Báo cáo khoa học: "Encoding Lexicalized Tree Adjoining Grammars with a Nonmonotonic Inheritance Hierarchy" potx

T h e issue of efficient representation for I_'rAG 1 is discussed by Vijay-Shanker & Schabes 1992, who 1As with all fully lexicMized grammar formalisms, there is really no conceptual dis

E n c o d i n g L e x i c a l i z e d Tree A d j o i n i n g G r a m m a r s w i t h a

N o n m o n o t o n i c I n h e r i t a n c e H i e r a r c h y

R o g e r E v a n s

I n f o r m a t i o n T e c h n o l o g y

R e s e a r c h I n s t i t u t e

U n i v e r s i t y o f B r i g h t o n

G e r a l d G a z d a r

S c h o o l o f C o g n i t i v e

C o m p u t i n g S c i e n c e s

U n i v e r s i t y o f S u s s e x

g e r a l d g © c o g s , susx ac uk

D a v i d W e i r

S c h o o l o f C o g n i t i v e ~z

C o m p u t i n g S c i e n c e s

U n i v e r s i t y o f S u s s e x

d a v ± d w © c o g s , s u s x a c u k

A b s t r a c t This paper shows how DATR, a widely used

formal language for lexical knowledge re-

presentation, can be used to define an I_TAG

lexicon as an inheritance hierarchy with in-

ternal lexical rules A b o t t o m - u p featu-

ral encoding is used for LTAG trees and

this allows lexical rules to be implemen-

ted as covariation constraints within fea-

ture structures Such an approach elimina-

tes the considerable redundancy otherwise

associated with an LTAG lexicon

1 I n t r o d u c t i o n

T h e Tree Adjoining G r a m m a r (lAG) formalism was

first introduced two decades ago (3oshi et al., 1975),

and since then there has been a steady stream of

theoretical work using the formalism But it is

only more recently that g r a m m a r s of non-trivial size

have been developed: Abeille, Bishop, Cote & Scha-

bes (1990) describe a feature-based Lexicalized Tree

Adjoining G r a m m a r ([_'lAG) for English which sub-

sequently became the basis for the g r a m m a r used in

the XTAG system, a wide-coverage [_TAG parser (Do-

ran et al., 1994b; Doran et al., 1994a; XTAG Rese-

arch Group, 1995) T h e advent of such large gram-

mars gives rise to questions of efficient representa-

tion, and the fully lexicalized character of the [TAG

formalism suggests that recent research into lexical

representation might be a place to look for answers

(see for example Briscoe ef a/.(1993); Daelemans &

Gazdar(1992)) In this paper we explore this sugge-

stion by showing how the lexical knowledge repre-

sentation language (LKRL) DA'lR (Evans & Gazdar,

1989a; Evans & Gazdar, 1989b) can be used to for-

mulate a compact, hierarchical encoding of an [-'lAG

T h e issue of efficient representation for I_'rAG 1 is

discussed by Vijay-Shanker & Schabes (1992), who

1As with all fully lexicMized grammar formalisms,

there is really no conceptual distinction to be drawn in

I_TAG between the lexicon and the grammar: tile gram-

rnatical rules are just lexical properties

draw attention to the considerable redundancy in- herent in [-TAG lexicons t h a t are expressed in a flat

m a n n e r with no sharing of structure or properties across the elementary trees For example, XTAG cur- rently includes over 100,000 lexemes, each of which

is associated with a family of trees (typically around 20) drawn from a set of over 500 elementary trees Many of these trees have structure in common, many

of the lexemes have the same tree families, and m a n y

of the trees within families are systematically rela- ted in ways which other formalisms capture using transformations or metarules However, the [TAG formalism itself does not provide any direct support for capturing such regularities

