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\begin{document}
\thispagestyle{empty}
\vspace*{2in}
\begin{center}
{\Large \bf Lexical Operations in a Unification-based Framework}\\
\smallskip
Ann Copestake and Ted Briscoe\\
\smallskip
University of Cambridge Computer Laboratory\\
New Museums Site, Pembroke Street, Cambridge, CB2 3QG, UK\\
\smallskip
June 1991\\
\smallskip
(in Proceedings of the ACL SIGLEX Workshop on Lexical semantics and
Knowledge Representation, Berkeley, California, pp.188-197)\\
\bigskip
ESPRIT BRA-3030 ACQUILEX Working Paper No 21
\end{center}
\newpage
\setcounter{page}{1}
\vspace{1.0in}
\protect\begin{center}
         {\Large {\bf
                   Lexical Operations in a Unification-based Framework
			 \\}}
 \bigskip
  {\small
    Ann Copestake, Ted Briscoe\\}
 \medskip
  {\it  Computer Laboratory, University of Cambridge, Pembroke Street,\\
Cambridge, CB2 3QG, UK\\
	aac@cl.cam.ac.uk ejb@cl.cam.ac.uk \\}
 \bigskip
\protect\end{center}
\medskip
\begin{abstract}
\small \addtolength{\baselineskip}{-.16\baselineskip} \noindent
We consider lexical operations and their representation in a unification
based lexicon and the role of lexical semantic
information.  We 
describe a unified treatment of the linguistic aspects of
sense extension
and derivational morphological processes which
delimit the range of possible coercions between lexemes
and give a preliminary account of how default
interpretations may arise.
\end{abstract}
\section{Introduction}

In this paper we consider the nature and extent of lexical operations,
arguing for a declarative and computationally tractable definition of
a lexical rule as a component of a unification-based lexicon employing
(default) inheritance and typed feature structures. We claim that this
notion of lexical rule is capable of capturing the linguistic element
of derivational morphological processes as well as metonymic and
metaphoric sense extensions, but is not adequate for the statement of
certain types of logical metonymy (e.g. Pustejovsky, 1989a). We argue that
such operations must be treated as, in part, `linguistic' because they
have morphological and syntactic consequences, undergo `blocking', are
triggered by grammatically-defined type mismatches and involve default
interpretations based on lexical organisation. However, we also argue
that such default interpretations can be overridden by contextual
information on the basis of more general and open-ended `pragmatic'
inference. Our account contrasts with that of, say, Hobbs et al.
(1987) who posit an underspecified and impoverished lexical semantic
representation which is enriched through an open-ended process of
abductive or deductive reasoning with world (or domain) knowledge. Our
lexical knowledge representation language does not support general
inference, although our lexical semantic representations are often
`richer' than those standardly assumed.

A standard example of metonymic sense extension is the use of a word
denoting a place to refer to (some of) the people inhabiting that
place (e.g. ``village'', ``palace''). This process seems to involve
the foregrounding of one component of the meaning of the place
denoting word -- we follow Pustejovsky (1989a,b,c) in assuming that
the lexical semantic representation of nouns includes information
about typical relations which the objects they denote enter into; in
particular, the ``qualia structure'' for such nouns will contain
(telic) information which allows direct access to the information
that they are inhabited. A well-known example of metaphoric sense
extension is that involving use of a word denoting an animal to refer
to humans (``John is a pig'', ``John is a wombat'' etc). Although the
sense extension from animals into metaphorical senses denoting humans
with some particular characteristic is apparently productive, the
actual characteristics involved, and even whether the word can be
applied to men or to women or both, cannot be predicted from knowledge
of the animal sense. Thus, the properties ascribed to a person by
``pig'' are arguably no more than stereotypical associations with the
animal, rather than central aspects of its meaning / qualia structure.
In the case of ``wombat'' we would argue that the association of
foolishness derives from the phonological form of the word, rather
than beliefs about the animal. Despite the more associative or
analogical nature of metaphorical sense extension, we would argue that
there is a core component to such processes which should be expressed
in terms of a lexical rule, rather than in terms of general purpose
reasoning. As with the metonymic cases (Pustejovsky, 1989c; Briscoe et
al., 1990), we believe that the notion of coercion during syntactic
and semantic interpretation provides an account of when a metaphorical
interpretation will be adopted, and we would like to characterise
coercion in terms of possible mappings defined by lexical rules.

