Lexical Rules: What are they? 
Andrew Bredenkamp, Stella Markantonatou and Louisa Sadler 
Department of Language and Linguistics 
University of Essex, UK 
{andrewb,m~trks,louisa}~essex.~c.uk 
Abstract 
Horizontal redundancy is inherent to lex- 
ica consisting of descriptions of fnlly 
formed objects. This causes an unwel- 
come expansion of the lexical database 
and increases parsing time. To eliminate 
it, direct relations between descriptions 
of fnlly formed objects are often defined. 
These are additional to the (Typed Mul- 
tiple) Inheritance Network which already 
structures the lexicon. Many implement- 
ations of horizontal relations, however, 
fail to generate lexieal entries on a needs- 
driven basis, so eliminate neither the 
problem of lexicon expansion nor that of 
inefficient parsing. Alternatively, we pro- 
pose that lexical entries are descriptions 
of objects open to contextnal specifica- 
tion of their properties on the basis of 
constraints defined within the type sys- 
tem. This guarantees that only those 
grammatical lexical entries are infered 
that are needed for efficient parsing. The 
proposal is extremely modest, making 
use of only basic inference power and ex- 
pressivity. 
1 Lexical Rules: what are they? 
Within the strongly lexical framework of HPSG, 
lexi('al rules are used to express relations among 
descriptions ..... a kind of indirect "horizontal re- 
latedness" (Pollard & Sag 1987, 209) which can be 
contrasted with the vertical relations between the 
type(s) of lexical elements. Type relations are, of 
course, captured directly as the monotonic (typed) 
multiple inheritance network itself, which struc- 
tures the lexicon. 
Typical examples of horizontal redundancy in 
the hierarchical lexicon thus conceived arc the Al- 
ternation phenomena (e.g. Dative Shift, the Locat- 
ive Alternation, ctc) and word formation phenom- 
ena (inflectional and derivational morphology). In 
fact, Pollard and Sag also refer to declension class 
membership and similar facts as horizontM rela- 
tions, and as we shall see, the boundary between 
vertical and horizontal relations is not immutably 
fixed once and for all. 
The notion of lexical rule is often given some 
status at the level of linguistic or psychological 
theory. (Pollard & Sag 1987) make reference to 
a generative or procedural interpretation of lexicM 
rules as a deductive mechanism which can be de- 
ployed on a needs only basis, for example, to gen- 
erate words from a single base form. The concep- 
tion of lexical rules as essential generative devices 
(rather than static statements expressing (sub-) 
regularities), is shared in much in:llnential work 
(e.g. (Bresnan 1982), (Pinker 1989)), although 
it is by no means universM, even within tIPSG. 
Viewed from an implcmentational perspective, on- 
the-fly application of lexicM rules brings with it a 
number of distinct advantages which follow from 
the drastic reduction in the size of the lexicM data- 
base (lexical construction is less time consmning 
and parsing time should be reduced as lexical look 
up is less ambiguous, etc). At first sight then it ap- 
pears that the benefit of adding an external Lexical 
l(ule component outweighs the disadvantages (ex- 
ternal powerNl mechanisms). We will first show 
that their role is less clear than this suggests and 
certainly more problematic, before suggesting in 
Section 2 an alternative which eschews any extra 
mechanisms. 
1.1 Horizontal and Vertical Redundancy 
The parallel drawn above between vertical related- 
ness (expressed with the type system) and ho- 
rizontM relatedness among descriptions of fully 
formed objects is however rather misleading. 
Monotonic multiple inheritance networks are most 
naturally used to represent generalisations over 
the properties that (groups of) linguistic objects 
163 
share - inspection of any network will eonfirin 
that they are usually deployed to express what 
is essentially a componential analysis of objects 
and of the relationship between them (defined on 
the basis of this analysis). On the other hand, 
horizontal relations among descriptions (very of- 
ten lnodelled by means of lexical rules) are es- 
sentially relations holding directly between objects 
themselves. While this intuition is clear, this is 
much less adequate an approach for morpholo- 
gical relatedness, where a componential approach 
may often appear just as natural as an object re- 
latedness view, especially if the formalism includes 
fimctionally dependent values, permitting the ex- 
pression of allomorphic wtriation and the like. In 
fact, many putatively horizontal relations may be 
simply re-expressed within a type hierarchy by 
viewing them Dom a compouential perspective, 
obviating the need for expressing them on the %o- 
rizontal" dimension which may lead 6o the use of 
lexical rules. 13ut this is only possible once one 
frees oneself from a view of lexical relatedness as 
something which holds essentially between words 
(objects which correspond to maximal types, that 
is types at the bottom of the type hierarchy). 
llorizontal relations are perhaps most naturally 
captm:ed by an extra device (Ll{s) external to the 
lexical network and associated inference mechan- 
ism-- see (Krieger gc Nerbonne 1993) and (Cal- 
cagno 1995) for recent ItPSG proposals. Some re- 
cent work ((Mem'ers 1995) and (l{iehemann 1994:)) 
partly departs fl:orn this view by expressing rela- 
tions between objects using the vertical axis (that 
is, using the type system), but again tile starting 
point is 'complete' lexical objects. 
