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\begin{document}

\begin{center}
{\Large\bf
Inheritance in lexical representation}\\
{\bf Ann Copestake}\\
CSLI, Stanford University,\\
Stanford, CA 94305, USA\\
{\tt aac@csli.stanford.edu}
\end{center}

\section{Introduction}

In this abstract I give an overview of some recent work on 
inheritance in lexical
representation.  I have not attempted to be comprehensive, in
particular, I will concentrate on work within unification or constraint based
approaches.  Since this overview can necessarily only
be very sketchy, I have given a fairly extensive bibliography.
See in particular, 
Daelemans \etal\ (1992) which gives an extensive review of inheritance in
natural language processing, and the collection of papers in 
Briscoe \etal\ (1993).

It is necessary for a theoretically
adequate lexical representation language to be able to
capture linguistically relevant generalisations about classes
of items which behave in similar ways with respect to phonology,
morphology, syntax or semantics.  Such mechanisms are now 
standardly assumed in the computational linguistics literature, but
for some examples of linguistic works where inheritance is explicitly
discussed, see
Pollard and Sag, 1987; Flickinger, 1987; 
Flickinger and Nerbonne, 1992; Sanfilippo, 1993.
One of the most important techniques is to specify constraints on
classes of lexical item, which will be inherited by subclasses.  
In some ways this is very similar to techniques from object-oriented 
programming, and indeed several researchers have explicitly used 
object-oriented techniques (e.g.~Daelemans,
1987).  But, in general, the assumption
is that special-purpose data structures are appropriate for linguistic
representation and that the operations available on these structures
should be restricted. 

It is sometimes assumed that the lexicon
will be compiled off-line: i.e.~all the lexical entries will be
expanded before parsing takes place.  This is, however, not feasible
for anything other than 
restricted domain systems if a lexicalist grammar framework
(e.g.~LFG, HPSG, categorial grammar)
is being assumed.  For example, a fully 
expanded entry in the ACQUILEX LKB system (e.g.~Copestake \etal, 1993) for an 
intransitive verb occupies about 10K of memory  
(using a categorial grammar with no detailed lexical
semantic information). 
Even a moderate
coverage lexicon would
have to contain at least 50,000 such entries (i.e.~it would occupy 500
Megabytes).\footnote{This estimate is conservative.
Learner's dictionaries of English 
tend to contain around
50,000 headwords, but many of these would be expanded into multiple
lexical structures. 
Furthermore, many grammars have more complex lexical structures than this.}
Obviously, data compression techniques could be
used to reduce the information stored, but standard compression
algorithms will only reduce the size of the entry by a factor of two or
so, whereas the use of
inheritance can easily reduce it by a factor of 100.  
Inheritance is therefore relevant from a computational viewpoint, as
well as a theoretical one.

The final reason for wanting to capture generalisations as efficiently
and perspicuously as possible, is to simplify the task of 
constructing, developing and maintaining a lexicon.  Strict inheritance
ensures consistency, e.g.~all intransitive verbs have to have the
properties specified for that class.  More stringent consistency
checks are possible, to ensure that a lexical entry 
does not have any spurious attributes, for example.  
Default inheritance, on the
other hand, allows for exceptions.  A default inheritance hierarchy can
always be reconstructed as a strict hierarchy, but at a cost of
increasing the number of classes and of making the generalisations less
obvious.  One of the main questions in lexical representation is whether
defaults should be used, and if so, how their use can be formalised. 
I discuss some recent work in \S\ref{defaults}, after briefly
considering monotonic inheritance and typed feature structures.


\section{Inheritance and typed feature structures}

Most computational
linguistic systems have some mechanism for
inheritance.  Most basically, a device is provided so that a name can be
provided as an abbreviation for a set of descriptions: if the
descriptions can include other abbreviatory names this gives an
equivalent effect to an inheritance hierarchy.
I will use the term {\it template}, as
in PATR-II (Shieber, 1986), for this style of inheritance mechanism,
though they are also often referred to as {\it macros}.   
Templates are part of the language for describing feature structures
({\sc fs}s)
and lexical entries in particular,
rather than being themselves part of the feature structure language.
The top of 
Figure~\ref{temptypes} shows an example of the use of templates.