An example of a derivational morphological process is the addition of
the ``er'' suffix to verbs, typically creating a noun denoting the
agent of the action denoted by the verb (e.g. ``teach'', ``teacher'').
There are several apparent differences between this type of process
and the metonymic and metaphoric sense extensions considered above.
The derivational rule involves a change of syntactic class, it affects
the argument structure of the derived predicate, it involves
affixation, and although there is a foregrounding of one aspect of the
verb meaning, the result would not traditionally be described as a
metonymic, or indeed metaphorical, usage. Nevertheless, there are
clearly derivational processes which do not affect syntactic class
(e.g. ``re-program'', ``un-reprogrammable'') and of sense extensions
which do; for example, countability of nouns changes depending on
whether they are interpreted as types, substances or portions (e.g.
``There was beer all over the table'', ``John drank a beer''). Not all
derivational processes affect argument structure (e.g. ``un-kind''),
whilst metonymic sense extensions (e.g. ``John enjoyed the film'',
John finished the beer'') can, at least given the analyses of
Pustejovsky (1989c) and Briscoe et al. (1990). Finally, processes of
conversion and derivation can be identical; for example, both
``purchase'' and ``replace'' have deverbal nominal forms ``purchase''
and ``replacement'', both nouns can denote the action involved and
take appropriate complements (``Bill's purchase of his new car'',
``Bill's replacement of John with Mary''), and both can denote the
result of the action (``Bill's purchases were many and varied''
``Bill's replacement was young''). Traditionally, this latter
resultative meaning would be described as metonymic and probably
specialised and non-productive. We think that our definition of
lexical rule will allow an account of both conversion and derivation
as productive syntactic and
semantic operations mapping between lexical entries. The difference
between metaphorical and metonymic operations is a matter of the
degree to which the interaction of the 
lexical rule with the basic entry
determines or circumscribes the
eventual interpretation.

There are other similarities between sense extension and derivational
morphology; clearly, productivity is an issue in both, and in
particular, sense extension processes may apparently be blocked
(preempted by synonymy), in a way comparable to the situation in
derivational morphology (see e.g. Bauer 1983:87f). For example, the
regular form ``stealer'' does not generally occur, apparently because
of the availability of ``thief''. Another productive metonymic sense
extension is that of animal denoting (count) nouns to (mass) nouns
denoting their meat (e.g. ``lamb''), but this process too is blocked
by the presence of a synonymous lexeme with different form (``pig'',
``pork''). By representing such processes in terms of lexical rules
mapping between entries, we hope to account for blocking in terms of
syntactic and semantic identity with an entry defined without recourse
to the relevant lexical rule. In addition, we hope to express sense
extension processes, and indeed derivational ones, as fully productive
processes which apply to finely specified subsets of the lexicon,
defined in terms of both syntactic and semantic properties expressed
in the type system underlying the organisation of the lexicon.

In Briscoe et al. (1990) we offered an account of logical metonymies
such as that involved in the interpretation of ``Bill enjoyed /
regretted that paper'', drawing on Pustejovsky (1989a), in
which a unary syntactic rule is used to coerce the entity-denoting NP
``that paper'' into an event-denoting NP with an underspecified
predicate.  We argued that a default specification of this predicate
is supplied by the qualia structure of the noun and that this is
determined by the organisation of the lexicon as a default inheritance
network.  Specifically, ``paper'' in the relevant sense will inherit a
telic role read$'$ and agentive role write$'$ and ``enjoy'' will by
default select the telic role of an NP object, whilst ``regret'' will
select the agentive role. We presented evidence based on corpus data
that such default interpretations are appropriate in unmarked
informationally-weak contexts, but that they are overridden in marked
contexts in which such an interpretation would be clearly
inappropriate. The corpus evidence suggests, firstly, that the
default interpretation is appropriate with most such logical
metonymies and, secondly, that where it is not, the context is
sufficient to block it.  By contrast, an account such as that of Hobbs
et al. (1987) has difficulty explaining why the default interpretation
is adopted in the {\it absence} of contextual information, unless the
effects of lexical organisation are reconstructed in terms of
weightings encoding preferences amongst inferences. Whilst this
account of the division of labour between default but circumscribed
linguistic processes and more open-ended inference remains attractive,
the treatment of coercion in this case as a unary syntactic rule, or in
Pustejovsky's (1989c) alternative account as a lexical rule,
seems inadequate. The interpretation of an individual-denoting nominal
or noun phrase as an event-denoting one may be more a matter of
systematic vagueness than ambiguity between determinate senses.
Pustejovsky (1989a) argues that in examples such as a), b) or c)
``long'' will have an interpretation in which it modifies the telic or
agentive role of ``book'' because it is an event modifier.

\begin{quote}
a) John bought and read the long book.\\
b) John enjoyed the long book.\\
c) John bought, read and enjoyed the long book.
\end{quote}

However, this coercion of ``book'' into, say, ``long book to read'' does
not preclude either an event-denoting or individual-denoting
interpretation of the complete NP, as a) and b) demonstrate (where
presumably ``read'' and ``bought'' select the straightforward
referential interpretation, whilst ``enjoy'' forces another round of
coercion). Furthermore, an example like c) which involves a ``crossed''
interpretation in which ``the long book'' is simultaneously
interpreted as individual- and event-denoting does not seem odd.
However, in cases of genuine ambiguity, as opposed to vagueness, such
readings are usually blocked (Zwicky \& Sadock, 1975):

\begin{quote}
a) John likes landing planes and so does Bill.
\newline
b) ? Peter's purchase of hi fi took hours and was expensive.
\newline
c) ? John played with and then ate his lamb.
\newline
d) John ate and enjoyed the salmon.
\newline
e) Bill picked up and finished his beer.
\newline
f) John wrote but later regretted that paper.
\end{quote}