Vijay-Shanker & Schabes address this problem by introducing a hierarchical lexicon structure with mo- notonic inheritance and lexical rules, using an ap- proach loosely based on t h a t of Flickinger (1987) but tailored for [TAG trees rather t h a n HPSG sub- categorization lists Becker (1993; 1994) proposes a slightly different solution, combining an inheritance component and a set of metarules 2 We share their perception of the problem and agree t h a t adopting

a hierarchical approach provides the best available solution to it However, rather than creating a hier- archical lexical formalism that is specific to the [_TAG problem, we have used DATR, an LKR.L that is al- ready quite widely known and used From an [TAG perspective, it makes sense to use an already availa-

these kinds of representational issues From a DATR perspective, I_TAG presents interesting problems ari- sing from its radically lexicalist character: all gram- matical relations, including unbounded dependency constructions, are represented lexically and are thus open to lexical generalization

There are also several further benefits to be gai- ned from using an established general purpose LKRL such as DATR First, it makes it easier to compare the resulting [TAG lexicon with those associated with other types oflexical syntax: there are existing DATR

2See Section 6 for further discussion of these approaches

7 7

lexicon fragments for HPSG, PATR and Word G r a m -

mar, among others Second, DATR is not restricted

to syntactic description, so one can take advantage

of existing analyses of other levels of lexical descrip-

tion, such as phonology, prosody, morphology, com-

positional semantics and lexical semantics 3 Third,

one can exploit existing formal and implementation

work on the language 4

S

V o N P I P P

Figure 1: An example LTAG tree for give

T h e principal unit of (syntactic) information asso-

ciated with an LTAG entry is a tree structure in which

the tree nodes are labeled with syntactic categories

and feature information and there is at least one

leaf node labeled with a l e x i c a l category (such lexi-

cal leaf nodes are known as a n c h o r s ) For example,

the canonical tree for a ditransitive verb such as give

is shown in figure 1 Following LTAG conventions

(for the time being), the node labels here are gross

syntactic category specifications to which additional

featural information m a y be added 5, and are anno-

t a t e d to indicate node t y p e : <> indicates an anchor

node, and I indicates a substitution node (where a

3See, for example, Bleiching (1992; 1994), Brown &

Hippisley (1994), Corbett & Fraser (1993), Cahill (1990;

1993), Cahill &: Evans (1990), Fraser &= Corbett (in

press), Gibbon (1992), Kilgarriff (1993), Kilgarriff &

Gazdar (1995), Reinhard & Gibbon (1991)

4See, for example, Andry et al (1992) on compila-

tion, Kilbury et al (1991) on coding DAGs, Duda & Geb-

hardi (1994) on dynamic querying, Langer (1994) on re-

verse querying, and Barg (1994), Light (1994), Light et

al (1993) and Kilbury et al (1994) on automatic ac-

quisition And there are at least a dozen different DATR

implementations available, on various platforms and pro-

gramming languages

Sin fact, [TAG commonly distinguishes two sets of

features at each node (top and bottota), but for simpli-

city we shall assume just one set in this paper

fully specified tree with a compatible root label may

be attached) 6

In representing such a tree in DATR, we do two things First, in keeping with the radically lexica- list character of LTAG, we describe the tree structure from its (lexical) anchor upwards 7, using a variant

of Kilbury's (1990) b o t t o m - u p encoding of trees In this encoding, a tree is described relative to a parti- cular distinguished leaf node (here the anchor node), using binary relations p a x e n t , l e f t and r i g h t , re- lating the node to the subtrees associated with its parent, and immediate-left and -right sisters, enco- ded in the same way Second, we e m b e d the resulting tree structure (i.e., the node relations and type in- formation) in the feature structure, so t h a t the tree relations ( l e f t , r i g h t and p a r e n t ) become features

T h e obvious analogy here is the use of f i r s t / r e s t features to encode subcategorisation lists in frame- works like HPSG

Thus the syntactic feature information directly as-

sociated with the entry for give relates to the label

for the v node (for example, the value of its c a t fea- ture is v, the value of t y p e is emchor), while speci- fications of subfeatures of p a r e n t relate to the label

of the vP node A simple b o t t o m - u p DATR represen- tation for the whole tree (apart from the node type information) follows:

G i v e :

<cat> v

<parent c a t > = v p

< p a r e n t l e f t c a t > = n p

<parent parent c a t > = s

<right cat> = n p

<right right cat> = p

<right right parent cat> = pp

<right right right cat> = n p

This says t h a t Give is a verb, with vp as its pa- rent, an s as its g r a n d p a r e n t and an NP to the left

of its parent It also has an NP to its right, and a tree rooted in a P to the right of that, with a PP parent and NP right sister T h e implied b o t t o m - u p tree structure is shown graphically in figure 2 Here the nodes are laid out just as in figure 1, b u t rela- ted via p a r e n t , l e f t and r i g h t links, rather than the more usual (implicitly ordered) daughter links Notice in particular t h a t the r i g h t link from the

object noun-phrase node points to the preposition

node, not its phrasal parent - this whole subtree is itself encoded b o t t o m - u p Nevertheless, the full tree structure is completely and accurately represented

by this encoding

s LTAG's other tree-building operation is a d j u n e t i o n , which allows a tree-fragment to be spliced into the body

of a tree However, we only need to concern ourselves here with the r e p r e s e n t a t i o n of the trees involved, not with the substitution/adjunction distinction

rThe tree in figure 1 has more than one anchor - in such cases it is generally easy to decide which anchor is the most appropriate root for the tree (here, the verb anchor)

n p °

a r e n t

v p

l e f t /

p a r e n t

" n p

r i g h t ~

r i g h t k

P

P P

a r e n t

n p

r i g h t

Figure 2: B o t t o m - u p encoding for G i v e

Once we a d o p t this representational strategy, wri-

ting an LTAG lexicon in DATR becomes similar to

writing any other type of lexicalist g r a m m a r ' s le-

xicon in an inheritance-based LKRL In HPSG, for

example, the subcategorisation frames are coded as

lists of categories, whilst in LTAG they are coded as

trees But, in b o t h cases, the p r o b l e m is one of con-

cisely describing feature structures associated with

lexical entries and relationships between lexical ent-

ries T h e s a m e kinds of generalization arise and the

s a m e techniques are applicable O f course, the pre-

sence of complete trees and the fully lexicalized ap-

proach provide scope for capturing generalizations

lexically t h a t are not available to approaches t h a t

only identify parent and sibling nodes, say, in the

lexical entries

Following conventional models of lexicon organisa-

tion, we would expect G i v e to have a m i n i m a l syn-

tactic specification itself, since syntactically it is a

completely regular ditransitive verb In fact n o n e

of the i n f o r m a t i o n introduced so far is specific to

Give So rather t h a n providing a completely expli-

cit DATR definition for Give, as we did above, a m o r e

plausible account uses an inheritance hierarchy defi-

ning a b s t r a c t intransitive, transitive and ditransitive

verbs to s u p p o r t G i v e ( a m o n g others), as shown in

figure 3

This basic organisational structure can be expres-

sed as the following DATR fragmentS:

8To gain the intuitive sense of this fragment, read

a line such as <> = VERB as "inherit everything from

the definition of VERB", and a line such as <parent> ==

PPTREE:<> as "inherit the p a r e n t subtree from the de-

finition of PPTREE' Inheritance in DATR is always by

default - locally defined feature specifications take prio-

rity over inherited ones

E a t V E K B + N P + P P V E R B + N P + N P

G i v e S p a r e Figure 3: T h e principal lexical hierarchy

VERB:

<> - - T R E E N O D E

< c a t > = = v

< t y p e > = = a n c h o r

< p a r e n t > = s V P T R E E : < >

V E R B + N P :

<> = = V E R B

< r i g h t > = = N P C O M P : < >

V E R B + N P + P P :

<> - = V E R B + N P

< r i g h t r i g h t > = = P T K E E : < >

< r i g h t r i g h t r o o t > = = to

V E R B + N P + N P :