One deficiency of languages such as PATR-II was that values were either
totally underspecified, in which case they were compatible with any
other value, or fully specified, in which case they were only
compatible with an identical value.  This could lead to very cumbersome
encodings being necessary, especially for selectional restrictions.  
One natural way
round this was to allow values to be partially specified using {\it sort}s
(e.g.~Calder, 1989), which allowed hierarchies to be directly encoded.  
Full sorted or typed feature structure languages take this
a step further, so that sorts (also known as types)
are associated
with every node in an {\sc fs}, not just the
terminal ones.  Constraints can be specified on sorts: these must be
satisfied by every {\sc fs} which has that sort, or any of its
subsorts. 
This, in effect,
makes inheritance a built-in part of the feature structure language.
HPSG (Pollard and Sag, 1987, 1994) uses this notion of sorts, but other
linguistic frameworks can also be implemented within a sorted (typed) feature
structure language.  

Sort
hierarchies with constraints differ fundamentally from 
templates in that the constraints on {\sc
fs}s are assumed to apply uniformly, however the {\sc
fs} arises, whereas templates only apply during a preliminary
processing phase associated with the evaluation of {\sc fs}
descriptions.  If we consider a description of a template as
inheriting from two template {\sc fs}s, the result will be subsumed by
their unification, just as a subtype of two sorts will have a
constraint which is subsumed by the unification of the constraints on
its parents.  But while templates are restricted to the descriptive
metalanguage, types are a part of the object language.  Thus, if we
define two templates, Intrans-verb and Monadic as shown in
Figure~\ref{temptypes} and define Monadic-stative-intrans-verb to
inherit from both of them, this does not affect the result of
unification of two {\sc fs}s which happen to be equal to the template
descriptions.  In contrast, consider the type system also shown in
Figure~\ref{temptypes}, which implies that whenever two {\sc fs}s of
types {\bf intrans-verb} and {\bf monadic} are unified, the result
must be of type {\bf monadic-stative-intrans-verb}, and therefore, to
be well-formed, must be subsumed by its constraint, which in this case
is more
specific than the unification of its parent constraints.
\begin{figure}
\begin{verbatim}
Intrans-verb
< SYN CAT > = verb
< SYN SUBJ SYN CAT > = np

Monadic
< SEM PRED > = pred
< SYN SUBJ SEM > = < SEM PRED ARG1 >

Monadic-stative-intrans-verb 
Monadic Intrans-verb
< SEM PRED > = stative
\end{verbatim}
\begin{tabular}{lll}
{\bf intrans-verb}  & $\implies$ & 
{\tiny
$\avmplus{\attval{SYN}{\avmplus{
             \attvaltyp{CAT}{verb}  \\
             \attval{SUBJ}{\avmplus{
                \attval{SYN}{\avmplus{
                         \attvaltyp{CAT}{np}}}}}}}}$
}\\[4mm]
{\bf monadic}  & $\implies$ & 
{\tiny
$\avmplus{\attval{SYN}{\avmplus{            
             \attval{SUBJ}{\avmplus{
                \attval{SEM}{\ind{1}}}}}} \\
         \attval{SEM}{\avmplus{
                  \attvaltyp{PRED}{pred}\\
                  \attval{ARG1}{\ind{1}}}}}$
}\\[4mm]
{\bf monadic-stative-intrans-verb}  & $\implies$ & {\bf monadic} $\wedge$
{\bf intrans-verb} $\wedge$
{\tiny
$\avmplus{\attval{SEM}{\avmplus{
                  \attvaltyp{PRED}{stative}}}}$}
\end{tabular}
\caption{Templates and sorts/types}
\label{temptypes}
\end{figure}

Confusingly, there are several
versions of typed feature structure languages (including 
Carpenter, 1992; Gerdemann and King, 1994; Krieger and Sch\"{a}fer, 1994;
Emele and Zajac, 1990; D\"{o}rre and Eisle, 1991; Smolka, 1989; 
Copestake \etal, 1993; Alshawi \etal, 1991).
Not all of these languages would allow the constraint specification
shown in Figure~1.
The function of sorts with respect to consistency checking is sometimes
emphasised rather more than their role in providing inheritance.
Recursive constraint specifications give systems enough power to
implement parsers and generators directly, though not very tractably
(see Carpenter, 1992; Emele and Zajac, 1990).
Several of the systems
mentioned above, however, compile out phrasal constraints to give
conventional grammar rules, in order to allow standard parsing
techniques to be used.