Thus a) has two, not four, readings in which both John and Bill like
watching planes landing or like landing them themselves, but not
readings in which the interpretation of ``landing planes'' varies
between conjuncts. Similarly, b) is odd because the first conjunct
forces a deverbal event-denoting interpretation of ``purchase'' whilst
the second strongly prefers a resultative reading and c) is odd
because the first conjunct prefers the animal-denoting interpretation
of ``lamb'' whilst the second selects the food-denoting one (although
the overall preferred interpretation will probably involve treating
``played with'' to mean something like `fiddle with or pick at
(food)'). By contrast, d-f) all involve moving between individual-
and event-denoting readings of the final NPs, but do not seem
problematic. 

These observations suggest to us that an adequate account of the
coercion process in these cases will involve positing systematic
vaguenesses in interpretation of NPs, perhaps along the lines of type
ladder polymorphism (e.g. Partee \& Rooth 1983) or in terms of lexical
operations which apply to the predicates, like ``enjoy'' which
introduce such logical metonymies (rather than to the NP objects of
these predicates). In this paper, though we concentrate on ambiguities
in interpretation which can be treated in terms of lexical rules which
apply to noun entries.  We illustrate our approach with reference
mainly to the process of `grinding'.  It is well known that any count
noun denoting a physical object can be used in a mass sense to denote
a substance derived from that object, when it occurs in a sufficiently
marked context.  We refer to this as `grinding' because the context
normally suggested is the ``Universal Grinder'' (see Pelletier and
Schubert 1986).  So if ``a table'' is ground up the result can be
referred to as ``table'' (``there was table all over the floor'').
Several regular sense extensions can be regarded as special cases of
`grinding', where the extension may have become established.
Thus besides the animal/meat examples, trees used for wood (``beech'')
have a sense denoting the wood, and so forth.  Before we describe this
process in detail, we present the framework in which our account will
be couched.

\section{The Lexical Representation Language}

Our lexical representation language is unification-based, allowing
complex interconnections between syntactic and semantic information to
be defined, and making a tight interface possible between the lexicon
and a parser/interpreter. It supports a restricted range of
operations; (default) unification, (default) inheritance and lexical
rule application. It does not support arbitrary inference.
The language is based on the use of typed feature structures similar
to those described in Carpenter (1990).  Feature structures must be
well-formed with respect to types and particular features will only be
appropriate to specified types and their subtypes.  Types are
hierarchically ordered; the association of {\em constraints} with
types allows non-default inheritance.  We augment this with a
restricted concept of default inheritance (allowing only `orthogonal'
multiple inheritance (Touretzky 1986)); default inheritance is
formalised in terms of default unification of feature structures
ordered by an inheritance hierarchy.  The type system constrains both
default inheritance and lexical rule application.  This
representation language is described in detail in Copestake et al
(1991); the following sections are an informal description illustrated
with relevant examples.

\subsection{The type system}

The type hierarchy defines a partial ordering (notated $\sqsubseteq$)
on the types and specifies
which types are {\em consistent}.  Only feature structures with
mutually consistent types can be unified --- two types which are
unordered in the hierarchy are assumed to be inconsistent
unless the user explicitly specifies a common subtype.
Every {\em consistent} set of types  $S\subseteq {\sf TYPE}$
has a unique greatest lower bound or
meet (notation  $\sqcap S$).  
This condition allows feature structures
to be typed deterministically --- if two feature structures of types
{\bf a}
and {\bf b} are unified the type of the result will be 
${\bf a} \sqcap {\bf b} $,
which must
be unique if it exists.  If ${\bf a} \sqcap {\bf b}$ 
does not exist unification fails.  Thus in the fragment of a type
hierarchy shown in Figure~1 {\bf artifact} and {\bf physobj} are
consistent; ${\bf artifact} \sqcap {\bf physobj} = {\bf artifact\_obj}$.
\setlength{\unitlength}{0.8in}
\begin{figure}
\begin{center}
\begin{picture}(6, 2.6)
\put(4,2.5){\makebox(0,0){nomrqs}}
\put(4,2.4){\line(-2, -1){0.7}}
\put(4,2.4){\line(2, -1){0.7}}
\put(5,2){\makebox(0,0){artifact}}
\put(5,1.9){\line(-2, -1){0.7}}
\put(3,2){\makebox(0,0){physobj}}
\put(3,1.9){\line(-2, -1){0.7}}
\put(3,1.9){\line(0, -1){0.7}}
\put(3,1.9){\line(2, -1){0.7}}
\put(4,1.5){\makebox(0,0){artifact\_obj}}
\put(4,1.4){\line(0, -1){0.3}}
\put(2,1.5){\makebox(0,0){ind\_obj}}
\put(2,1.4){\line(-2, -1){0.7}}
\put(2,1.4){\line(0, -1){0.3}}
\put(1,1){\makebox(0,0){creature}}
\put(1,0.9){\line(2, -1){0.7}}
\put(1,0.9){\line(-2, -1){0.7}}
\put(0,0.5){\makebox(0,0){person}}
\put(2,0.5){\makebox(0,0){animal}}
\put(2,1){\makebox(0,0){inan\_obj}}
\put(3,1){\makebox(0,0){substance}}
\put(3,0.9){\line(2, -1){0.7}}
\put(4,1){\makebox(0,0){food}}
\put(4,0.9){\line(0, -1){0.3}}
\put(4,0.5){\makebox(0,0){food\_substance}}
% \put(4,0.4){\line(0, -1){0.3}}
% \put(4,0){\makebox(0,0)[b]{meat}}
\end{picture}
\caption{A fragment of a type hierarchy}
\end{center}
\end{figure}