<> = = V E B B + N P

< r i g h t r i g h t > = = N P C O M P : < >

Die:

<> = = V E R B

< r o o t > = = die

Eat:

<> = = V E K B + N P

< r o o t > = = eat

Give:

<> = = V E R B + N P + P P

< r o o t > = = give

Spare:

<> = = V E R B + N P + N P

< r o o t > = = spare

Ignoring for the m o m e n t the references to

T R E E N O D E , V P T R E E , N P C O M P a n d P T R E E ( w h i c h w e shall define shortly), we see t h a t V E R B defines basic features for all verb entries (and can be used directly for intransitives such as Die), VERB+NP inherits ~ o m VERB b u t a d d s an NP c o m p l e m e n t to the right of the verb (for transitives), V E K B + N P + P P inherits ~ o m VERB+NP but adds a further P P c o m p l e m e n t and so

79

on Entries for regular verb lexemes are then mi-

n i m a l - syntactically they j u s t inherit e v e r y t h i n g

f r o m the a b s t r a c t definitions

This DATR f r a g m e n t is incomplete, because it neg-

lects to define the internal structure of the TREEtlODE

and the various subtree nodes in the lexical hierar-

chy Each such node is a description of an LTAG tree

at some degree of a b s t r a c t i o n 9 T h e following DATR

s t a t e m e n t s complete the fragment, by providing de-

finitions for this internal structure:

T R E E N O D E :

< > = = u n d e r

< t y p e > = = i n t e r n a l

STREE:

<> == T R E E N O D E

< c a t > = = s

V P T R E E :

< > = = T R E E N O D E

< c a t > = = v p

< p a r e n t > = = S T R E E : < >

< l e f t > = = N P C O M P : < >

N P C O M P :

< > = = T R E E N O D E

< c a t > - - n p

< t y p e > = = s u b s t i t u t i o n

P P T R E E :

<> == T R E E N O D E

< c a t > = = p p

P T R E E :

< > = = T R E E N O D E

< c a t > I = p

<type> == anchor

<parent> == PPTREE:<>

Here, TREENODE represents an a b s t r a c t node in an

LTAG tree and provides a (default) t y p e of i n t e r n a l

Notice t h a t VERB is itself a TREENODE (but with the

nondefault t y p e a n c h o r ) , and the other definitions

here define the remaining tree nodes t h a t arise in

our small lexicon: VPTREE is the node for VERB's pa-

rent, S T R E E for VEKB's g r a n d p a r e n t , N P C O M P defines

the structure needed for NP c o m p l e m e n t substitution

nodes, etc 1°

Taken together, these definitions provide a speci-

fication for G i v e j u s t as we had it before, b u t with

the addition of t y p e and r o o t features T h e y also

s u p p o r t some other verbs too, and it should be clear

t h a t the basic technique extends readily to a wide

range of other verbs and other p a r t s of speech Also,

although the trees we have described are all i n i t i a l

9Even the lexeme nodes are abstract - individual

word forms might be represented by further more specific

nodes attached below the lexemes in the hierarchy

1°Our example makes much use'of multiple inheritance

(thus, for example, VPTREE inherits from TREENODE,

STREE and NPCOMP) but a/l such multiple inheritance is

orthogonal in DATR: no path can inherit from more than

one node

trees (in LTAG terminology), we can describe a u x i -

l i a r y trees, which include a leaf node of type f o o t

j u s t as easily A simple e x a m p l e is provided by the following definition for auxiliary verbs:

AUXVERB :