The systems mentioned above are all monotonic.  If they allow for
defaults at all, they do so as part of the description language:
i.e. they allow some version of default templates as well as sorts.


\section{Default inheritance}
\label{defaults}

Many authors have argued for the utility of defaults in inheritance-based
accounts of lexical organisation (e.g.~Boguraev and Pustejovsky, 1990;
Briscoe \etal, 1990; Lascarides and Copestake, 1995a;
Vossen and Copestake, 1993; Daelemans 1987; Evans
and Gazdar 1989a,b; Flickinger \etal, 1985; Flickinger, 1987;
Flickinger and Nerbonne, 1992; Krieger and Nerbonne, 1993; Shieber,
1986a and others).  One frequent motivation is to capture phenomena of
blocking, or the overriding of regularities by subregularities (e.g.
Calder, 1989; Copestake and Briscoe, 1992; Briscoe \etal, 1995).
Approaches to formalising and implementing inheritance-based lexicons
include utilising object-oriented programming techniques (Daelemans,
1987; Flickinger \etal, 1985), knowledge representation languages
(Pustejovsky and Boguraev, 1993; Flickinger, 1987), overwriting templates
(Karttunen, 1986; Shieber, 1986a) and various definitions of default
unification (see below). 

In order to provide an account of defaults which is closely
integrated with the usual monotonic operations on {\sc fs}s, 
it is natural to assume a notion of default unification.
Most definitions (e.g. Bouma
1990, 1992; Copestake, 1993; Carpenter, 1993; Russell \etal, 1991,
1993)
have followed Kaplan (1987) in assuming that this is
an asymmetric binary operation, with one default {\sc fs} being
regarded as adding consistent information to a non-default {\sc fs}.
The result is taken to be either a single {\sc fs} or a disjunction of
{\sc fs}s.  Although this asymmetry is useful for some applications,
it is not ideal for lexical inheritance, because
inheritance
order must be stipulated, since default unification is not
associative under any of these definitions. Apart from this,
individual specifications of defaults which pertain to a class cannot
be evaluated incrementally with an asymmetric operation because the
information contributed by earlier defaults becomes non-default.
Furthermore, non-associativity makes default unification unsuitable
for use in situations where the application of defaults cannot be
circumscribed.  

Young and Rounds (1993),
Lascarides \etal\ (in press) and Lascarides and
Copestake (1995b) attempt to address this problems by defining a symmetric,
order independent version of default unification on typed feature
structures.  In these accounts, defeasible (i.e.~default)
information is marked explicitly in {\sc fs}s rather than treating
default unification as an asymmetric operation on a 
defeasible {\sc fs} and an indefeasible {\sc fs}.  
The defeasible information, if it
survives unification, persists as defeasible information, via the
explicit marking.  Lascarides \etal\ refer to
this approach as `persistent' default
unification.

Lascarides and Copestake (1995b) argue that
ideally, default unification should have the following characteristics:
\begin{enumerate}
\item Non-default information can be distinguished from
default information and is always preserved.
\item Default unification behaves like monotonic unification in the
cases where monotonic unification would succeed.
\item Default unification returns a single result, deterministically.
\item Defaults can be given a precedence ordering such that more
specific information overrides less specific information.
(Young and Rounds (1993) definition does not meet this criterion and
Lascarides \etal\ (in press) does not meet it completely.)
\item Default unification can be described using a binary, order
independent (i.e., commutative and associative) operation.
\item Default unification never fails unless there is conflict in
non-default information.
\end{enumerate}
 
A trivial example of the use of the version of default unification
described by Lascarides and Copestake (1995b) is given in
Figure~\ref{final-eg}.   
This is a schematic 
representation of the morphology of English verbs where there is
an attribute for the past tense form (PST)
and another for the past particle (PSP).
Normally
these are the same, and this can be represented by default reentrancy
(coindexation) as
shown in the constraint for {\bf regular-verb}.
The notation uses a slash to delimit the
default part of the {\sc fs} from the non-default. 
The PST and PSP forms differ 
in some classes of irregular verbs
(e.g. {\it speak, spoke, spoken}), here given as {\bf psp-diff-vb},
and thus the reentrancy has to be overridden, but the
specification of the vowel change and suffixation for this 
class is itself stated as defeasible, because of verbs such as {\it weave} 
which are also found with the regular suffixation pattern
({\it wove}/{\it weaved}, {\it woven}/{\it weaved}). 

