is, $B$
nonmonotonically follows from
the $KB$ augmented with $A$ but not from the $KB$ alone).  So in
words, the Interpretation Constraint 
states that if (a)
$\beta$ is to
be connected to $\alpha$ with a discourse relation, and $\beta$ and
$\alpha$ are both true,
and (b) if the KB that includes not only the update
task of $\beta$ to $\alpha$, but also the information $\beta'$
nonmonotonically leads to a discourse of only weak coherence or no
coherence at all, 
then normally (c) $\beta'$ doesn't hold.
This rule applies to (\ref{goat1})
whenever $\beta'$ is an assumption that the metonymy
in $\beta$ is resolved to an event that's unrelated to
eating, because as we've stated, such an assumption produces a weak
narrative.  However, the Interpretation Constraint doesn't apply if 
the metonymy is resolved to an event which is related to eating.  This is
because in this case, the event condition of eating in $\alpha$ is a
subtype of the event condition of enjoy eating in $\beta$, and the
book in $\beta$ is taken to be a part of the library in $\alpha$.  So
Subtype applies in the monotonic component, thereby yielding ${\em
Elaboration}(\alpha,\beta)$ in the nonmonotonic component.  So there's
no need for a distinct common topic between $\alpha$ and $\beta$
anymore: {\em Elaboration} dictates that $\alpha$ is the topic of the
discourse.

Consequently, {\sc dmp} on the Interpretation Constraint
rules out all resolutions of metonymy apart from {\em eat}, and so $KB_h$
yields a nonmonotonic conclusion that $\mbox{{\em eat}}(e',x,y)$ holds.
Therefore at the discourse level, the following rules apply, and
conflict (assuming $e'$ can't be both a reading and eating):
\begin{examples}
\item   $*\mbox{{\em read}}(e',x,y)>\mbox{{\em read}}(e',x,y)$\\
$(*\mbox{{\em read}}(e',x,y) \wedge \beth(KB_h,\mbox{{\em
eat}}(e',x,y))) > \mbox{{\em eat}}(e',x,y)$
\end{examples}
So by the Specificity Principle, $\mbox{{\em
    eat}}(e',x,y)$ is inferred.  This
leads to the nonmonotonic
conclusion that $\mbox{{\em Elaboration}}(\alpha,\beta)$ holds via
Subtype and Elaboration.

These examples provide further motivation for conventionalising some
aspects of metonymy.  For
suppose we were to compute metonymy {\em solely} within
pragmatics.  Then we would need to replace the
information in Figures~\ref{telic} and \ref{enjoyfig}
with $>$-rules in {\sc dice}.   Such a strategy is technically
possible, but 
representation of pragmatic information
would be trickier.  For example, to interpret
(\ref{sentencegoat})
correctly, the real world knowledge
that goats don't read
must win over the $>$-rules concerning generalisations about
{\em enjoy} on telic roles.  This means that the antecedent of this
rule would have to be more specific, otherwise the
logic won't resolve the conflict in the right way.  Indeed, there is
currently no logic for nonmonotonic reasoning which resolves conflict
between unrelated default rules without assuming 
prioritorisation mechanisms that are extraneous to the logic itself.  So Goats
 Don't Read would have to be replaced with something like
(\ref{dont}), so that it could compete with the $>$-rule
(\ref{cornerenjoy}) which replaces the information in
Figures~\ref{telic} and \ref{enjoyfig} relevant to {\em enjoy the book}:
\begin{examples}
\item   \label{cornerenjoy}     $(\mbox{{\em enjoy}}(e,x,e') \wedge
\mbox{{\em literature}}(y)) >
\mbox{{\em read}}(e',x,y)$
\item   \label{dont}   
{\small $(\mbox{{\em enjoy}}(e,x,e') \wedge
\mbox{{\em goat}}(x) \wedge \mbox{{\em literature}}(y)) > \neg
  \mbox{{\em read}}(e',x,y)$
}
\end{examples}
This rule is self-evidently extremely specific, but a rule of this form
is required for Specificity to hold.
But by spreading the load between pragmatics and the lexicon, and having
communication links between them, we can `loosen up' how we
represent information.