1.2 Why avoid Horizontal RelationsY 
Horizontal relations have a number of undesirable 
features as well as requiring an external meclmn- 
ism. HorizontM relations (between objects) are 
in principle pretty much unconstrained. Vertical 
relations are more constrained becmlse they are 
based on componential analysis, starting out Dora 
the set of properties that objects have. On the 
other hand, any object can be related to any other 
object by stipulation in an external mechanism. In 
architectural terms, it is simply accidental (if for- 
tuitous) that lexical rules are often used to relate 
minimMly different objects -- they are capable of 
much more promiscious behaviour. 
This state of,affairs is amply demonstrated in 
the literature, which abounds with attempts to 
constrain horizontal relations by appeal to subsi- 
diary principles (predicate locality in LFG, con- 
straints of a psycholinguistic nature in the work of 
(Pinker 1989), etc). Horizontal relations must be 
constrained to account for 'exceptional' behaviour, 
that is, for those words which do not participate 
to a given horizontal relation despite the fact that 
their description makes them appropriate candid- 
ares for the relation (verb alternations offer several 
examples of these situtation, for instance, 'giving' 
verbs which do not exhibit the so-called 'dative 
shift' phenomenon). 
Modelling of'exceptional' behaviour leads either 
to an extreme complexity of the type system or 
to non-lnonotonic solutions (Flickinger 1987) b(> 
cause it turns out that certain horizontM relations, 
usually defined over types, nmst be blocked for in- 
dividuM objects. 
1.3 hnplementing Horizontal Relations 
Several different implementations of horizontal re- 
lations exist. All of them add extra machinery 
and some add extra expressive power to the core 
mechanism. 
Most frequently, horizontM relations are imple- 
mented as unary rules operating at parsing time 
within a dcrivationM component. Such a compon- 
ent is tided to the inheritance machinery fbr in- 
dependent reasons, mainly because of' the limited 
expressivity of the type systeul. With Ll/.s, some 
lexical entry is considered as 'basic' and all other 
lexical entries are derived fl:om it introducing oth- 
erwise unjustified directionality to the grammar. 
In addition, the derivational implementation of ho- 
rizontal relations fails to produce lexical entries a.s 
needed, instead, it produces lexica.l entries accord- 
ing to the system's internM algorithm of searching 
the rule space. Considerable ambiguity is intro- 
duced with unpleasant results for parsing time. 
Extra machinery for blocking these rules in or- 
der to account for exceptional behaviour is also 
necessary. 
Alternatively, Lt{s may be compiled out bat, 
nnder this approach too, problems like direction- 
ality and the blocking of Ll{s as well as expensive 
ambiguity at parsing time remain unsolved. 
2 An alternative proposal 
In this paper we explore an alternative to hori- 
zontal relatedness which exploits the idea that it is 
often possible to conceive of the linguistic objects 
in such a way as to eliminate potential sources 
of ambiguity and additional external mechanisms. 
To illustrate our approach we will propose an ac- 
count of a subset of Verb Alternation phenom- 
ena which rely on what are essentially underspe- 
cilled lexicM entries. The lexicon will then con- 
tain one (verbal) entry and the system will rely 
only on the existing resources (the type hierarchy) 
164 
to provide the different interpretations of the pre- 
dicate which license the distinct eoml)lementation 
patterns. Analysis is incremental and determin- 
istic and the procedure relies mainly on what we 
will call 'trivial type inference'. In the sections 
that follow \[irst we discuss the linguistic at)l)roaeh 
underlying our proposal, second we eOmlmre our 
proposal to existing underspecification tq)proaches 
and finally, we give some details of the implementa- 
tion which relies on no special fc'+~tures or external 
devices. 
2.1 -Underspeeificatlon 
We will exemplify ore- approach by treating a 
subset of verb alternati(ms which conform to 
the following general schema (\]). These include 
the so-called spray/load (locative) Mtornation, the 
wipe~clear a.lternation, the b~vak/hit alternation 
etc (l,evin 19!)a). 