The constraints on types are thus a combination of non-default and
default information, and the specificity ordering on the defaults is
given by the type hierarchy.  In this approach, therefore, both
non-default and default inheritance is fully integrated into the object
language.  This therefore differs
from systems such as DATR, where the default description language is separate
from the feature structure language.  
I have given the morphology example for expository purposes, but for more
motivation for the use of persistent defaults, see Lascarides \etal\ (in
press) and also Lascarides and Copestake (1995a).
\begin{figure}
\setlength{\unitlength}{0.5in}
\begin{center}
\begin{picture}(2.5,4.0)(-0.25, -0.1)
\thicklines
\put(1, 3.9){\makebox(0,0){{\tiny $\avmplus{\att{verb}\\
\attval{PST}{/\myvaluebold{+ed}}}$}}}
\put(1, 3.6){\line(0, -1){0.5}}
\put(1, 2.6){\makebox(0,0){{\tiny $\avmplus{\att{regular-verb}\\
\attval{PST}{/\ind{1}}\\ \attval{PSP}{/\ind{1}}}$}}}
\put(1, 2.1){\line(-1, -1){0.5}}
\put(1, 2.1){\line(1, -1){0.5}}
\put(0, 1.3){\makebox(0,0){{\tiny $\avmplus{\att{pst-t-vb}\\ \attvaltyp{PST}{$/$+t}}$}}}
\put(2.1, 1.3){\makebox(0,0){{\tiny $\avmplus{\att{stg-vb}\\ \attvaltyp{PST}{$/$stg-vow}}$}}}
\put(2, 1){\line(0, -1){0.5}}
\put(2.2, 0){\makebox(0,0){{\tiny $\avmplus{\att{psp-diff-vb}\\ \attvaltyp{PSP}{$/$+en}}$}}}
\end{picture}
\end{center}
\caption{Default Inheritance Hierarchy}
\label{final-eg}
\end{figure}

\section*{References}

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#5.}
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\newcommand{\forthjournart}[4]{\item #1 (#4) `#2', {\it #3,}}
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#3,} #4, pp.~#5.}
\newcommand{\forthprocart}[5]{\item #1 (#5) `#2', 
to appear in {\it Proceedings of the #3,} #4}
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#3,} #4.}

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

\unpub{Alshawi, H., D.J.~Arnold, R.~Backofen, D.M.~Carter, J.~Lindop,
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\procart{Briscoe, E.J., A.~Copestake and B.K.~Boguraev}
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\book{Briscoe, E.J., A.~Copestake and V.~de~Paiva (eds)}
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\bookart{Briscoe, E.J., A.~Copestake and A.~Lascarides}
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application to templates and inheritance}
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    {1993}


\bookart{Copestake, A.}
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    {223--245}
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\unpub{Copestake, A.}
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{Doctoral dissertation, University of Sussex,
available as Cognitive Science Research Paper CSRP 280}
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{15--67}
{1995}

\bookart{Copestake, A., A.~Sanfilippo,
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    {The ACQUILEX LKB: an introduction}
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\journart{Daelemans, W., K.~de Smedt and G.~Gazdar}
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\unpub{D\"{o}rre, J. and A.~Eisle} 
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\procart{Emele, M. and R.~Zajac}
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        {293--298} 
        {1990}

\procart{Evans, R. and G.~Gazdar}
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{4th Conference of the European Chapter of the Association 
for Computational Linguistics (EACL-1989)}
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{66--71}
{1989a}

\bookart{Evans, R. and G.~Gazdar}
{The semantics of DATR}
{79--87}
{Proceedings of the Seventh Conference of
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\unpub{Flickinger,  D.}
        {Lexical rules in the hierarchical lexicon}
        {PhD thesis, Stanford University} 
        {1987}


\procart{Flickinger, D., C.~Pollard and T.~Wasow}
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        {23rd Annual Meeting of the Association for Computational
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        {University of Chicago}
        {262--268}
        {1985} 