Now consider (\ref{fasttext}), where {\em fast typist} means {\em
  typist who runs fast}.
\begin{examples}
\item   [\ref{fasttext}]
\begin{subexamples}
\item
All the office personnel took part in the company sports day last
week.  
\item One of the typists was a good athlete, but the
other was struggling to finish the courses.  
\item The fast typist
came first in the 100m.
\end{subexamples}
\end{examples}
The
axioms Defaults Survive
and Discourse Wins capture this.  In outline,
the Interpretation Constraint in
{\sc dice} blocks the assumption that {\em the fast typist} in
(\ref{fasttext}c) is different from the typists mentioned in
(\ref{fasttext}a,b) because this would lead to a weak discourse.  
Consequently, Subtype and
Elaboration yield the intuitive attachment that
(\ref{fasttext}c) is an {\em Elaboration} of (\ref{fasttext}a,b).

As we've mentioned,
{\em the fast typist} must identify a unique typist from
(\ref{fasttext}a,b).  There are two typists, 
who have been differentiated only on the grounds
of their athletic ability.  So verifying the uniqueness condition 
is possible only if {\em fast} is equated with
athletic ability.  Thus $\emb(KB_h,\mbox{{\em fast}}(e') \wedge
\mbox{{\em run}}(e',x))$ holds (where $\mbox{{\em typist}}(x)\in
KB_h$).  So Defaults Survive and Discourse Wins both apply, and they
have the consequents
$\mbox{{\em type}}(e',x)$ and $\mbox{{\em run}}(e',x)$ respectively.
Assuming that $e'$ can't be both a typing and a running, these rules
conflict.  And so by the Specificity Principle, $\mbox{{\em run}}(e',x)$
is nonmonotonically inferred.  In contrast, in `neutral'
(i.e., uninformative) discourse
contexts, {\sc dmp} on Defaults Survive will yield that
{\em fast typist} means {\em typist who types fast}.

\subsection{Compound nouns}

A general schema for endocentric compound
interpretation is shown in Figure~\ref{compschema}, 
with an underspecified predicate, {\bf pred}, 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}.
This 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
\mbox{\small\bf pred}(\ind{x},\ind{y})}\\
                  \attval{QUALIA}{\ind{7} \ \ \myvaluebold{nomqualia}}}
\mbox{\normalsize $\rightarrow$}$\hfill \mbox{}%\\ \mbox{}\hfill
$\avmplus{\att{lex-noun}\\
                  \attval{ORTH}{\ind{1}}\\
                  \attvaltyp{SYN}{noun-cat}\\
                  \attval{SEM}{\ind{3}\ \ \mbox{\small\bf P}(\ind{y})}\\
                  \attvaltyp{QUALIA}{nomqualia}},
\avmplus{\att{lex-noun}\\
                  \attval{ORTH}{\ind{2}}\\
                  \attvaltyp{SYN}{noun-cat}\\
                  \attval{SEM}{\ind{5}\ \ \mbox{\small\bf Q}(\ind{x})}\\
                  \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{\small\bf pred/made-of-substance}(\ind{x},\ind{y})}\\
                  \attvaltyp{QUALIA}{artefact}}
\mbox{\normalsize $\rightarrow$}$ \hfill \mbox{}\\ \mbox{}\hfill
$\avmplus{\att{lex-uncount-noun}\\
                  \attval{SEM}{\ind{3}\ \ \mbox{\small\bf P}(\ind{y})}\\
                  \attvaltyp{QUALIA}{substance}},
\avmplus{\att{lex-count-noun}\\
                  \attval{SEM}{\ind{5}\ \ \mbox{\small\bf Q}(\ind{x})}\\
                  \attvaltyp{QUALIA}{artefact}}
$
}
\caption{A compound noun subschema}
\label{subschema}
\end{figure*}

