Multiple Default Inheritance in a Unification-Based 
Graham Russell 
John Carroll* 
Susan Warwick-Armstrong 
ISSCO, 54 route des Acacias, 
1227 Geneva, Switzerland 
elu@dlvsun.unige.ch 
Lexicon 
Abstract 
A formalism is presented for lexical specification in 
unification-based grammars which exploits defeasi- 
ble multiple inheritance to express regularity, sub- 
regularity, and exceptions in classifying the prop- 
erties of words. Such systems are in the general 
case intractable; the present proposal represents an 
attempt to reduce complexity while retaining suf- 
ficient expressive power for the task at hand. Illus- 
trative examples are given of morphological analy- 
ses from English and German. 
1 Introduction 
The primary task of a computational lexicon is to 
associate character strings representing word forms 
with information able to constrain the distribution 
of those word forms within a sentence. 1 The or- 
ganization of a lexicon requires the ability, on the 
one hand, to make general statements about classes 
of words, and, on the other, to express excep- 
tions to such statements affecting individual words 
and subclasses of words. These considerations 
have provoked interest in applying to the lexicon 
AI knowledge representation techniques involving 
the notions of inheritance and default. 2 The sys- 
*current address: Cambridge University Computer Lab- 
oratory, New Museums Site, Pembroke Street, Cambridge 
CB2 3QG, UK. 
OWe are indebted to Af-.al Ballim, Mark Johnson, and 
anonymous referees for valuable comments on this paper. 
tin the general case, the relation between forms and in- 
formation is many-to-many (rather than one-to-many as of- 
ten assumed) and this observation has influenced the choice 
of facilities incorporated within the system. See 3.2 below 
for an example of how distinct forms share identical mor- 
phosyntactic specifications. 
2See e.g. Daelemaus and Gazdar eds. (1990), and the 
references in Gazdar (1990). The work of Hudson (1984) 
extends this general approach to sentence syntax. 
tem described here is part of the ELU s unification 
grammar development environment intended for 
research in machine translation, comprising parser, 
generator, transfer mechanism and lexical compo- 
nents. The user language resembles that of PATR- 
II (Shieber, 1986), but provides a larger range of 
data types and more powerful means of stating re- 
lations between them. Among the requirements 
imposed by the context within which this system 
is used are (i) the ability to both analyse and gen- 
erate complex word forms, (ii) full integration with 
existing parts of the ELU environment, and (iii) the 
ability to accommodate a relatively large number 
of words. 
2 Classes and Inheritance 
An ELU lexicon consists of a number of 'classes', 
each of which is a structured collection of con- 
straint equations and macro calls encoding infor- 
mation common to a set of words, together with 
links to other more general 'superc\]asses'. For ex- 
ample, if an 'intransitive' class is used to express 
the common syntactic properties shared by all in- 
transitive verbs, then particular instances of in- 
transitive verbs can be made to inherit this infor- 
mation by specifying the 'intransitive' class as one 
of their superclasses - it then becomes unneces- 
saw to specify the relevant properties individually 
for each such verb. The lexicon may be thought 
of as a tangled hierarchy of classes linked by in- 
heritance paths, with, at the most specific level, 
lexicai classes and, at the most general, classes for 
which no superclasses have been defined, and which 
therefore inherit no information from elsewhere. 
S "Environnement Linguistique d'Unlfication" - see Esti- 
val (1990), and, for a description of the earlier UD system 
on which E~u is based, Johnson and Rosner (1989). 
215 
Lexical entries are themselves classes, 4 and any in- 
formation they contain is standardly specific to an 
individual word; lexical and non-lexical classes dif- 
fer in that analysis and generation take only the 
former as entry points to the lexicon. 
Inheritance of a feature value from a superclass 
may be overridden by a conflicting value for that 
feature in a more specific class. This means, for ex- 
ample, that it is possible to place in the class which 
expresses general properties of verbs an equation 
such as '<* aux> = no' (i.e. "typical verbs are not 
auxiliaries"), while placing the contradictory spec- 
ification '<* aux> = yes' in s subclass from which 
only anTiliaries inherit. The ability to encode ex- 
ceptional properties of lexical items is extremely 
attractive from the linguistic point of view; the 
lower the position in the hierarchy at which the 
property appears, the more exceptional it may be 
considered. 
