Applying Lexical Rules Under Subsumption 
Erhard W. Hinrichs 
Dept. o\[ Linguistics 
University of T~bingcn 
Wilhelmstr. \] \]3 
D- 72074 Tiibingen 
Germany 
eh~sf s. nphil, uni-tuebingen, de 
Tsuneko Nakazawa 
NTT Laboratories 
1-2356 Take, Yokosuka 238-03 
,Japan 
t suneko©nttnly, nit. j p 
Abstract 
Lexical rules are used in constraint- 
based grammar formalisms such as 
llead-Driven l)hrase Structure Grammar 
(IIPSG) (Pollard and Sag 1994) to ex- 
press generalizations atnong lexical en- 
tries. '\['his paper discusses a number of 
lexical rules from recent I\[PSG analy- 
ses of German (tlinri<;hs and Nakazawa 
1994) and shows that the grammar in 
some cases vastly overgenerates and in 
other cases introduces massive spurious 
structural ambiguity, if lexical rules ap: 
ply under unification. Such l)rot)lems of 
overgeneration or spurious ambiguity do 
not arise, if a lexical rule al)plies to a 
given lexical ent;ry iff the lexical entry 
is subsumed by the left:hand side of the 
lexical rule. I,'inally, the paper discusses 
computational consequcnce~s of at)plying 
lexical rules under subsuml)tion. 
1 Introduction 
Current linguistic theories place an increasing 
amount of grammatical information in the lexicon 
and employ a variety of mechanisms to express 
generalizations across lexical entries: templates 
(Flickinger 1987, Shieber 1986), inheritance hier- 
archies (Flickinger 1987, Pollard and Sag 11994), 
and lexical rules (Bresnan 1982, I)owty 1982, Gaz- 
daret al. 1985, Pollard and Sag 1994). Lexical 
rules (henceibrth: LRs) have been subjected to 
particularly close s<:rutiny. 'Fhis research has tb- 
cused on two important issues: 1. how the use 
of LRs affects the generative power of grammar 
formalisms and the computational complexity of 
parsing algorithms (Uszkoreit and Peters 1986, 
Carpenter 1991), and 2. how to provide a de- 
notational semantics for LRs (Calcagno and PoP 
lard 1995, Meurers 1995). In this paper we ad- 
dress neither of these two issues. Instead we will 
concentrate on a question that we c<msider to be 
of equal importance, but that has received sur- 
prisingly little attention: Under what conditions 
should an I,R be applicable to a given lexical entry 
(henceforth: LE)? For gramrnar formalisms that 
employ the notion of unitication of attribute-value 
structures, two criteria for applicability naturally 
suggest themselves: 
1. llypolhcsis A: A lexical rule applies to a lexi- 
cal entry ifr the lexi<:al entry unifies with the 
left-hand side of t;he lexical rule. 
2. Hypothesis B: A lexical rule applies to a lex- 
ical entry iff the lexical entry is subsumed by 
the left-hand side of the lexical rule) 
Without much argument, it is cotnmonly as- 
sume<t that llypothesis A is correct (el. Pollard 
and Sag 1994, (\]alcagno and Pollar<t :1995, and 
Meurers 1995). This paper argues that 11ypoth- 
esis A should be rejected on empirical grounds. 
We discuss a number of Ll{s that have been 
used in IIPSG analyses of German (tlinri<:hs and 
Nakazawa 1994) and show that the grammar will 
either vastly overgenerate and accept ungrammat- 
ical sentences or introduce spurious structural am- 
biguity for grammatical sentences, if ltypothesis A 
is adopted. Itowever, no such problems ofovergeu- 
eration or spurious ambiguity arise, if one adopts 
llypothesis B, instead. 
It would go beyond tim scope of this paper to 
present a flJly worked-out proposal on how to i>ro - 
cess LRs in a coml)utational system for IIPSG. 