Our system differs somewhat from that described by Carpenter (1990) in
that we adopt a different notion of well-formedness of typed feature
structures.  In our system every type must have exactly one associated
feature structure which acts as a constraint on all feature structures
of that type; by subsuming all well-formed feature structures of that
type.  The constraint also defines which features are {\em
appropriate} for a particular type; a well formed feature structure
may only contain appropriate features.  Constraints are inherited by
all subtypes of a type, but a subtype may introduce new features
(which will be inherited as appropriate features by all its subtypes).
A constraint on a type is a well-formed feature structure of that
type; all constraints must therefore be mutually consistent.
Constraints can be seen as extending the PATR-II notion of templates
(eg. Shieber, 1986) in that the inheritance of constraints allows
concise definitions of all feature structures, not just lexical
entries; but in an untyped system, such as PATR-II, there is no
restriction on the features that can occur in a feature structure.

For example the constraints associated with the
types {\bf artifact} and {\bf physobj} might be:
\begin{quote}
{\scriptsize
   $\avmplus{\att{artifact}\\
                  \attvaltyp{telic}{formula}}$}\\
{\scriptsize
   $\avmplus{\att{physobj}\\
                  \attvaltyp{form}{physform}\\
                  \attvaltyp{physical-state}{solid}}$}
\end{quote}
Bold case indicates types; thus, for instance {\bf formula}
is a type and any feature structure of type {\bf artifact} 
must have a feature structure of type {\bf formula} as the value for
its {\sc telic} (purpose) feature.  {\bf formula} is intended to represent a 
formula in predicate logic, it therefore has a complex constraint
itself:
\begin{quote}
{\scriptsize
   $\avmplus{\att{formula}\\
                  \attvaltyp{ind}{entity}\\
                  \attvaltyp{pred}{logical-pred}\\
                  \attvaltyp{args}{arg-list}}$}
\end{quote}
In contrast {\bf solid} is an atomic type, it has no appropriate
features and its constraint is simply the atomic feature structure
[{\bf solid}].

The constraint on {\bf
artifact\_obj} will contain information inherited from both parents,
thus:
\begin{quote}
{\scriptsize
   $\avmplus{\att{artifact\_obj}\\
                  \attvaltyp{form}{physform}\\
                  \attvaltyp{physical-state}{solid}\\
                  \attvaltyp{telic}{formula}}$}
\end{quote}
Further examples of constraints and features which we will use 
in examples
in this
paper are:
\begin{quote}
{\scriptsize
   $\avmplus{\att{ind\_obj}\\
               \attval{form}{\avmplus{\att{physform}\\
               \attvaltyp{shape}{individuated}}}}$}\\
{\scriptsize
   $\avmplus{\att{creature}\\
                  \attvaltyp{age}{scalar}\\
                  \attvaltyp{sex}{gender}}$}\\
{\scriptsize
   $\avmplus{\att{animal}\\
                  \attvaltyp{edible}{boolean}}$}\\
{\scriptsize
   $\avmplus{\att{substance}\\
               \attval{form}{\avmplus{\att{physform}\\
               \attvaltyp{shape}{unindividuated}}}}$}\\
{\scriptsize
   $\avmplus{\att{food}\\
                  \attval{telic}{\avmplus{\att{formula}\\
                          \attvaltyp{pred}{eat}}}}$}
\end{quote}

We shall also make use of the following types to define syntactic
properties etc:
\begin{quote}
{\bf lex-sign} $\sqsubseteq $ {\bf top} \hspace{0.1in}
{\scriptsize
   $\avmplus{\att{lex-sign}\\
             \attvaltyp{orth}{string}}$}\\
{\bf noun} $\sqsubseteq $ {\bf lex-sign} \hspace{0.1in}
{\scriptsize
   $\avmplus{\att{noun}\\
             \attval{syntax}{\avmplus{\attvaltyp{count}{boolean}}}\\
             \attvaltyp{rqs}{nomrqs}}$}\\
{\bf count-noun} $\sqsubseteq $ {\bf lex-sign} \hspace{0.1in}
{\scriptsize
   $\avmplus{\att{noun}\\
             \attval{syntax}{\avmplus{\attvaltyp{count}{$+$}}}}$}\\
{\bf mass-noun} $\sqsubseteq $ {\bf lex-sign} \hspace{0.1in}
{\scriptsize
   $\avmplus{\att{noun}\\
             \attval{syntax}{\avmplus{\attvaltyp{count}{$-$}}}}$}
\end{quote}