A class definition consists of the compiler direc- 
tive '#Class' (for a non-lexicai class) or '#Word' 
(for a lexical class), followed by the name of that 
class, a possibly empty list of direct superclasses, 
a possible empty 'main' or default equation set, 
and sere or more 'variant' equation sets. The su- 
perclass declaration states from which classes the 
current class inherits; if more than one such super- 
class is specified, their order is significant, more 
specific classes appearing to the left of more gen- 
eral ones. If the current class is one of the most 
general in the lexicon, it inherits no information, 
and its superclass list is empty. 
Following the superclass declaration are sere or 
more equations representing default information, 
which we refer to as the 'main' equation set. These 
may be overridden by eontlleting information in 
a more specific class. Each equation in a main 
set functions as an independent constraint, in a 
msnner which will be clarified below. 
Variant equation sets, loosely speaking, corre- 
spend to alternatives at the same conceptual level 
in the hiersrchy, and in msny cases reflect the tra- 
ditional ides of 'paradigm'. Equations within a 
variant set are absolute constraints, in contrast to 
those in the main set; if they conflict with informs- 
tion in a more specific class, failure of unification 
occurs in the normal way. Also, unlike the main 
set, each variant set functions as a single, possibly 
complex, constraint (see section 2.2). A feature 
4Thus no distinction is made between classes and 'in- 
stances', as in e.g. KL-ONE (Schmolse and Lipkis, 1983) 
structure is created for each variant set that suc- 
cessfully unifies with the single structure arising 
from the main set. Each variant set is preceded 
by the vertical bar ' \['. The order of variant sets 
within a class is not significant, although, if a main 
set is employed, it must precede any variant sets. 
The following simplified example illustrates the 
form and interaction of class definitions. In equs. 
tions, unification variables have initial capitals, 
and negation of constants is indicated by ' '. 'kk' 
is the string concatenation operator - an equation 
of the form X = Y kk Z unifies X nondeterministi- 
cally with the result of concatenating ¥ and Z. 
#Word walk (Intransitive Verb) 
<stem>= walk 
#Class Intransitive () 
<sub©at> = \[SubJ\] 
<$nbJ cat> =np 
#Class Verb () 
<aOX> m no 
<cat> m V 
I 
<tense> = past 
<~onO = <stem> kk ed I 
=presont 
<form>= <steuO kk s 
i 
<aSr> = "s83 
<tense> - present 
<form> = <stem> 
The lexiesl class walk is declared as having 
two direct superclasses, Intransitive and Verb; 
its main set contains just one equation, which 
sets the value of the feature stem to be walk. 
Intransitive has no direct superclasses, and its 
main equation set assigns to the value of subcat 
a list with one element, a feature structure in 
which the value of cat is rip. Neither walk 
nor Intransitive has sny variant equation sets. 
Verb, by contrast, has three, in addition to two 
main set equations. The latter assign, by default, 
the values of cat and aux. The three variants ac- 
counted for by this example are the past tense verb, 
in which the value of form unifies with the result 
of concatenatin 8 the value of stem with the string 
'ed', the third person singular form, in which the 
suffix string is 's', and the form representing other 
combinations of person and number in the present 
tense; in the last case, the form value is simply 
identical to the stem value. 5 
5We ignore for the moment the question of mor- 
phogrsphemic effects in sufllxstion - see section 3.3 below. 
216 
2.1 Class Precedence 
In an ELU lexicon, a class may inherit directly from 
more than one superclass, thus permitting 'multi- 
ple inheritance' (Touretsky, 1986: 7ft.), in contrast 
to 'simple inheritance' in which direct inheritance 
is allowed from only one superclass at a time. The 
main advantage that multiple inheritance offers 
over simple inheritance is the ability to inherit sev- 
eral (orthogonal or complementary) sets of proper- 
ties from classes in more than one path through the 
hierarchy. In the lexical context, it has often been 
observed that morphological and syntactic proper- 
ties are essentially disjoint; the subeategorisation 
class of a verb is not predictable from its conjuga- 
tion class, and vice versa, for example. Multiple 
inheritance permits the two types of information 
to be separated by isolating them in distinct sub- 
hierarchies. 