Itowever, as discussed in section 6, it is worth not- 
ing that the subsumption test for I,l{ application 
<'.an be integrated straightforwardly into two re- 
cent proposals by van Noord and Bouma (:1994) 
and by Meurers and Minnen (1995) of how to im- 
plement lab in a processing system for HPSG. 
l'Fhis paper will not provide a formal definition of 
subsumption or nnificiation for typed feature struc- 
tures. Instead, we refer the reader to the standard 
definitions of Kasper and Rounds (1986) and Carpen- 
tel: (1992), among many <)tilers. Informally speaking, 
two feature structures are unifiable itf they do not con- 
tab incompatible information. One feature structure 
subsumes another iff the intormation contained in the 
former is less specific than in the latter. 
543 
PPLR: 
IPLR: 
SUIIJ 
COMPS 
SUBJ 
COMPS 
\[IIF, ADIVI'~ORM pass \] 
sP > -*/val, \[SUB  \[CAS,  no,,,\] >\] \[ \[CAS  acc\] I \[\] > h \[COMPS \[\] 
\] \[-HEAI)IVFORM pass \] \] 
NP > + hal, \[SUI{J < > 
E~\[CAS\]~ geil V dat\] I \[\] > k t C°MPs ( \[\]\]\[C,'ASlC gen v dat\] I\[\]) 
lqgure 1: Passive Lcxical l{ules for German Kiss 1992 
2 Passive by Lexical Rule 
It has been assumed in a variety of syntactic 
fi'ameworks that the active/passive alternation 
should be treated as a lexical process: Bresnan 
(1982) in LFG, Dowty (1982) in Categorial Gram- 
mar, and Pollard and Sag (1987) for IIPSG. Ger- 
man exhibits two types of passNes: personal pas- 
sives, as in (lb), and impersonal passives, as in 
(2b,3b). 
(l) 3. Peter sah den Mann. 
'Peter saw the man.' b. 
1)er Mann wurde gesehen. 
'The man was seen.' 
(2) a. Peter half dem Mann. 
'Peter helped the man.' 
b. Dem Mann wurde geholfen. 
'The man was helped.' 
(3) a. Die Veteranen gedachten der 'l~)ten. 
'The veterans commemorated the dead.' 
b. Der 'Poten wurde gedaeht. 
'The dead were commemorated.' 
For personal passives the accusative object NP 
of a transitive verb, e.g. den Mann in (la), in its 
active form corresponds to an NP with nomina- 
tive case, e.g. der Mann in (11)). In impersonal 
passives a datiw; or genitive NP complement of a 
transitive verb, e.g. the dative NP dem Mann in 
(2), exhibits the same case assignment in the ac- 
tive and passive forms. 'IS formMly capture the 
relationship between the l, Es for active and pas- 
sive forms of German verbs in IlPSG, Kiss (1992) 
formulates the LRs in Fig. 1 (henceforth referred 
to as the PPLt{ and the IPLR, respectively), u 
The LRs in b'ig. I employ the HPSG feature 
geometry of Pollard and Sag (1994). a '\]'he spec- 
illcation of a syntactic category (CNI') in tlPSO 
>However, see Kathol (1994) and Pollard (1994) for 
an account of German passive without LRs. 
aIn order to reduce the size of the feature struc- 
tures, prefixes of paths that begin with the SYNSEM 
attribute have been omitted as much as possible in 
Fig. 1 and all other feature structures that are shown 
in this paper. 
According to Kiss, specifying two different case wtl- 
ues under one reentrancy (cf. tags \[~ in the PPLR) is 
a shorthand notation for identity of the two categories 
in all respects, except for the case value. '\]'he original 
includes the feature VALENCE (abbreviated as 
VAL in lqg. 1), which in turn specifies for verbs 
under the features SUILI and COMPS the sub- 
ject and non-subject complements. COMPS takes 
a list of categories, (:ailed synsem objects, as its 
vahn;. If the list is nomempty, the h:ftmost cate 
gory in the list represents the direct object. The 
intended effect of the PPI, I{ is to promote the di- 
rect object of a. transitive verb in the l,l,\] for the 
actiw~' form to the subject of the passive form. l,'ol: 
impersonal passives the COMPS list of any transi- 
tive verb whose leftmost complement is marked by 
genitive or dative case remains unchanged, while 
the singleton list of the subject value of the active 
form becomes the empty list in the I,E for the 
passive form. Note that the case specifications on 
the left-hand side of the rules m:e crucial since they 
condition which classes of transitive verbs appear 
in personal and impersonal passives. 