The feature structure below is
well-formed since it
contains all the 
appropriate features and no inappropriate ones,
it is subsumed by the constraints on
its type and all its substructures are well-formed.
\begin{quote}
{\scriptsize
   $\avmplus{\att{count-noun}\\
             \attvaltyp{orth}{``haddock''}\\
             \attval{syntax}{\avmplus{\attvaltyp{count}{$+$}}}\\
             \attval{rqs}{\avmplus{\att{animal}\\
                              \attvaltyp{sex}{gender}\\
                              \attvaltyp{age}{scalar}\\
                              \attvaltyp{edible}{boolean}\\
                              \attvaltyp{physical-state}{solid}\\
                              \attval{form}{\avmplus{\att{physform}\\
                                  \attvaltyp{shape}{individuated}}}}}}$}
\end{quote}

Given the type system introduced above, a lexical entry, such as:
\begin{verbatim}
haddock 1 count-noun
       <rqs> = animal.
\end{verbatim}
would be expanded out into such a feature structure\footnote{The
actual type system being employed is considerably more complex, since
only the relevant features are being shown in these examples.}.

\subsection{Default inheritance}

To allow default inheritance we introduce the concept of {\em psort};
a feature structure from which another feature structure inherits
information, by default.  The hierarchical ordering on psorts (which
must be consistent with the type hierarchy) provides an order on
defaults.  Default inheritance is implemented by a version of default
unification.  Only orthogonal multiple inheritance (Touretzky 1986) is
allowed; information inherited from multiple parents must not be
contradictory.  (A default inheritance hierarchy which connects
semantic parts of lexical entries can be derived semi-automatically
from taxonomies extracted from conventional dictionaries, see
Copestake, 1990a).  We refer to this particular case of the psort
hierarchy as an IS\_A hierarchy.  Values of features can be associated
either manually or semi-automatically with psorts in the IS\_A
hierarchy; the more specific word senses then inherit them, by
default.  (Defaults may also be useful in the representation of
syntactic information in the lexicon (e.g. Flickinger, 1987).)

Since the type system constrains the psort
system it also constrains multiple default inheritance.
If the value of the {\sc food-temperature} feature for 
``drink 2 (1)'' is {\bf low} then
this information would
be inherited by the entry for ``beer'' which is below
``drink 2 (1)'' in the IS\_A hierarchy.
However inherited information may be overridden by 
associating other values with psorts lower in the hierarchy;
for example
although ``tea''
is under ``drink 2 (1)'' in the hierarchy,
its {\sc food-temperature} can be specified to be {\bf high} rather than
{\bf low}. 

Types and features thus provide an organisation on the information
which is necessary for interaction with lexical and syntactic rules.
The IS\_A hierarchy is motivated by defining its semantics in terms of
the real world entities corresponding to the word senses and
demonstrating that default inheritance of attributes in the lexicon
correlates with default reasoning about properties of the entities.
Copestake (1990a) outlines a preliminary attempt to formalise the
relationship between this aspect of lexical semantics and world
knowledge.

\subsection{Lexical rules}

A lexical rule is a feature structure of type {\bf lexical-rule}.  
The expanded constraint for the type is:
\begin{quote}
{\scriptsize
   $\avmplus{\att{lexical\_rule}\\
             \attvaltyp{0}{lex\_sign}\\
             \attvaltyp{1}{lex\_sign}}$} 
\end{quote}
thus all lexical rules have to have the features 0 and 1 which must
both have values which are of type {\bf lex\_sign}.  

New lexical signs may be generated by unifying a copy of
the lexical entry with the feature structure at the end of the path 
\verb|<1>|
in a copy of the lexical rule --- the feature structure at the end of
the path \verb|<0>| is then the new lexical sign.  Lexical rules are indexed by
the type of their ``input'' and ``output'' feature 
structures, so they will only be applied to entries
of the appropriate type and will only create well-typed entries.

A number of productive or quasi-productive phenomena, such as deverbal
nominalisation, `grinding',  and so forth, can be
represented as lexical rules which generate further lexical entries. 
A general type for grinding lexical rules
could be specified in our system as follows:
\begin{quote}
{\bf grinding} $\sqsubseteq$ {\bf lexical\_rule} \hspace{0.1in}
{\scriptsize
   $\avmplus{\att{grinding}\\
             \attval{1}{\avmplus{\att{count-noun}\\
                         \attval{orth\ \ \ }{\ind{1}}\\
                         \attvaltyp{rqs}{ind\_obj}}}\\
             \attval{0}{\avmplus{\att{mass-noun}\\
                         \attval{orth\ \ \ }{\ind{1}}\\ 
                         \attvaltyp{rqs}{substance}}}}$}
\end{quote}
The effect of the lexical rule is to transform a count noun with the
`relativised qualia structure' (RQS, Calzolari, 1991) 
properties appropriate to 
an individuated physical object {\bf ind\_obj} into a mass noun
with properties appropriate for a substance {\bf substance}. Thus the
core component of grinding is a linguistic, syntactic operation which
affects syntactic realisation, such as the
ability to appear without a determiner, correlated with an abstract
and underspecified semantic operation. We would claim that specific
predicational and syntactic contexts will result in coercion
(application of the lexical rule) and that this much, at least, of the
`grinding' family of sense extensions must be seen as a non-default
and essentially linguistic process.