The question to be resolved in systems em- 
ploying multiple inheritance is that of precedence: 
which of several superclasses with conflicting prop- 
erties is to be inherited from? ELU employs the 
class precedence algorithm of the Common Lisp 
Object System (CLOS) to compute a total order- 
ing on the superclasses of a lexicsl class, s The 
resulting 'class precedence list' (CPL) contains the 
class itself and all of its superclasses, from most 
specific to most general, and forms the basis for 
the defaulting behaviour of the lexicon. As an ex- 
ample, consider the following lexicon: 
#Word It (B D) #Class B (C) ZClass C (Y) #Class D (E) 
#Class E (P) #Class F () 
Here, the superclass declarations embody the or- 
derin 8 constraints A < B, A < D, B < D, B < C, C < 
F, D < E, and E < F; from these are derived a to- 
tal order assigning to the lexical class A the CPL 
(A,B,C,D,E,F). 
2.2 Inheritance of Properties 
A lexical class such as walk in the example above 
corresponds to a family offeature structures. Here, 
as in most analyses, members of this family rep- 
resent morphosyntactically distinct realizations of 
a single basic lexeme. Consulting the lexicon in- 
volves determining membership of the set of fea- 
ture structures associated with a given lexical class; 
s See Steele (1990: 782ff.) for details of the aIgorithm, and 
Keene (1989:118ff.) for discussion. In circumstances where 
no such total ordering is possible, the system reports an 
error. 
the precedence relation encoded in the CPL con- 
trols the order in which defeasible information is 
considered, each class in the CPL adding first de- 
fault and then non-default information to each FS 
produced by the previous class. 
More formally, we define default eztension, su- 
perclass eztension, and global ez~e~sion as follows: 7 
(1) The default eztension of a FS ~ with respect 
to a set of FSs • is 
if U ({~b} U ~) :f: _1_, and .1_ otherwise. 
(2) The superclass ez~ension of a FS ~b with re- 
spect to a class c having a main equation set 
M and variant sets Vl,...v, is the set 
I ~be J.}, 
where M s is the smallest set of FSs such that 
each m E M describes some m ~ E M s, ¢~s is 
the default extension of~b with respect to M e, 
and v~ is the feature structure described by 
vl. We refer to this set as E(~b, c). 
(3) The global eztensio~, of a lexlcvd class having 
the CPL (cl,...c,) is F~, where Fo = {T}, 
and 
r,>0= U{~ IVY, ~ r,_l, • = E(~, c,)}. 
With regard to (I), each of the FSs in W that can 
unify with ~b does so - those that cannot, because 
they conflict with information already present, are 
ignored. The condition requiring ~ to be unifiable 
with the result of unifying the elements of • takes 
account of the potential order-sensitivity of the de- 
faulting operation - only those main sets having 
this property can be applied without regard to or- 
def. If this condition is met then the application 
of defaults always succeeds, producing a feature 
structure which, if no member of the default set 
is applicable, is identical to ~b. This interpretation 
of default unification is essentially that of Bouma 
(1990). 
The superclass extension E(~, c) is formed by 
applying to ~ any default equations in the main set 
of c, and then applying to the result each variant 
set in c; for variant sets Vl,... v,,, the result of this 
7'A U B' here denotes the unification of A and B, 'T' 
denotes the most general, 'empty' FS, which unifies with all 
others, and '_L' denotes the inconsistent FS, equated with 
failure of unification. 
217 
second stage is the set of FSs {@1,...@~}, where 
each ~ is the result of successfully unifying ~b with 
some different vj. 
To speak in procedural terms, the global exten- 
sion of a lexicai class L with the CPL C is com- 
puted as follows: T is the empty FS which is input 
to C; each c~ in C yields as its superelass extension 
a set of FSs, each member of which is input to the 
remainder of C, (c~+l,...c,). The global exten- 
sion of L is then the yield of the most general class 
in its CPL - expressed in a slightly different way, 
the global extension of L is the result of applying 
to T the CPL of L. 
It is possible to exert quite fine control over in- 
heritance; one property may override another when 
assigned in a main equation set, but cause failure 
when assigned in a variant set. Normally, variant 
sets are defined so as to be mutually exclusive; a FS 
that unifies with more than one of the variant sets 
is in effect multiplied, s The inheritance systems 
of Calder (1989) and Flickinger (1987) make use 
of lexical rules - the ELU lexicon does not provide 
such devices, although some of their functionality 
may be reproduced by the variant set mechanism. 