(~) v Nl'j \[l'~ Np~\] -+ v NP~ \[P~ Nt'.j\] 
We adopt the view that verb l)redicatcs are open 
to contextual information (which ntttst I)e contras- 
ted to the approaches whereby verb predicates are 
treated am fully formed objects which dictate tit+; 
exact nature of their dependents). Consider the 
predicate load: 
(2) The peasant loaded the horses. 
(3) The peasant loaded the horses on the boat. 
(4) The peasant loaded tit(: horses with hay. 
(2) is ambiguous I)ctwc,m (3)and (4:) ,inch one 
of which is not ambiguous. 'l'he contextual factor 
that resolves the ambiguity is the semantics of the 
head of the prepositional complement which here 
is tt~ken to specii~y whether the direct ob.ieet of the 
verb is understood as the location and the oblique 
complement as the locatum or v\[ee versa. The cru- 
tim a.ssumption here is that prepositions have their 
own semantics, an idea first exploited in ((lawron 
1!)86). 
We use/IPSG to model our approach. (5) gives 
the fragment of the type system constraining the 
wdues of the SYNSEMILOC\]CONTINUCLEUS path in 
the (word) description of prepositions which par- 
ticipate to the locative alternation l)henomenon. 
IH!'I, ± At{GI 
co~+tc'nt A II.G2 co;it e~tt 
\[,++ 1\[ \] ...... ......... ItEI, with ItEI, on V i+t ... AI/.G 1 (loe.atio~t) AI{GI (locat~tm) AI{G2 (locat~m) AI{G2 (location) 
We %rthermore assume that the semantics of 
the predicates include a pointer to the semantics of 
the prepositional complements they license. This 
pointer is included as an extra feature of the 
value of SYNSF, IVI\[LOC\[CONT\[NUCLEUS. This fea- 
t/ire we ttalile SFM(ANTIC) CONS('FII.AINq'S) a, tl(\[ 
we make it apl)rol)riate tbr the same values that 
the prepositional SYNSEMII,OC\[CONT\]NUCI,EUS is 
assigned. The lexica\] entry for to load would look 
as in ((~). 
+L ......... {++,+I ........ <++7> 
ltl¢I, load \[~\]1 
|^,.,2 \[L~ 
f; \[ )N 'l' It* NT IAtl+i\[ ~ \[\] 
| ............ +\[ ..... , 
\[ (o,,.,~t\[ ..... 
The lexieal entry for the pre4)osition with is 
given I)el()w: 
......... (+:~) 
+ ..... ....... + .......... ,::::, 
with_contact Alt{+2 ~\[~\] J 
(6) is an mtdcrspcciJicd entry which gets filr- 
ther specified at parsing time when art appropri- 
ate PP is a tta+ehed, l"or instance, if a with-\[)l ~ is 
encountered, then tm interpretation according Lo 
which the location sm'faccs as the direct object of 
the verb is injured. 
There are some theoretical reasons why we have 
chosen to include a "pointer" to prepositional se- 
mantics rather than making it compatible (uui\[i- 
M)le) to verbal semantics as Weehsler (Wechsler 
1994) has proposed, l,'irstly, if verl)al and pre- 
positional semantics were uniliable then we would 
not bc able to explicitly state, in the semantics the 
relation which each feature structure encodes as 
there would be a clash of constants (relation nanms 
are constants). Secondly, identifying the semantics 
of verbs with ttmt of prepositions does not allow 
for expressing certain types of diverse behaviour 
within the class of a.lternating verbs. For instauce, 
both load and stuff show locative, alternation, but 
only the former admits optional PP complements. 
With to stuff the interpretation under which lees- 
lion is a direct object admits an optional P I ) eotn- 
plement (8) while the interpretation under u, hich 
Iocatum is a direct argument admits an obligat- 
ory one (9). Similarly, while both versions of to 
load are related to passive adjectives (loaded carl, 
loaded hay), only the "location" version is related 
165 
cont~tct optional obligatory Oll-GO~ 
on_con.opt on_con-obl with-con_opt with_con~bl 
Figure 1: Type system fragment encoding prepos- 
itional alternation 
to such an adjective in the case of to stuff (stuffed 
pillow, *stuffed feathers). The exact treatment of 
such phenomena, however, goes beyond the scope 
of our discussion here which concentrates on the 
use of underspecification. 
(8) Mary stuffed the pillow with feathers. 
(9) Mary stuffed the feathers into the pillow. 
Optionality of PP complements can also be cap- 
tured easily with this proposal. With to load (2), 
(3) and (4), the PP complement is optional. The 
grammar must have access to three different ver- 
sions of to load, one with zero PP complements and 
two with a PP complement participating in the al- 
ternation discussed above. One approach would 
involve defining two lexieal rules; an alternative 
would be to express all three possibilities directly. 