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{\small\bf wickerwork}(\ind{4})
 \wedge \mbox{\small\bf chair}(\ind{6}) \wedge \mbox{\small\bf pred/made-of-substance}(\ind{6},\ind{4})}\\
                  \attvaltyp{QUALIA}{artefact}}
$
}

In normal
contexts, this interpretation will stand.  However, since the
compounding
predicate is
defeasible, it can be pragmatically overridden along the same lines as
the examples discussed above.
In a context such as (\ref{chairtext}),
an alternative interpretation is found, since the default
interpretation is contradicted by the context: 
\begin{examples}
\item   [\ref{chairtext}]
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 made of red plastic, for example.
\end{examples}
The pragmatic interpretation of {\em were made of red plastic} blocks
the inference that the {\em chairs} were made of wickerwork.
Moreover, the discourse structure of (\ref{chairtext})---and in
particular, the line of reasoning in {\sc dice} that leads to 
{\em Elaboration}---yields a
nonmonotonic inference from $KB_h$ that {\em wickerwork chair} is to be
interpreted as {\em chair which is sat on by someone who works on wickerwork}.
So by the Specificity Principle on Defaults survive and Discourse
Wins, the established meaning of {\em wickerwork chair} is overridden
in (\ref{chairtext}); instead it means {\em chairs made of red plastic,
which are sat on by people working with wickerwork}.

Briscoe \etal (1990)
claim that lexical generalisations are only
cancelled in contexts that are informationally rich.  We
have illuminated in a formal setting exactly what this means.
According to Defaults Survive and Discourse Wins, a lexical
generalisation $*\phi$ can be cancelled only if $\emb(KB_h,\neg\phi)$.
So a discourse context is `informationally rich' if, independently of
all default lexical generalisations, there are discourse clues which
enable one to nonmonotonically conclude the exception.  



\section{Conclusion}

Many lexical generalisations are of the sort where there are
exceptions to the rules, which are triggered by information 
outside the lexicon.  This poses a challenge to monotonic
accounts of the lexicon and to those which 
treat defaults as an abbreviatory convention
and restrict their use to the
description language.

Using an account of lexical organisation involving
{\em persistent} default unification, we showed that
links to a pragmatic
component were possible with just two axioms: the first ensures that lexical
generalisations normally apply in a discourse context, while the second
ensures that normally, discourse information about how a word should
be interpreted---if there is any---wins over defaults from the lexicon.  This
accounted for exceptions to lexical generalisations in a discourse
context in two areas: logical metonymy and compound nouns.
Moreover, the axioms clarified in a formal setting the claim
in Briscoe \etal (1990), that exceptions to
lexical generalisations can only be triggered by discourse contexts
which are informationally rich.

This is just a first step towards linking lexical and pragmatic
knowledge.  Much more needs to be done, to achieve a robust theory of
lexical interpretation in a discourse context.
Nevertheless, these first results indicate the
kinds of operations that one needs in both components for them to
communicate properly.  In the grammar and lexicon, persistent defaults are
needed, while in pragmatics, the Specificity Principle and
embedded defaults are a crucial part of the account.

\section*{Acknowledgements}

We are grateful to Ted Briscoe, Nicholas Asher, Dan Flickinger
and 
Dani\`{e}le Godard and to participants at {\sc salt} and the 1995 {\sc aaai}
spring symposium on representation and acquisition of lexical knowledge
for their helpful comments on material presented here.  This work was
partially supported by the ESPRIT Acquilex-II, project BR-7315, grant to
Cambridge University.


\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{\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{\forthjournart}[4]{\item #1 (in press) `#2', {\it #3}}
% article in journal no page numbers
% #3 name of journal
% #4 volume
\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}


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   {\leftmargin 0.5in
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    \parsep 0pt plus 1pt}



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\end{list}

\end{document}