< > = = T R E E N O D E

< c a t > = V

< t y p e > = = a n c h o r

< p a r e n t c a t > = = v p

< r i g h t c u t > = = v p

< r i g h t type> == f o o t

4 L e x i c a l r u l e s Having established a basic structure for our LTAG

lexicon, we now t u r n our a t t e n t i o n towards captu- ring other kinds of relationship a m o n g trees We noted above t h a t lexical entries are actually associa- ted with t r e e f a m i l i e s , a n d t h a t these group to- gether trees t h a t are related to each other T h u s in the s a m e family as a s t a n d a r d ditransitive verb, we

m i g h t find the full passive, the agentless passive, the dative alternation, the various relative clauses, and

so forth It is clear t h a t these families correspond closely to the o u t p u t s of t r a n s f o r m a t i o n s or m e t a r u - les in other frameworks, b u t the XTAG s y s t e m cur- rently has no f o r m a l c o m p o n e n t for describing the relationships a m o n g families nor m e c h a n i s m s for ge- nerating t h e m A n d so far we have said nothing

a b o u t t h e m either - we have only characterized sin- gle trees

However, LTAG's large d o m a i n of locality m e a n s

t h a t a l l such relationships can be viewed as directly lexical, and ~hus expressible by lexical rules In fact

we can go further t h a n this: because we have em- bedded the d o m a i n of these lexical rules, n a m e l y the LTAG tree structures, within the feature structures,

we can view such lexical rules as covariation cons- traints within feature structures, in m u c h the s a m e way t h a t the covariation of, say, syntactic and m o r - phological f o r m is treated In particular, we can use the m e c h a n i s m s t h a t DATR already provides for fea- ture covariation, rather t h a n having to invoke in ad- dition some special p u r p o s e lexical rule machinery

We consider six construction types found in the XTAG g r a m m a r : passive, dative, subject-auxiliary inversion, wh-questions, relative clauses and topica- lisation Our basic a p p r o a c h to each of these is the same Lexical rules are specified by defining a deri- ved o u t p u t tree structure in t e r m s of an i n p u t tree structure, where each of these structures is a set of feature specifications of the sort defined above Each lexical rule has a n a m e , and the input and o u t p u t tree structures for rule f o o are referenced by pre- fixing feature p a t h s of the sort given above with

< i n p u t f o o .> or < o u t p u t f o o .> So for ex- ample, the category of the p a r e n t tree node of the

o u t p u t of the passive rule m i g h t be referenced as

< o u t p u t p a s s i v e p a r e n t c a t > We define a very general default, s t a t i n g t h a t the o u t p u t is the s a m e

as the i n p u t , so t h a t lexical relationships need only

concern themselves with c o m p o n e n t s they modify

T h i s a p p r o a c h to f o r m u l a t i n g lexical rules in DAIR

is quite general and in no way restricted t o / T A G : it

can be readily a d a p t e d for application in the context

of any feature-based lexicalist g r a m m a r formalism

Using this approach, the dative lexical rule can be

given a minimalist i m p l e m e n t a t i o n by the addition

of the following single line to VERB+NP+PP, defined

above

VERB+NP+PP :

<output dative right right> == NPCOMP:<>

This causes the second complement to a ditran-

sitive verb in the dative alternation to be an NP,

rather than a P P as in the unmodified case Subject-

auxiliary inversion can be achieved similarly by just

specifying the output tree structure without refe-

rence to the input structure (note the addition here

of a form feature specifying verb form):

AUXVERB :

< o u t p u t a u x i n v f o r m > == f i n i t e - i n v

< o u t p u t a u x i n v p a r e n t c a t > == s

<output auxinv r i g h t cat> == s

Passive is slightly m o r e complex, in t h a t it has to

m o d i f y the given i n p u t tree structure rather t h a n

s i m p l y overwriting p a r t of it T h e definitions for pas-

sive occur at the VERB+NP node, since by default, any

transitive or subclass of transitive has a passive form

Individual transitive verbs, or whole subclasses, can

override this default, leaving their passive tree struc-

ture undefined if required For agentless passives,

the necessary additions to the VERB+NP node are as

followsn:

VERB+NP :

<output passive form> == passive

<output passive right> ==

"<input passive right r i g h t > "