We specialise the grinding rule to allow for cases 
such as the animal/meat regular sense extension explicitly.
The typed framework provides us with a natural
method of characterising the subparts of the lexicon to which such
rules should apply.
The lexical rules can, in effect, be parameterised by inheritance in 
the type system.
As our theory of lexical organisation allows us to
make fine distinctions between classes of lexemes, 
in terms of both syntactic and semantic properties encoded in the type
system, we expect that many processes which have been characterised as
partially productive or semantic specialisations of productive
processes will be characterisable as fully productive rules of sense
extension applying to smaller semantically coherent subsets of the
lexicon.  
  
For example given the type hierarchy shown in Figure~1 we can give 
rules which inherit information from {\bf grinding} 
such as animal\_grinding: 
\begin{quote}
animal\_grinding \hspace{0.1in}
{\scriptsize
   $\avmplus{\att{grinding}\\
             \attval{1}{\avmplus{\attval{rqs}{\avmplus{\att{animal}\\
                                  \attvaltyp{edible}{+}}}}}\\
             \attval{0}{\avmplus{\attvaltyp{rqs}{food\_substance}}}}$}
\end{quote}
Thus given the lexical entry for ``haddock'' shown above
we can apply the lexical rule to generate a sense meaning
``haddock-flesh''
(partially represented as):
\begin{quote}
{\scriptsize
   $\avmplus{\att{mass-noun}\\
             \attvaltyp{orth}{haddock}\\
             \attval{syntax}{\avmplus{\attvaltyp{count}{$-$}}}\\
             \attval{rqs}{\avmplus{\att{food\_substance}\\
                              \attval{telic}{\avmplus{\att{formula}\\
                                   \attvaltyp{pred}{eat}}}}}}$}
\end{quote}
(where the specification of the value {\bf eat} for the telic role
arises from the constraint on the type {\bf food\_substance},
inherited from {\bf food}, and the type mass-noun arises from
{\bf grinding}.) It would not be possible to apply this lexical rule to
``book'' and get a sense denoting ``book-flesh'' because ``book'' has
the type {\bf inanimate\_obj} which is incompatible with {\bf animal}.
It would still be possible to apply the general lexical rule for
grinding and to get a mass use of ``book'' but the denotation of the
mass sense would be underspecified.  We would expect the context to
provide a more specific interpretation of the mass sense in such a
(less-conventionalised) case.

Furthermore, our approach provides a natural mechanism for dealing
with semantic specialisation or restriction.  
We can
represent lexicalised items as inheriting information by default from
a psort which is the result of applying an appropriate lexical rule to
the base form.  Such items may have specific information associated
with them.  In cases where the lexical rule predicts the extended
sense exactly, the specific information will duplicate information
already present.  If the rule is correct, but incomplete, the specific
information will augment the inherited information. If it is partially
incorrect, the more specific information will override that inherited
from the result of lexical rule application.  In an untyped system
this representation would not constrain the structures associated with
lexicalised derived forms, since the entire feature structure output
by the lexical rule might be overridden.  However default inheritance
is constrained by the type system so that information may only be
inherited from a structure of the same or higher type, and thus this
treatment predicts that a derived form can never have a type which is
incompatible with that determined by the lexical rule.

We can illustrate the manner in which this type of semi-productivity
might be dealt with if we assume that we are attempting to construct a
lexicon semi-automatically from a conventional dictionary (e.g.
Copestake, 1990a).
If the result of applying a lexical rule to a sense is
notated as sense+rule-name (eg lamb\_1+animal\_grinding) then the
representation of the sense lamb (2) (``the meat'', from the {\it Longman
Dictionary of Contemporary English} LDOCE) might be:
\begin{verbatim}
lamb 2 < lamb_1+animal_grinding.
\end{verbatim}
In this case
no extra information need be added.  In contrast the entry for
lamb (3) (``a young gentle person'' LDOCE) 
might augment the information inherited from the lexical rule:
\begin{verbatim}
lamb 3 < lamb_1+animal_metaphor
< rqs : age > = low.
\end{verbatim}
In the case of ``haddock'', where no LDOCE entry is found, the structure
derived from the lexical rule alone would be used.