Viewed procedurally, the PPI,I{, is meant to ap-- 
ply to \[,Es for transitiw; verbs such as kau,\[en as 
shown in |+'ig. 2. 4 For transitive verbs it makes 
no ditthrence whether we use unitication or sub 
sumption as the test of ;,pplicability tbr the PP l, lC 
'\['he LE for any transitive verb is more specific 
than the feature stru<-ture of the input descrip- 
tion of the PPI,I{, since the PHON wdue and the 
COMPS and SOl+;1 wJues will be further instan- 
dated than in the input description of the PPM~. 
In particular, the COMPS list of the PPLR is 
entirely schematic R)r any non-empty list of cat- 
egories whose tlrst element is an accusative N P, 
while the COMPS vahle for kaufi'.n is a list with 
exactly one element that has the same category 
and case spc'cification as the NP in the PIq, R. 
Therefore, {;he LE will both unify with and be 
subsumed by the input Datnre structure of the 
IJPLI{. However, as we will see in the next section, 
the choice of subsumption or unification makes a 
crucial dilDrence when \[,Es are themselves highly 
schematic and underspecitled. 
tbrmulation of the I,Rs by Kiss (1992) differs from the 
version presented here in minor definitionM details. 
ttowever, these differences are entirely orthogonal to 
the theoretical issues discussed in this paper. 
4l"ollowing abbreviatory conventions in HPSG, the 
subscripted tags in Pig. 2 stand for the index va.lues 
contained in the CONq?I'\]NT specifications of the NPs. 
544 
~ll)()?'d 
I)I\]ON ( k~tul'en ) 
(.A~ "~ /w," "',, su~.~ ( N P\[.o.,\]m~ ) 
... L COMPS ( N,,\[;,,~:,:\]GI ) P" :j 
"WO i'd 
PlION ( gcka, u\[t ) 
F \[ II I!:AI)IvI''O:t{M P~'~ \] 
/ F""'"' \] \] | L L (2oM pS () J 
" / F \] / / 
L Ll~ou(',lrr E~\]J 
I:'igm:c 2: ApldYing IJ,c I>PI,I{ to the al)t,'~wia.tc'd 1,1'; For l, hc v¢~'~'l~ ka*tflen, ('lmy') 
3 Argument Composition in the 
Lexicon 
Tim notion of nrgulnent composil;ion wa.s Iirsl; in 
/,roduccd inl;o tJm I/I)SG lil.crt~tm:c l)y Ilinrichs 
nnd Nttka,znwa (1989) to account for the topica.l- 
ization of w, rhM c(mstituents aml ff)r the auxiliary 
()CI'lll UI. flip ('onsl;ruction in a 
\]11 (~ornHtll VE\]I, BAI, (?()MI'I,EXLS~ i,c. lllai,l vcA'bs 
t.ogethcr with non-linitc auxiliaries, such as /e.~e~ 
k(';m~en c~m bc toldca.lize.d, ;ts show. iu (4). 
(4) l:'s('n kiinncn wird <'r cs. 
rca.d (:;m will hcit 
'lie will be able rca.d il;.' 
In addition, the verbM complex serves as the, do- 
main over which auxilim:ics c;u, t><', I'ronl,ed. This 
so-called AUXII,IAII.Y I,'1,11' c(ms(.rucl.ion i)osil.k)ns 
finite auxilia, rics such as ",:ird in (5) to the M't 
in {,he vcrl)a.l COml>h',x , insl.~nd of 1,h<~ customa.ry 
scntencc-lina.I posit,ion for suhordim:d;c cla.uses. 