Both are problematic, of course. Consider the situ- 
ation when the grammar has two PS rules for VPs, 
one for discharging a \[NP,NP\] SUBCAT list and one 
for discharging a \[NP,NP, PP\] list. Without harm- 
ing generality, assume that the bivalent version of 
to load is in the lexicon and two lexical rules gen- 
erate the trivalent versions. To process a trivalent 
version, the parser will backtrack on the bivalent 
version, will use a lexical rule and then, it will 
either succeed or it will backtrack again and use a 
second lexical rule. 
To avoid this, the following solution may be ad- 
opted. First, the type system is augmented to al- 
low for declaring the property of being an optional 
or an obligatory prepositional complement, as in 
figure 1. 
Second, a PS structure rule is introduced of the 
following sort: 
VP --+ V\[SUBCAT\[NP,NP,P(optional)P\]\], NP 
Only one trivalent, underspecified version of to 
load is necessary. The parsing of a trivalent ver- 
sion as before would involve backtracking on the 
rule dealing with optional complements but then 
the rule dealing with obligatory ones would be 
chosen and it would succeed anyway. 
Only limited inference power is necessary for 
this set up to work: the system must be able to 
infer that the unification of a subtype with its su- 
pertype is of the type of the subtype. This 'trivial 
inference power' is independently needed to deal, 
for instance, with (10): if NP1 is a subtype of NP 
then rule (10) will work only if trivial inference 
power is available when the sequence NP1, VP is 
encountered. 
(10) S --+ NP, VP 
There are proposals in the literature which 
build on the idea of using underspecified entries. 
However, several of them use additional, external 
powerful mechanisms to simulate type inference. 
(van Noord ~: Bouma 1994) use underspecified 
verb entries and FP~OLOG delayed evaluation tech- 
niques to insert adjuncts in Dutch VPs without 
using lexical rules which would cater for the ne- 
cessary variations of the subcategorisation list of 
verbs. In another proposal using underspeciflc- 
ation (Sanfilippo 1995) type inference (feature 
structure grounding) is simulated by relying on 
an external mechanism as powerful as PItOLOG. 
In dealing with different complementation pat- 
tern phenomena, Sanfilippo constructs type sys- 
tem fragments where the meet of the alternative 
complements is defined and subtypes verbs accord- 
ing to complement types. Therefore, the informa- 
tion about the alternation is duplicated in the type 
system as it is encoded both on tile complement 
types and the verb types. The same information 
is encoded again on a table of clauses which relate 
a verbal "meet" type with a maximal complement 
type and a maximal verb type. Such type resolving 
clauses are provided for each alternation pattern. 
PS rules are annotated with procedures which pick 
up the correct verb type resolving clause when the 
appropriate complement is encountered. Both the 
clauses and the searching procedures are mechan- 
isms external to the inferencing mechanism that is 
directly related with the type system. Sanfilippo's 
approach, though powerful and flexible, seems ex- 
travagant for phenomena like verb alternations of 
the kind discussed here as well as inflection phem- 
omena of the kind discussed in (Krieger & Ner- 
bonne 1993). In such cases the system can take 
advantage of the fact that type inference can be 
driven by the combination of the information that 
is related to two separate strings (preposition and 
verb, verb ending and verb stem) as is exemplified 
in our proposal. 
Furthermore, in our approach no horizontal re- 
lations exist as the lexicon contains only one entry 
and no other entry is ever generated. Instead, the 
single lexical entry is interpreted on the fly, each 
time according to well-specified constraints. Con- 
sequently, no ambiguity problems result with a 
nice effect, on parsing time. In this sense, using un- 
derspecification defined in the type system is more 
166 
econolnic than using lexical rules or a "static" ver- 
sion of underspecification which is defined in the 
lexicon. For instance, (Krieger &: Nerbonne :1993) 
have used a specialised macro, the so-called dis- 
tributive (or named) disjunction, in a treatment 
of German verb inflectional morphology: 
While it is true that distributive disjunction 
does not add any expressive power to the sys- 
tem (though a piece of machinery, the specialised 
macro, must be supported), if the macro is ever 
called all the legal combinations are thereby gem 
crated and added to the lexicon. In this, the situ- 
ation is precisely the same us with lexieal rules, for 
in each case, what is provided is simply a compact 
representation of an ambiguity. 
This can be also exemplified from the domain 
of Verb Alternation phenomena. (11) will generate 
two lexical entries with at1 identical I'IION string. 