We can regard morphological rules as a particular type of lexical rule
where the orthography of the output is not equal to that of the input
(we assume that the regular spelling changes involved in affixation
will be dealt with by a separate system, e.g. Cahill, 1990).  In this
case we could represent irregular forms as having an orthographic form
which overrides that produced by rule application.  In principle,
multiple lexical rules may be applied in sequence.  
For example the resultative senses of ``replacement'' and ``purchase''
mentioned in the introduction would be the result of applying a
metonymic sense extension rule to the result of the nominalisation process.
All outputs of
lexical rules must be potentially valid lexical entries.  In the case
of conversion or zero-derivational processes we wish to restrict the
set of lexical rules so that application may not be circular --- that
is if there is a lexical rule which could generate the set of feature
structures F2 from the set F1, no other lexical rule or sequence of
lexical rules may be specified which could generate any member of F1,
or a feature structure subsuming any member of F1, starting from any
member of the set F2, since lexical rule application would not then
terminate.  (We can check for such potential
circularities relatively efficiently by looking at the type of the
feature structure that a lexical rule generates rather than the entire
feature structure.)  However, this condition is overrestrictive in
general because some types of derivational rule can apply to their own
output iteratively (``meta-meta-theory'', ``anti-anti-missile'',
``great-great-grandmother'', ``re-re-program''). This observation
suggests that we need to distinguish types of lexical rule, such as at
least derivational rules and processes of conversion, and associate
slightly different constraints with them.

\section{Grinding}

In this section we justify our treatment of grinding as a lexical rule
and show why relatively complex semantic information is needed to
adequately account for this sense extension.

The first point to consider is that grinding processes appear to be
genuinely productive.
Thus we find:
\begin{quote} Badger hams are a
delicacy in China while mole is eaten in many parts of Africa.
\end{quote}
in the Lancaster-Bergen/Oslo (LOB) corpus.
We therefore cannot assume that the ground senses 
are necessarily
lexicalised, even in the relatively conventionalised uses to mean
meat, fur etc. 

One approach which allows for this productivity is to treat 
all nouns as being initially underspecified
with respect to the count/mass distinction.
Thus it is possible to produce a grammar where nouns are 
initially undefined with respect to a syntactic count feature and
where lamb$'$ is, in effect, taken as denoting both animals and meat
and so on
(see the ``p-theory'' in Pelletier and Schubert 1986
and also Copestake 1990b).
In contexts where one interpretation is forced (``a piece of lamb'' vs
``two lambs'') the predicate can be restricted to denote either 
count or the mass senses (in this case either the animal or the meat
senses).
However this seems to predict that NPs such as ``the lamb'' are vague
rather than ambiguous between count and mass readings.  Thus the
peculiarity of sentences such as: 
\begin{quote}
? John fed and carved the lamb.
\end{quote}
is not accounted for (see also the introduction).
It is perhaps significant that in most dictionaries the mass
sense is specified as well as a count sense for the conventionalised
grinding examples we have been considering.
Lexicographers are sometimes
aware of the regularity of the extension (Atkins 1990) but have no way
of representing this in a conventional dictionary.  We thus regard a
noun like ``lamb'' as ambiguous between mass and count senses rather
than vague, and the mass (meat) sense as an extension of the count
(animal) sense,
specified by lexical rule.  (There are cases where it is
reasonable to claim that a nominal should be underspecified with
respect to the count/mass distinction; it is frequently unclear
whether individuation is occurring with nouns like ``data'', however
in the grinding examples there is a clear change in meaning.)

Our current treatment thus has
similarities to the ``s-theory'' of Pelletier and Schubert (1986)
where ``lexical extension
rules'' are used to produce mass nouns from count nouns.
However these rules merely change the value of the syntactic count
feature, apply a predicate operator which is the
same for all cases of grinding,
and mark the mass sense resulting 
as ``+EXT'' which is supposed to suggest that
it is in some way abnormal.  This is clearly inadequate:
\begin{quote}
John carved the lamb.
\end{quote}
would be marked ``+EXT'' for the reading where lamb was used in a mass
sense and not for the count sense reading.
By having an inheritance ordering on lexical rules we can express the
conventionalised processes that apply to semantically specified
parts of the lexicon  
and account for the possibility of multiple
distinct mass senses being possible; for example ``rabbit'' is given
distinct senses in LDOCE for the meat and the fur, and (in context) an
underspecified sense is available:
\begin{quote}
After several lorries had run over the body, there was
rabbit splattered all over the road.
\end{quote}

Although
the denotation of the count sense and
the mass sense are distinct there clearly is some
relationship between them.  
A full account of sense extension must be able to represent relationships
between the senses' denotations.
For grinding in general the most specific
claim that can apparently be made is that the ground sense denotes
some ``stuff'' which was at some past time part of one or more
individuals denoted by the count sense.
(We can formally specify this relationship between the ground sense $G$
and the base sense $B$ as 
\begin{quote}
$\forall x, t [ G(x, t) \implies \exists y, t' [ \clos{B}(y, t') \wedge
t'\leq t \wedge x \opart y ]]$
\end{quote}
using the formalisation developed in Copestake (1990a) following
Krifka (1987) where nominal predicates are taken as being true of
quantities of matter at some time index, where $\clos{B}$ 
denotes a potentially plural entity,
and where $\opart$ represents
a relationship of material constituency.
In the lexicon we actually use a feature {\sc origin} which can 
be taken as an abbreviation for the relationship
specified above.)