Here, the first line stipulates the form of the verb

in the output tree to be passive, while the second line

redefines the complement structure: the output of

passive has as its first complement the second com-

plement of its input, thereby discarding the first

complement of its input Since complements are

daisy-chained, all the others m o v e up too

Wh-questions, relative clauses and topicalisation

are slightly different, in that the application of the

lexical rule causes structure to be added to the top

of the tree (above the s node) Although these con-

structions involve unbounded dependencies, the un-

boundedness is taken care of by the [TAG adjunction

mechanism: for lexical purposes the dependency is

local Since the relevant lexical rules can apply to

sentences that contain any kind of verb, they need

to be stated at the VERB node Thus, for exam-

ple, topicalisation and wh-questions can be defined

as follows:

11Oversimplifying slightly, the double quotes in

"<input passive right right>" mean that that D A T R

path will not be evaluated locally (i.e., at the VERB+NP

node), but rather at the relevant lexeme node (e.g., Eat

or Give)

VERB :

<output topic parent parent parent cat>

<output topic parent "parent left cat> = = n p

<output topic parent parent left form>

== normal

<output whq> == "<output topic>"

<output whq parent parent left form> == vh Here an additional NP and s are attached above the original s node to create a topicalised struc- ture T h e wh-rule inherits f r o m the topicalisation rule, changing j u s t one thing: the form of the new

NP is m a r k e d as wh, r a t h e r t h a n as n o r m a l In the full f r a g m e n t 12, the NP added by these rules is also syntactically cross-referenced to a specific NP m a r - ked as null in the i n p u t tree However, space does not p e r m i t presentation or discussion of the DATR code t h a t achieves this here

5 A p p l y i n g l e x i c a l r u l e s

As explained above, each lexical rule is defined to operate on its own notion of an i n p u t and produce its own o u t p u t In order for the rules to have an ef- fect, the various i n p u t and o u t p u t p a t h s have to be linked together using inheritance, creating a chain of inheritances between the base, t h a t is, the canonical definitions we introduced in section 3, and s u r f a c e

tree structures of the lexical entry For example, to ' a p p l y ' the dative rule to our G i v e definition, we could construct a definition such as this:

Give-dat :

<> ffi= Give

<input dative> == <>

<surface> == <output dative>

Values for paths prefixed with surface inherit from the o u t p u t of the dative rule T h e input of the dative rule inherits f r o m the base (unprefixed) case, which inherits f r o m Give T h e dative rule de- finition (just the o n e l i n e introduced above, plus the default t h a t o u t p u t inherits f r o m input) thus media- tes between q i v e and the surface of G i v e - d a t This chain can be extended by inserting additional in- heritance specifications (such as passive) Note t h a t

s u r f a c e defaults to the base case, so all entries have

a s u r f a c e defined

However, in our full fragment, additional support

is provided to achieve and constrain this rule chai- ning Word definitions include boolean features in- dicating which rules to apply, and the presence of these features trigger inheritance between appro- priate i n p u t and o u t p u t p a t h s and the base and

s u r f a c e specifications at the ends of the chain For example, Wordl is an alternative way of specifying the dative alternant of Give, b u t results in inhe- ritance linking equivalent to t h a t found in G i v e - d a t above:

12The full version of this DAIR fragment includes all the components discussed above in a single coherent, but slightly more complex account It is available on request from the authors

W o r d l :

< > = = G i v e

< a l t d a t i v e > = = t r u e

More interestingly, Nord2 properly describes a wh-

question based on the agentless passive of the dative

of Give

W o r d 2 :