(5) lch ghmlm m(:ht, da.13 cr ~'s wird lose., kSnncl,. 
l bdiew, \[,ot tim*holt will read (:a.n 
'1 don'l; 1)clicvc th{:d; hc will 1)c a.I)lc 1;o I'e~M it. 
'tbpica.lization {rod auxilia.ry-tlip, I, hus, t)rovidc 
cru(:ia\] evidence for i;re;~l;ing Ina, in verbs a.ud aux- 
iliaries as constil,ucnLs. The prol)oscd consl;itueiH; 
sLrllcl;urc l'cquircs that, sul)ca.tcgorizal.io,l in for,w> 
lion M>out non-wM)al COml)h;m0,nts is l>rOl/agal;ed 
from the main verb to the l,op of the vcrlml com- 
f>lcx. In IIPS(~ l,his can he achieved by structure 
shnring the complements of the ina.in vcrt) with the 
subcal;egorization in form;d;ion of each ~mxiliary in 
I;hc scnl;ence. '\['his lends to I,Es for auxiliaries such 
:'II:PS(~ pra.cticioucrs h~tve a,doptcd the notion of 
arg*tmcnt compositio*t to ~tcc:ou nt for a, wu:icty of syn-. L~t(:ti<: 
coimtrncl, ions in <lift>rent \]~ulgua,gcs, including 
citric-climbing in /t~di~m (Mona.chest :199;I), the syn-- 
t~(:l;i(: properl, ies of ~tuxilia, rics in /g'cnch (Alto*lid a, nd 
(',oda, rd 1994), nnd (:ross-scriM dcpc'ndcncics in Dutch (ll.entier 1994). 
as kSnncn '<:~m' show. in Fig. 3. 
l l/) 0 i'd 
PIION (k6n.cn } 
\[IIEA I)1VI"O I{.M hsc \] 
' \[VAI,I(:OMPS (\[~+ ( V \[( oml's \[~ ) 
where \[\] - list(-, \[>'YNSI:M I ...IIIEAI) .... "b\]) 
I:igurc 3: A l)brcvintcd I,E I'or auxiliary kSnue~l 
k&m, en requires a lmsc infinilJw~' coml)h;t~mnt~ 
a.s imli<'atcd in tl," (;OMITS vMuc in Fig. 3. The 
(JOMI>S value of kSnnc.n also conta, ins ~ (possibly 
cinl)t,y ) list o\[' non-w~rl)a.l categories (idcnl, ilicd by 
tim ta.g 1) that I, he gow~'rned w'xt) sul>ca.tc.goriz~s 
for. c; In other words, the COMICS vMuc of the 
governed vcrh is merged with the (7OMI'S list of 
t'gnncn itsclr. Formally this merging is nchic;vcd 
t)y al)l)en<ling the COMI'S list of' the governed 
v(;rh with l.h(~ olm-ch~mcnt list 1;hal. collsisl;s o\[' 
l.h(; govern('d v(;rh its('lF. Sin(:(' auxilia.rics Im.vc I.() 
bc able Ix) c(md)inc with dill'crcnl~ types of vcrl)s 
(%g. intra.nsitives, I, ra.nsitivcs, ditra.nsil.ivcs, etc.), 
the (',()M I'S lis~ oF I, hc governed w',rh has l,o r<,: 
main uudcrslmcilicd. It. is this undcrspccilication 
in the I,i!3 for a.uxilia.rics l.hat, m~kcs n crucial (li\[: 
I'crcncc in tlm nl)l)lic;d)ility oF l,l{s. 
4 Subsumption and Unification 
Revisited 
l:'or interactions hctwcett tim I,Es f'or mJxiliarics 
such as kgnncn and the ims,~ivc: I,I{ for (;erman, it 
mal¢cs ~ <'.ruciM difforcncc whc(,hm' the I,l{ appli<'~s 
under unifica.|;ion or mMcr subsumption. Firs/, 
consi<h;r mliIical;ion as the tcsl, for nl, lJicability 
of' l,l{s. Since the M.\] for k5n'nc~z does not; c,o,tain 
~my infornm.tion that is inconsistent with the in. 
t>ul; s/~ccilication o\[" the I>PI,I{ in Fig. l, bhc rule 
is a.I)plic, al)h~' a.nd will produce the derived LI:, for 
c; For lurthcr dc(,a.ils a.s to wily Lh(" list of ra.isc'd clc. 