The approach described here differs from some 
previous proposals for default inheritance in 
unification-based lexicons in that the process of 
building FSs is monotonic - classes may add infor- 
mation to a FS, but are unable to remove or alter 
it. Thus, given a CPL (ci,...c.), any FS F admit- 
ted by a class c~ subsumes every FS that can be cre- 
ated by applying to F the classes (c~ + I,... c,~), m 
n. Karttunen (1986) and Shieber (1986) describe 
systems in which FSs may be modified by default 
statements in such a way that this property does 
not automatically hold. These schemes permit 
default statements to override the effect of ear- 
lier statements, whereas default information in the 
ELU lexicon may itself be overridden. 
We now turn to some examples illustrating the 
r61e of defeasible inheritance in the lexicon. 
3 Example Analyses 
3.1 German Separable Verbs 
Two large classes of German verbs are the sep- 
arable and inseparable prefixed compound verbs. 
The former are of interest syntactically because, 
as their name suggests, the prefix is a bound 
SSee 3.2 below for a case where such multiple matches 
are desirable. 
morpheme only in certain syntactic environments, 
namely when the verb is untensed or head of a 
verb-final clause. 9 Members of both classes share 
morphological, but not necessarily syntactic, prop- 
erties of the verb which corresponds in form to 
their stem. The separable-prefix verb weglau/en 
('run away') and inseparable verlau/en ('elapse') 
are two such verbs, which the lexicon should be 
able to relate to their apparent stem lau/en ('run'). 
Since word definitions are classes, they can be 
inherited from like any non-lexical class. Thus the 
lexical classes verlaufen and weglaufen may in- 
herit from lanfen, itself a lexical class: x° 
# Word woglau~on (we s lau~on) 
<s~ = weglaufen 
# Word vorlaufsn (vet laufsn) 
<S~ i vorla~en 
# Class we s (separable) <morph 
prolix> = wog 
# Class vet (non_sopLTabls) <morph prefix> = 
vet 
# Word lau~en (verb) Base_stun= lauf 
<smu> = laufon 
# Class non_separable () Proflx = <morphprefix> 
# Class sspazablo O 
l Prefix = <morphprsfix> 
<lyn 4~v> = no <sya in, l> = "tn,f 
I Proflx 
= '' <syn 
Inv> =yos 
.<synia~l> = "la.f 
I 
# Class 
Prefix = <moxphprofix> <synin~l> =~ 
verb O 
<cat> m v 
Prefix = '' <morph pref~x> = 
Prefix && 
<syn 4.e1> = inf <form> = P_be && on 
I 
<form> = P_bs k& • <syn infl> = prss_Indic_s8_l 
9Within the syntactic analysis assumed here, the distri- 
bution of verbs is controlled by a binary feature inv, whose 
value in these contexts is no. 
lea number of simplifications have been made here; 
\]aufen is in reality a member of a subclass of the strong 
verbs, and the verb class itself has been truncated, so that 
it accounts for only bare infinitive and first person singu- 
lar present tense indicative forms. Past participle formation 
also interacts with the presence of separable and inseparable 
prefixes. 
218 
The lexical classes weglaufen and verlaufen each 
have two immediate superclasses, containing in- 
formation connected with the prefix and stem. 
The classes weg and vet set the value of the 
morph:prefix path of the verb (overriding the 
value given in the main set of verb), and specify in- 
heritance from the separable and non.separable 
classes respectively. The former of these unifies the 
variable Prefix with either the empty string (in 
the case of tensed 'inverted' verbs) or the value of 
morph : prefix (for other variants), while the lat- 
ter sets the value uniquely for all forms of the verb 
in question. As the value of sere is fixed in the main 
equation set ofweglaufen and verlaufen, the cor- 
responding equation in laufen is overridden, but 
Base.stem unifies with lauf. Finally, in verb, the 
main set supplies default values for Prefix and 
morph : prefix (which in the cases under consid- 
eration will not be applicable), unifies P_bs with 
the result of concatenating the strings Prefix and 
Base_stem, and for each value of syn infl assigns 
to form the concatenation of P_bs with the appro- 
priate sufftx string. 