A good theory of sense extension should give some treatment of
blocking, which appears to occur with some cases of regular sense
extension in a way that seems similar to derivational morphology.  For
example the use of ``pig'' to denote the meat seems to be blocked by
the existence of ``pork'' --- ``pig'' can be used in the extended
sense but such a use is marked, suggesting for example that the meat
is distinctly inferior.  To account for this we need to be able to
recognise that ``pork'' is equivalent to the sense obtained from
``pig'' using the lexical rule.  Although there are many problems with
this (what do we mean by equivalence, why does this apparently not
apply to metaphorical sense extension) in order to do it at all we
clearly need a rich representation which indicates information such as
``origin''.

Bauer (1983) distinguishes two types of non-productivity (which he
refers to as {\it established} senses) -- lexicalisation and
institutionalisation. Lexicalisation is defined as irregular and
unpredictable modification of some or all of the semantic, syntactic
or phonological properties of a derived form. Institutionalisation, by
contrast, involves restriction, rather than modification along one of
these dimensions; thus ``telephone box'' is institutionalised to mean
telephone kiosk unambiguously, although the liberal rules of noun
compounding predict other possibilities. In our approach, we can treat
institutionalisation as a form of blocking in which forms such as
``telephone box'' would have separate entries equivalent to one
productive meaning predicted by a putative lexical rule of
compounding. This would predict a strong preference for this
interpretation (except in a marked context). Bauer (1983:58) points
out that some treatment along these lines will be required since the
other meanings are not completely ruled out, and therefore simply
listing them as independent entries will be inadequate. The more
specific rules of grinding (as opposed to the most general rule) are
instances of productive institutionalisation within sub-classes in that
the specific interpretations they introduce can be overridden in
marked contexts.

Similarly, lexicalisation is usually a partial process which affects
one aspect of a derived lexical entry, whilst the rest remains
productive. Bauer gives the example of ``disbelieve'' which can
be productively derived through a lexical rule which prefixes ``dis+''
to the verb ``believe'' with a predictable change of meaning, except
that ``disbelieve'' does not inherit the syntactic properties of
``believe'' because it cannot take sentential or infinitival
complements. The productive aspects of the relation between the two
verbs can be expressed by a lexical rule for ``dis+'' prefixation,
whilst the non-productive aspects can be captured naturally in this
framework by positing an independent entry for ``disbelieve'' which
overrides some of the information provided by the lexical rule.

We think of lexical rules as defining the limits of coercion amongst
lexemes and argue that lexical rule application, or 
selection of the derived entry (which is equivalent in
many cases), will be forced when the
type of the basic entry is incompatible with the syntactic or
predicational context in which the lexeme occurs. Consider
the following example, taken from the Lancaster-Bergen/Oslo (LOB)
corpus:
\begin{quote} 
More
than 1,000 union men and their families arrived to play bowls, eat
barbecued chicken and row on his fish-infested lake.  
\end{quote} 
The application of a grinding lexical rule is
triggered by a combination of syntactic and semantic effects arising
from the context (for example the predicate ``eat''
takes an object denoting food in preference to an animal,
the bare NP ``mole'' in the earlier example
must have a
negative value for the syntactic feature count).  By
default, the most specific lexical rule applicable will be used, in
this case ``animal\_grinding'' as opposed to the general grinding rule 
and so the interpretation of
``chicken'' as ``chicken-flesh'' and ``mole'' as ``mole-flesh'' is
possible, by default. More open-ended (non-lexical) reasoning might
cause the default interpretation of the mass sense to be overridden in
some marked informationally-rich contexts. 
For example:
\begin{quote}
John bit into the lamb.\\
It kicked and struggled.
\end{quote}
We assume a similar account of the overriding of default
interpretations with these types of example as we offered in the case
of logical metonymies (Briscoe et al., 1990).

\section{Conclusion}

We have argued that our notion of lexical rule can capture the
productive linguistic element of derivational morphological processes
and metonymic and metaphorical sense extensions.  In order to do this
adequately we need rich lexical semantic information but we do not
need to resort to general deductive or abductive inference on
unconstrained world knowledge.  By using semantic information to
structure the lexicon, by means of types and inheritance, we can
represent relationships between lexical rules and view them as
essentially fully productive over defined subparts of the lexicon, while
providing an initial 
account of blocking and lexicalisation.
However the work described here is at a preliminary stage.  We need to provide
detailed accounts of a range of derivation and conversion
processes to see how adequately we can
represent them as lexical rules, while structuring the lexicon and type
system appropriately to constrain their operation.

\section*{Acknowledgements}
This 
work was supported by Esprit BRA-3030,
ACQUILEX `The Acquisition of lexical knowledge
for Natural Language Processing systems'. 

\section*{References}
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{\it #3}}
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#3,} #4, pp.#5}
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#3,} #4}

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\end{document}