,mints h~m to be restricted to (xmta.in only non-verba\] 
(:~m~gorics sec \]linrichs and N~tkaza.wa. (1994). 
545 
k6nnen in Fig. 4. 
word 
PHON { k6nnen ) 
'ItEADJVFORM bse \] 
SUBS \[\] 
'" VAL COMPS <\[~(~\[CASEacc\]}l\[~\] )\[~ ) 
. + < V \[COMPS 
__+ 
word 
|PITON ( gekonnt ) 
| \[HEAD\[VFORM pass \] 
/"" /VA\] \[SUBJ {\[~\] \[CASE nom\] ) \] J 
L \[ ' \[COMPS <~\]+ < V \[COMPS\[~ )) \] 
Figure 4: Applying the PPLR to kdnnen under 
unification 
When the LE for k6nnen is unified with the left- 
hand side of the PPLR, the COMPS list of kb'nnen 
- and, via structure sharing, the COMPS value 
of the governed verb - becomes further instanti- 
ate& This COMPS list now contains as its left- 
most element a category with accusative case. In 
accordance with the PPLR, this leftmost element 
is promoted to the SUBJ value of kdnnen, while 
the remainder of the COMPS list of the verb gov- 
erned by k6nnen, identified by tag 3, is retained. 
Ilowever, this derived LE would have the unde- 
sirable consequence that it admits ill-formed sen- 
tences such as (6). 
(6) * Das Auto wurde kaufen gekonnt. 
the car was bought can 
In (6) the auxiliary k6nnen has been passivized 
and the direct object of the transitive verb has 
been promoted as the subject of k6nnen. |low- 
ever, since in German only main verbs can be pas- 
sivized, the sentence is ungrammatical. 7 
Ungrammatical sentences such as (6) can be 
successfiflly ruled out if the PPLR, is applied to an 
I,E only if the input specification of the LR sub- 
sumes the LE (Hypothesis B). The subsumption 
requirement for LR application is based on the in- 
sight that LRs should apply only to LEs that are 
instantiated at least to the extent that the input 
description of the LR minimally requires. In the 
case at hand, the list of raised arguments in the 
LE for kdnnen in Fig. 3 is totally unspecified - it 
can be any list of non-verbal synsem objects, in- 
chiding the empty list. The COMPS list of the 
left-hand side of the PPLR, on the other hand} 
requires the leftmost element to carry accusative 
>rhere are some cases of "long distance" passives, 
i.e. passives which involve the complelnent of an em- 
bedded verb, that at least some German speakers ac- 
cept, e.g. Der Hund wurde vergesscn zu f£ttcrn ('It 
was forgotten to feed the dog'): However, we are not 
aware of any German speakers that would allow pas- 
sives with raising verbs such as k6nnen. 
case. Therefore the COMPS list of kSnnen does 
not subsume the COMPS list on the left-hand 
side of the PPLR, or vice versa. Accordingly, no 
subsutnption relationship exists between the input 
specification of the PPM{ as a whole and the LE 
for kb'nnen, tIence if tIypothesis B is assumed, 
the Lt{ can be successfiflly blocked, s However, 
even under subsumption nothing blocks the PPLR 
from applying to the transitive verb kaufen, as 
discussed in section 2. Therefore the grammatical 
sentence in (7) can be derived successfully. 
(7) Das Anto wnrde gekauft. 
'The car was bought.' 