Values for sere (antics) are provided in main set 
equations; those in weglaufen and verlaufen are 
thus correctly able to override that in laufen. 
3.2 English Irregular Verbs 
In most cases, lexical items that realize certain 
morphosyntactic properties in irregular forms do 
not also have regular realizations of those proper- 
ties; thus *sinked is not a well-formed alternative 
to sank or sunk, on the analogy of e.g. walked. 
This phenomenon has frequently been discussed 
in both theoretical and computational morphol- 
ogy, under the title of 'blocking', and it appears to 
provide clear motivation for a default-based hier- 
archical approach to lexical organization. 11 There 
are exceptions to this general rule, however, and 
inheritance mechanisms must be sufficiently flexi- 
ble to permit deviation from the strict behaviour 
illustrated above. 
Consider the small class of English verbs includ- 
ing dream, lean, learn and burn; these have, for 
many speakers, alternate past finite and past par- 
ticiple forms: e.g. dreamed and dreamt. The fol- 
lowing fragment produces the correct pairings of 
strings and feature structures, the written form of 
the word being encoded as the value of the form 
llSee e.g. Calder (1989). 
feature: 12 
#Word walk (verb) 
<bass> = walk 
#Word sink (verb) 
<bass> = sink 
P_Fin_Form = silk 
PSP_Form = sunk 
#Word dream (dual-past verb) 
<base> = dream 
#Class dual-past 0 
I 
PSP_Form = <base> k& t 
P_Fin_Form = <bass> &k t 
~morph> = pasttinlts/pastnon~inits 
I 
#Class verb () 
<oat> = v 
PSP_Porm = <bass> It& sd 
P_Fin_Form = <bass> &k od 
J <morplO = present_nones3 
<~orm~ = <bass> 
<morph> = prsssnt_ss3 <~orm> = <bass> &k s 
~rph~ - ptstnon:einito 
<form> = PSP_Fozm 
<nOXl~lO . ptstflnlts 
<fo~O = p_F4e_Fo~n 
The main set equations in s/nk override those in its 
superclass verb, so that the variants in the latter 
class which give rise to past participle and past 
tensed forms associate the appropriate information 
with the strings sunk and sank, respectively. The 
class walk, on the other hand, contains nothing to 
pre-empt the equations in verb, and so its past 
forms are constructed from its value for base and 
the suffix string ed. 
The lex/cai class dream differs from these in hay- 
ing as one of its direct superclasses dual-past, 
which contains two variant sets, the second of 
which is empty (recall that variant sets are pre- 
ceded by the vertical bar 'I'). Moreover, this class 
is more specific than the other superclass verb, 
and so its equations assigning to PaP_Form and 
P_Fin_Form the string formed by concatenating 
the value of base and t have precedence over the 
contradictory statements in the main set of verb. 
Note that this set also includes a disjunctive con- 
straint to the effect that the value of morph in this 
FS must be either pastfinite or pastnonfinite. 
The dual_past class thus describes two feature 
IZAgain, the analysis sketched here is simplified; several 
variants within the verb class have been omitted, and all in- 
fleetional information is embodied as the value of the single 
feature morph. 
219 
structures, but adds no information to the sec- 
ond. The absence of contradictory specifications 
permits the equations in the main set of verb to 
apply, in addition to those in the first variant set 
of dual-past. The second, empty, variant set in 
dual-past permits this class also to inherit all the 
properties of its superclass, i.e. those of regular 
verbs like walk; among these is that of forming the 
two past forms by suffixing ed to the stem, which 
produces the regular dreamed past forms. 
3.3 Word-Form Manipulation 
The string concatenation operator '&&' allows the 
lexicon writer to manipulate word forms with ELU 
equations and macros. In particular, &t can be 
used to add or remove prefixes and suE3xes, and 
also to effect internal modifications, such as Ger- 
man Umlaut, by removing a string of characters 
from one end, changing the remainder, and then 
replacing the first string. In this section we show 
briefly how unification, string concatenation, and 
defensible inheritance combine to permit the anal- 
ysis of some of the numerous orthographic changes 
that accompany English inflectional sufftxation. 