<> = = G i v e

< a l t w h q > = = t r u e

< a l t d a t i v e > = = t r u e

< a l t p a s s i v e > = = t r u e

< p a r e n t l e f t f o r m > = - n u l l

Notice here the final line of Nord2 which specifies

the location of the ' e x t r a c t e d ' NP (the subject, in this

case), by m a r k i n g it as null As noted above, the full

version of the whq lexical rule uses this to specify a

cross-reference relationship between the wh-NP and

the null NP

We can, if we wish, encode constraints on the app-

licability of rules in the m a p p i n g f r o m boolean flags

to actual inheritance specifications Thus, for e x a m -

ple, whq, t e l , and t o p i c are m u t u a l l y exclusive

I f such constraints are violated, then no value for

s u r f a c e gets defined T h u s Word3 i m p r o p e r l y a t t -

e m p t s topicalisation in addition to wh-question for-

m a t i o n , and, as a result, will fail to define a s u r f a c e

tree s t r u c t u r e at all:

Word3 :

< > = = G i v e

< a l t w h q > m = t r u e

< a l t t o p i c > = = t r u e

< a l t d a t i v e > -~, t r u e

< a l t p a s s i v e > -= t r u e

< p a r e n t l e f t f o r m > = = n u l l

T h i s a p p r o a c h to lexical rules allows t h e m to be

specified at the a p p r o p r i a t e point in the lexicM hier-

archy, b u t overridden or modified in subclasses or

lexemes as a p p r o p r i a t e It also allows default gene-

ralisation over the lexical rules themselves, and con-

trol over their application T h e last section showed

how the whq lexical rule could be built by a single mi-

nor addition to t h a t for topicalisation However, it is

worth noting t h a t , in c o m m o n with other DATR spe-

cifications, the lexical rules presented here are r u l e

i n s t a n c e s which can only be applied once to any

given lexeme - multiple application could be sup-

ported, by m a k i n g multiple instances inherit f r o m

some c o m m o n rule specification, b u t in our current

t r e a t m e n t such instances would require different rule

names

6 C o m p a r i s o n w i t h r e l a t e d w o r k

As noted above, Vijay-Shanker & Schabes (1992)

have also proposed an inheritance-based approach

to this p r o b l e m T h e y use m o n o t o n i c inheritance to

build up p a r t i a l descriptions of trees: each descrip-

tion is a finite set of dominance, i m m e d i a t e domi-

nance and linear precedence s t a t e m e n t s a b o u t tree

nodes in a tree description language developed by

Rogers & Vijay-Shanker (1992), and category infor-

m a t i o n is located in the node labels

T h i s differs f r o m our a p p r o a c h in a n u m b e r of ways First, our use of n o n m o n o t o n i c inheritance allows us to m a n i p u l a t e total instead of partial de- scriptions of trees T h e a b s t r a c t verb class in the Vijay-Shanker & Schabes account subsumes b o t h in- transitive and transitive verb classes b u t is not iden- tical to either - a minimal-satisfying-model step is required to m a p partial tree descriptions into actual trees In our analysis, VERB is the intransitive verb class, with c o m p l e m e n t s specifically m a r k e d as un- defined: thus VERB : < r i g h t > == u n d e r is inherited

f r o m TREENODE and VERB+NP j u s t overrides this com-

p l e m e n t specification to add an NP c o m p l e m e n t Se- cond, we describe trees using only local tree relations (between adjacent nodes in the tree), while Vijay- Shanker &5 Schabes also use a nonlocal dominance relation

B o t h these properties are crucial to our embed- ding of the tree structure in the feature structure

We want the category i n f o r m a t i o n at each tree node

to be partial in the conventional sense, so t h a t in actual use such categories can be extended (by uni- fication or whatever) So the feature structures t h a t

we associate with lexical entries m u s t be viewed as partial But we do n o t want the tree structure to

be extendible in the s a m e way: we do not want an intransitive verb to be applicable in a transitive con- text, by unifying in a c o m p l e m e n t NP So the tree structures we define m u s t be t o t a l descriptions 13