\journart{Flickinger, D. and J.~Nerbonne}
{Inheritance and complementation: A case study of {\it easy}
adjectives and related nouns}
         {Computational Linguistics}
         {18.3}
         {269--310}
         {1992}



\procartnopp{Gerdemann, D. and P.~King}
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specifications for typed feature structures}
      {15th Int. Conf. on Comp. Ling. (COLING-94)}
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\bookart{Kaplan, R.}
  {Three seductions of computational psycholinguistics}
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  {P.~Whitelock, H.~Somers, P.~Bennett, R.~Johnson, and M.~McGee Wood}
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\procart{Karttunen, L.}
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grammars}
        {11th Int. Conf. on Comp. Ling. (COLING-86)}
        {Bonn, Germany}
        {74--80}
        {1986}

\bookart{Kreiger, H. and J.~Nerbonne}
    {Feature-based inheritance networks for computational lexicons}
    {90--136}
    {Inheritance, defaults and the lexicon}
    {E.~J.~Briscoe, A.~Copestake and V.~de~Paiva}
    {Cambridge University Press, Cambridge, England}
    {1993}

\unpub{Krieger, H-U, and U.~Sch\"{a}fer}
   {TDL --- A type description language for HPSG}
   {DFKI, Saarbr\"{u}cken, Germany}
   {1994}

\procartnopp{Lascarides, A. and A.~Copestake}
{The pragmatics of word meaning}
{SALT V}
{Cornell University}
{1995a}

\unpub{Lascarides, A. and A.~Copestake}
        {A logic for order independent typed default unification}
        {{\sc acquilex} research report}
        {1995b}


\forthjournart{Lascarides, A., E.J.~Briscoe, N.~Asher and A.~Copestake}
{Order independent and persistent typed default unification}
{Linguistics and Philosophy}
{1995}

\book{Pollard,  C. and I. Sag}
 {An information-based approach to syntax and semantics: 
Volume~1 fundamentals} 
 {CSLI Lecture Notes 13, Stanford CA}
 {1987} 

\book{Pollard, C. and I. Sag}
    {Head-driven Phrase Structure Grammar}
    {{\sc csli} lecture notes series,
     Chicago University Press, Chicago}
    {1994}

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

\procart{Russell, G., J.~Carroll and  S.~Warwick}
{Multiple default
inheritance in a unification-based lexicon} 
{29th Annual Meeting of the Association for Computational 
Linguistics (ACL-91)}
{Berkeley, California}
{215--221}
{1991}

\bookart{Russell, G., A.~Ballim,
J.~Carroll and  S.~Warwick-Armstrong}
{A practical approach to multiple default inheritance for unification-based 
lexicons}
    {137--147}
    {Inheritance, defaults and the lexicon}
    {E.~J.~Briscoe, A.~Copestake and V.~de~Paiva}
    {Cambridge University Press, Cambridge, England}
    {1993}


\bookart{Sanfilippo, A.}
    {LKB encoding of lexical knowledge}
    {190--222}
    {Inheritance, defaults and the lexicon}
    {E.~J.~Briscoe, A.~Copestake and V.~de~Paiva}
    {Cambridge University Press, Cambridge, England}
    {1993}

\book{Shieber, S.~M.}
{An introduction to unification-based approaches to grammar}
{CSLI Lecture Notes 4, Stanford CA}
{1986}

\unpub{Smolka, G.}
   {Feature constraint logic for unification grammars}
   {IWBS Report 93, IWBS-IBM, Stuttgart, Germany}
   {1989}

\bookart{Vossen, P. and A.~Copestake}
    {Untangling definition structure into knowledge representation}
    {246--274}
    {Inheritance, Defaults and the Lexicon}
    {E.~J.~Briscoe, A.~Copestake and V.~de~Paiva}
    {Cambridge University Press, Cambridge, England}
    {1993}


\procart{Young, M. and W.~Rounds}
        {A logical semantics for nonmonotonic sorts}
        {31st Annual Meeting of the Association for 
Computational Linguistics (ACL-93)}
        {Columbus, Ohio}
        {209--215}
        {1993}



\end{list}
}

\noindent ACQUILEX Technical reports can be obtained by emailing a request
to {\tt cide@cup.cam.ac.uk} ---
many ACQUILEX papers are also available by ftp from 
{\tt ftp://ftp.cl.cam.ac.uk/papers/acquilex/} 

\end{document}