The inflectional paradigms of English nouns, 
verbs, and adjectives are complicated by a num- 
ber of orthographic effects; big, hop, etc. undergo 
a doubling of the final stem character in e.g. big- 
ger, hopped, stems such as/oz, bush, and arch take 
an epenthetic • before the plural or third singu- 
lar present suiflx s, stem-final ie becomes y before 
the present participle suifL~ ing, and so on. Pe- 
ripheral alternations of this kind are accomplished 
quite straightforwardly by macros like those in the 
following lexicon fragment (in which invocations of 
user-defined macros are introduced by ': ,):is 
Final_Sibilant(Strin s) 
$trin$= _ I~eh/c~/e/x/s 
Ftnal_Y(Striag,Prefiz) String = ~reftx I~ y 
Prefix= &k b/c/4/~/g/h/j/k/i/m/n/p/r/s/t/v/w/x/z 
# Word try (verb_spe11~) <base> = try 
# Word watch (verb_spe\].I/a 8) 
<base> = watch 
13As before, this is s somewhat sbbre~sted version of s 
full descrip~on; the verb and vo~bJpolliag classes require 
additional variant sets to account for other morphosyntsc~c 
prope~|es. Other st~ng-predicste macros, in particular OK, 
must be defined in order to ester for the ~ range of spelling 
changes observed in verbal inflee~on. 
# Class verb_spelling (verb) 
I 
!Final_T(<base>,P) 
Base_P_PSP = P && i 
Base_3SG = P &k ie J 
!F~al_Sibilant(<baee>) 
Base_3SG = <base> k& • 
I !OK(<base>) 
#Class verb () 
<cat> = v Base_3SG 
= <base> 
Baso_P_PSP = <bass> PSP_Form- Baso_P_PSP k& 
od SG3_Fozmffi Base_3SG k& s 
J ! Sing3 
<form> = SG3_Form 
I ; PastNonFin 
<form> = PSP_Form 
Two macros definitions are shown here; Final_¥ 
is true of a pair of strings String and Prefix iff 
String consists of Prefix followed by y and the 
final character of Prefix is one of the set denoted 
by the disjunction b/c.., z, while Final_Sibilant 
is true of a given string iff that string terminates in 
sh, ch, s, z, or z. OK is a macro which is true of only 
those strings to which neither Final.Sibilant nor 
Final_Y apply. 
The class verbJpellJ.ng contains three variant 
equation sets, the first two of which assign values to 
variables according to the form of the string which 
is the value of the base feature. If Final_¥ is appli- 
cable, Base.P-PSP is unified with the concatenation 
of the second argument to the macro (e.g. tr) and 
is, while Base_3SG is unified with e.g. tr and i. 
If FJ.na1.Slbilant is applicable, then Base.3SG is 
unified with the concatenation of the value of base 
(e.g. watch) and e. If neither of these is applica- 
ble (because the base string does not match the 
patterns in the macro definitions), the variables 
are bound not within this class, but in the main 
equation set of its superc\]ass verb. Here, their val- 
ues are unified directly with that of base, and the 
eventual values of the form feature result from con- 
catenation of the appropriate suiflx strings, giving 
values of watched, watches, tried, and tries. 
4 Summary 
The lexicon system presented above is fully inte- 
grated into the ELU environment; in particular, 
the result of analysis and the starting point for 
generation is the same type of feature structure as 
that produced by ELU grammars, and the equa- 
220 
tions within classes are of the same sort as those 
used elsewhere in a linguistic description, being 
able to exploit re-entrancy, negation, disjunction, 
direct manipulation of lists, etc. 
For the purpose of experimenting with the struc- 
ture of the class hierarchy and the distribution of 
information within individual classes, the lexicon is 
held in memory, and is accessed directly by means 
of an exhaustive search. Once a stable descrip- 
tion is achieved, and the coverage of the lexicon in- 
creases, a more efficient access mechanism exists, in 
which possible word-forms are pre-computed, and 
used to index into a disk file of class definitions. 
We have presented an implemented treatment of 
a framework for lexical description which is both 
practical from the perspective of efficiency and at- 
tractive in its reflection of the natural organiza- 
tion of a lexicon into nested and intersecting gen- 
eralizations and exceptions. The system extends 
traditional unification with a multiple default in- 
heritance mechanism, for which a declarative se- 
mantics is provided. 

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