5 Avoiding Spurious Ambiguity 
This section will consider the interaction of 
highly schematic LEs with another LR com- 
monly used in IIPSG: the Complement Ex- 
traction LR, formulated for English by Pol- 
lard and Sag (1994). Fig. 5 shows the ver- 
sion of the Complement Extraction LexicM Rule 
for German (henceforth: CELRG) that has 
been proposed by Hinrichs and Nakazawa (1994). 
\[LOCALI...ICOMP ~ ( ... , \[\] \[phrase\] .... ) \] 
NONLOCAI, IINII ER\[SLAStI \[\] j \[ 
LOCALICATIVALICOMPS 
Figure 5: Complement Extraction Lexical Rule 
for German - Hinrichs and Nakazawa 1994 
The CELRG moves an element from the 
COMPS list of a verb to its SI,ASH set. The 
value of the feature SLASH contains those items 
that are realized in left dislocated position, e.g. as 
a topicalized constituent in sentenceqnitiM posi- 
tion. Analogous to the applicability of tile PPLR, 
the CELt{G is applicable to LEs of transitive verbs 
such as kaufcn shown in Fig. 2, under both uni- 
fication and subsumption. \[File result of such an 
application is the same as shown in Fig. 2, except 
that the direct object is placed on the SLASH set 
instead of the SUB3 list. For the analysis of sen- 
8The reader may wonder whether one couldn't get 
around the requirement that the LR for passive apply 
under subsmnption by restricting the rule to apply 
only to main verbs. At first glance this seems like a 
possible way-out, since the cases that we havc con- 
sidered problematic for applying the LR under unifi- 
cation involve LEs of auxiliaries. IIowever, the (:lass 
of argument raising verbs is not restricted to auxil- 
iaries. Verbs such as verstehen ('know how'), as in Er 
versteht Parser zu implementiercn ('He knows how to 
impleInent parsers.'), fall into the same class. But 
verstehen is a main verb, not an auxiliary. Thus, 
even if the LR would be reformulated to apply 'only 
to auxiliaries, the following ungrammaticM sentence 
could not be excluded: * Parser werden verstanden 
zu implementieren. 
546 
\[I\] NP 
I 
1)as Buch V* NP I I 
wird Peter 
v \[SLAS|  {}\] 
V \[SLASH {\[\]\]} \] 
vc \[SLAS. \] 
VC \[SI, ASIf {\[1\]} \] V* 
V \[SLASH {\[1\]}\] V* k6nnen 
I I 
gekauft haben 
1,'igure 6: Analysis Tre.e for Sentence (8) 
tence (8), the tree in Fig. 6 illustrates the perco- 
lation of the relevant SLASH value that is intro- 
duced via the CEIA{G in the LE for kaufcn. 9 
(8) l)as Buch wird Peter gekauft haben kgnnen. 
the book will Peter bought have can 
'Peter will have been able to buy the book.' 
The SLASII wdue in Fig. 6 is percolated h'om 
the non-terminal node for the verb ka'ufl:n, by the 
Nonlocal I,'eaturc Principle to the sister node of 
the topicalized constitueut des Buck 'Fhe top lo- 
cal tree is licensed by the llead-Filler II) Schema 
which binds oil' the SLASII wdue so that the sen- 
tence node has an empty SI,ASH set;./° 
The CEI, I{G restricts topicalized constituents 
to phrasal categories. This restriction is neces- 
sary to rule out sentences such as (9) in which a 
single lexicM item, i.e. a word in terms of the type 
hierarchy of HPSG, is t, opiealized. 
(9) * K6nnen wird Peter des Auto gekauft haben. 