A n d of course, our use of only local relations al- lows a direct m a p p i n g f r o m tree structure to feature

p a t h , which would not be possible at all if nonlocal relations were present

So while these differences m a y seem small, they al- low us to take this significant representational step - significant because it is the tree structure e m b e d d i n g

t h a t allows us to view lexical rules as feature cova- riation constraints T h e result is t h a t while Vijay- Shanker & Schabes use a tree description language,

a category description language and a further for-

m a l i s m for lexical rules, we can c a p t u r e everything

in one f r a m e w o r k all of whose c o m p o n e n t s (non- monotonicity, covariation constraint handling, etc.) have already been independently m o t i v a t e d for other aspects of lexical description 14

Becket's recent work (1993; 1994) is also directed

at exactly the p r o b l e m we address in the present paper Like him, we have e m p l o y e d an inheritance hierarchy And, like him, we have employed a set of lexical rules (corresponding to his metarules) T h e key differences between our account and his are (i) 13Note that simplified fragment presented here does not get this right It makes all feature specifications total descriptions To correct this we would need to change TREENODE so that only the values of <right>, < l e f t > and

<parent> default to under

14As in the work cited in footnote 3, above

that we have been able to use an existing lexical

knowledge representation language, rather than de-

signing a formal system t h a t is specific to [TAG, and

(ii) t h a t we have expressed our lexical rules in ex-

actly the same language as that we have used to

define the hierarchy, rather than invoking two quite

different formal systems

Becket's sharp distinction between his metarules

and his hierarchy gives rise to some problems t h a t

our approach avoids Firstly, he notes that his meta-

rules are subject to lexical exceptions and proposes

to deal with these by stating "for each entry in the

(syntactic) lexicon which metarules are applica-

ble for this entry" (1993,126) We have no need to

carry over this use of (recta)rule features since, in

our account, lexical rules are not distinct from any

other kind of property in the inheritance hierarchy

T h e y can be stated at the most inclusive relevant

node and can then be overridden at the exceptional

descendant nodes Nothing specific needs to be said

about the nonexceptional nodes

Secondly, his metarules m a y themselves be more

or less similar to each other and he suggests

(1994,11) t h a t these similarities could be captured

if the metarules were also to be organized in a hier-

archy However, our approach allows us to deal with

any such similarities in the main lexical hierarchy

itself 15 rather than by setting up a separate hierar-

chical component just for metarules (which appears

to be what Becket has in mind)

Thirdly, as he himself notes (1993,128), because

his metarules m a p from elementary trees that are in

the inheritance hierarchy to elementary trees that

are outside it, most of the elementary trees actually

used are not directly connected to the hierarchy (alt-

hough their derived status with respect to it can be

reconstructed) Our approach keeps all elementary

trees, whether or not they have been partly defined

by a lexical rule, entirely within the lexical hierarchy

In fact, Becker himself considers the possibility

of capturing all the significant generalizations by

using just one of the two mechanisms t h a t he pro-

poses: "one might want to reconsider the usage of

one mechanism for phenomena in both dimensions"

(1993,135) But, as he goes on to point out, his exi-

sting type of inheritance network is not up to taking

on the task performed by his metarules because the

former is monotonic whilst his metarules are not

However, he does suggest a way in which the hierar-

chy could be completely replaced by metarules but

argues against adopting it (1993,136)

As will be apparent from the earlier sections of

this paper, we believe that Becker's insights about

the organization of an ['lAG lexicon can be better

expressed if the metarule component is replaced by

lSAs illustrated by the way in which the whq lexical

rule inherits from that for topicalisation in the example

given above

an encoding of (largely equivalent) lexical rules that are an integral part of a n o n m o n o t o n i c inheritance hierarchy that stands as a description of all the ele- mentary trees

Acknowledgements

A precursor of th'is paper was presented at the Sep- tember 1994 TAG+ Workshop in Paris We thank the referees for that event and the ACL-95 referees for a number of helpful comments We are also gra- teful to Aravind Joshi, Bill Keller, Owen Rambow

K Vijay-Shanker and T h e XTAG Group This rese- arch was partly supported by grants to Evans from

S E R C / E P S t ~ C (UK) and to Gazdar from ESRC

(UK)

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