can will 1)eter the car bought have 
As in the ease of the PPLR, the difference be- 
tween Hypotheses A and B comes into play when 
we consider the interaction of the (21!'LtLG with 
highly schematic entries such as the ones Ilin- 
richs and Nakazawa (1994) assume for attxiliaries 
in German. If Hypothesis A is assumed, then the 
CEI,I{G will be applicable to the type of I,E shown 
for kSnnen in Fig. 3, since such an I,l'\] will unify 
with the input descrit)tion of the LI{,. One of the 
possible outputs of the I3{ to such an auxiliary 
entry wouht look identical to l;he putative, out- 
put of the PPLIt shown in Fig. 4, expect that 
one of the elements from the COMPS list of the 
auxiliary is assigned to the SLASH set instead of 
the SUBJ list;. However, this would have the un- 
desirable consequence that the SLASII wdne in 
9The tree in Fig. 6 ~Lssumcs the tlat constituent 
structure for Germ~tn cbutse structure proposed by 
tIinrichs and Nakazttwa (1994). However, the issue 
raised with respc'ct to the CEI,RG in this p~tper is 
orthogonal to overall assumptions of German obtuse 
structure. 
1°See Pollard and Sag (1994) and ltinrichs and 
Nakazawa (1.994) for further details on the Nonlocal 
Feature Principle and the Head-Filler ID Schema. 
the analysis of topicalized sentences that contain 
auxiliaries could originate in the LE for the main 
verb, but also in the LE for each auxiliary present 
in the sentence. Hence, in addition to the. tree in 
Fig. 6, three additionM trees are admitted for sen- 
tence (81) in which the SLASII value originates in 
one of the pre-terminal nodes for the anxiliaries. 
These nodes are marked lbr emphasis by an aster- 
isk in Fig. 6. This ambiguity is, of course, totally 
spurious since it does not correlate with a differ- 
ence in semantics or any other relevant linguistic 
property of the sentence. I!'rom a computational 
perspective, such spurious ambiguities are highly 
undesirable since they force the parser into con- 
sidering multiple analyses where a single analysis 
suflbes. The spurious ambiguity that we have just 
identified is particularly pernicious, since it; would 
aiD.el a wide range of sentences in any grammar of 
German that employs argument composition and 
the (JEI~I{G: all assertion main clauses that con- 
tMn auxiliaries would be affected since in assertion 
clauses the initiM constituent is the result of top- 
icalization. 
Once again undesirable consequences of over- 
applying an Lit under unification can be avoided 
if applicability of LRs instead requires subsump- 
tion (llypothesis B). Since the CEM{G limits 
extracted constituents to phr~ses and since the 
COMPS list; of an auxiliary does not restrict, its 
elements in the same w~ty, the LI,\] for auxiliaries 
~md the input description of the CEI,I{G do not 
stand in a subsumption relation, llenee under lly- 
pothesis B the CI,3,RG applies only to main verbs, 
and the tree in Fig. 6 is the only tree admitted. 
6 Computational Consequences 
Finally, we will consider the computational impli- 
cations that the adoption of lfypothesis B has for 
the processing of LRs in a computational system. 
Since consensus on how to provide an adequate 
denote|tonal semantics for I,Rs has not yet been 
reached, it would go well beyond the scope of this 
paper to develop a fully worked-out proposal on 
how to process lJ{s. n A very promising approach 
USee CMcagno and Pollard (1995) ~tt(l Menrers 
(11995) for further discussion. 
547 
on how to integrate LRs into processing systems 
for HPSG has been developed independently by 
wm Noord and Bouma (1994) and by Meurers and 
Minnen (1995). It turns out that the conclusions 
reached in this paper can be easily integrated in 
the general framework that these authors provide. 
Common to these two proposals is the idea of 
treating LRs as (ltorn clause) constraints on LF, s 
of the kind shown schematically in Fig. 7. 
derive-lexical-entry (X0 ,Xn):- 
base-lexical-entry(X0), 
lo×-rule  (Xo,X,), ..., lex-rule, (X,_ 
Figure 7: l,exical rules as Horn Clause constraints 
on relations between lexical entries 
l)efinite clause schemata as in Fig. 7 (for n 
0) define relations between base LEs listed in the 
lexicon and derived l, Es that are obtained via the 
application of a sequence of LRs. Each I,R is then 
viewed as a two-place definite relation as illns- 
\[rated in Fi R. 8 for the l'Pl,t{ of Fig. l. 
\[SUBJ { NP ) \] 
lex-rule( \[COMPS {\[~\[CASE acc\] \[\[~) ' 
\[ HF'A1)IVFORM pass ~ \] Fs< J (@\[CASE 
no,n\] >\] ) 
VA\], \[COMPS \[\] 
.J 
l,'igure 8: The PPI, R encoded as a definite 
relation 
It is important to distinguish two tasks that 
need to be performed in computing with lexical 
rules: 12 
1. the algorithm that decides for a given lexicaI 
entry whether a lexical rule is applicable to 
it, and 
2. the algorithm that; computes for a given lex- 
ical entry the output specification of the lex~ 
ical rule, i.e. the derived lexical entry. 
The subsumption test for lexical rule applica- 
tion that we have argued for in this paper pertains 
to the first task. The execution of the definite 
clauses of the kind shown schematically in Fig. 7, 
which encode the possible relations between base 
mid derived lexical entries, pertains to the second 
task. 
Regarding the first task, in van Noord and 
Bouma's approach the sequences of lexical rules 
that are applicable to a given base lexical entry 
have to be specified by the grammar developer 
along with delay statements, which allow goal 
freezing at run riffle of not sufficiently ins\[an\[f- 
ated relations. In Meurers and Minnen's approach 
such sequences are automatically generated from 
12This distinctkm is rightly emphasized by Cab 
cagno and Pollard (1995). 
the set of base lexical entries and the set of lexi- 
cal rules specified by the grammar. The allowable 
sequences of lexi('al rules are compiled into finite 
state automata which are in turn encoded as de\[: 
inite clause attachments to base lexical entries. 
Note thai; both approaches are general enough 
to accommodate different assumptions about the 
applicability of lexicat rules to lexical entries, 
i.e. they are compatible with both Itypotheses 
A and B. Whether or not at given lexical rule ap- 
plies to a. lexical entry in van Noord and l{ouma's 
al)proach needs to be stipulated by the grarnmar 
writer who is in theory fl:ee to use either a unifi- 
cation or subsumption test. In Meurers and Min- 
hen's approach the deduction rules for automat- 
ically generating a finite-state encoding of lexi- 
cal rules can likewise be based on a subsumption 
check or a unification clieck. In this paper we have 
argued on empirical grollnds that subsumption 
should be the relevant operatiw-, criterion. The 
theoretical results of tit(', present paper c~m there- 
fore be straightforwardly integrated into a lexical 
rule compiler of the sort described by Meurers and 
Minneu in which applicability of lexieal rules is 
checked automatically under subsumption. 
7 Conclusion 
'\['his paper has discussed a number of lexical 
rules from recent IIPSG analyses of German (llin- 
richs and Nakazawa 1994) and has shown that 
the grammar ill some eases vastly ow~rgenerates 
and in other cases introduces massive spurious 
structural ambiguity, if lexical rules apply under 
unificationY ~ l\[owew'.r, no such problems of over- 
generation or spurious ambiguity arise, if a lexical 
rule applies to a giwm lexieM entry iff the lexi- 
cal entry is subsumed by the. left-hand side of the 
lexica\[ rule. Finally we have shown that tile sub- 
sumption test for the applicability of lexical rules 
(;an be. integrated straightforwardly into the pro- 
posals by wm Noord and lk)mna (1994) and by 
Meurers and Minnen (11!)95) of how to implemeut 
lexical rules in a processing system for IIPSG. 
13\[t is worth pointing out that the importauce of 
subsunlption tt~s been noted for other linguistic phe- 
nomena as well. \]hfilding proposals originating with 
(\]azdar et al. (1985), Bayer and Johnson (1995) ha.ve 
pointed out that the grammar of (cross-categorical) co- 
ordimttion for English will make the right predictions 
if the mother category ot7 the conjunction schema is re- 
quired to subsume tile c~ttegory of ca.oh coI0un(:t. \[~y 
contrast, if the feb\[lion between the mother category 
ttnd each daughter category is that of unifialfility,'then 
the resulting gra.mm~tr vastly overge,erates. 
548 
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