(\]*) .... < ....... > 
\[ ...... <N\[",\[~ , WI'I'H_I\]IJ:\[~> \]V 
....... ILo<: \[ ...... <Ivp:lTi\] .... pp:~> 
IIIlll, load 
.m( ....... 
Unlike lexical rules, ou\]: approach does }lot 
face any blocking problem. A w:rbal pre- 
dicate that does not alternate (such us the 
predicate to put (12),(13)), is assigued the 
upppropriate most specific semantics for its 
SYNSEM ILOC iCONTiNUOLI~US iSEM .(iONS attribute 
---for to put that would be on-contact in order to 
make sure that the locatum argument always sur- 
faces as the direct object; of the verb predicate. 
(12) John put his shoes on the shelf. 
(13) *John put the shelf with his shoes. 
3 Implementation 
The appro~tch described in Section 2 can bc i\[nple- 
mented in any environment that supports Typed 
Inheritmme because it is monotonic and demands 
only 'trivial inference power'. For the purposes of 
experimentation a grammar fragment was iml)le- 
mented in the ALEI' system - a lean formalism with 
a simple inheritance type system, and a siml)\]e 
context free rule backbone. I:'rocessiug in this 
system is normally divided into separate structure 
building and feature decoration rule coati>orients , 
however for our l>ui'poses no use was made of this 
distinction. 
For the construction of the VP, a simple rule 
was used (VP -+ V NP PP), of the following form 
(14): 
04) 
Id :{a ign=>phrasal : { 
aynsom=>synsom:{ 
Ioel=>lool:{ 
cat=>cat :{ 
head=>HEAD, 
subj:>\[SUBJ\] , 
comps->\[\]}, 
cont~nt=>Cont ent }}}} 
< \[ 
ld : {s ign=>l~ X \[col : { 
aynsom->syns~m: { 
loel->locl:{ 
ca%=>cat :< 
hoad=>llEAD=>vo rb : {}, 
sub j=> \[SUB J} , 
comps~> \[OBJ I ,OBJ2\] } 
contont=>Content}}}}. 
Id :{si~n=>phPasal :{ 
synsem~>OBJ l~>synsom:{ 
locl=>loel:{ 
taro>cat ;{ 
h~ad=>noun :~}}}}}}, 
ld :{sil~n=>phrasal : { 
synsom=>OBJ2=>myns om: { 
locl:>locl :{ 
cat=>cat :{ 
h~ad=>prop : {} }}}}}\] , 
The relewmt lexical entries for the fragnient 
were as follows. The verbal entry (load) subcat- 
egorizes for a single NP subject and NI' and PP 
complenmnts (15). This entry has underspeeified 
semantics with respect to the semantic constraints 
on its second and third argmnents (as suggested 
in (8)). These are provided by (structure sharing 
with) the SI,'M_CONSTI~ feature of third argument, 
the prepositional phrase (the variable 'Arg3'). 
(:Is) 
load " 
hh{ 
s ign=>st~m:{ 
m PHON_LEX\[Ioad\] , 
aynaem=>synnem :{ 
loc l=>locl : { 
cat=>cat :-\[ 
head=>v~rb :{}, 
sub j=> \[synsem:{locl=>l ocl :{ 
cat=>cat :{ 
hoad:>nom: {}, 
subj->I\]. 
c 0ml>S=> \[\] , 
apr=>\[\]}, 
contont:>Argl }}\] , 
comJ)a=> \[syllaolu: {lec I=> foe I : ~ 
cad'>cat :{ 
h~ad=>nom: {}, 
subj->\[} , 
comps=>\[\] , 
spr=>\[\]}, 
content=>Ar52}}, 
synsom:{locl=>locl :{ 
cat=>cat :{ 
hoad=>prop: {}, subj => 
\[\], 
comps=>\[\], 
spr=>C\]}, 
conton~=>Arg3}}\]}, 
oolltont~Yr_l>s oR : { 
ps oa=>argS_psoa : { 
rel=>rol :{ 
ro l_namQ=>load}, 
~r~l=>Argl, 
arg2=>Arg2=>ro l_pso~ :{ 
sore_cons\[ l-=> 
1 oc_all;o l'n al~ i on : { 
arg2_s~a ~o=>A2Z}}, 
arg3=>A rg8=> ro i_ p s o a : { 
167 
som_constr=> 
loc_altornation:{ 
arg2_stato=>A2S, 
argS_sta~o:>hSS}}}}}}}}. 
The prepositional entries now simply provide 
the "missing" part of the semantics, nanMy the 
Ioeum/locatum distinction: 
(16) 
with " 
ld:< 
sign=>loxical:{ 
m PHON_LEX\[with\], 
synsem=>synsem:{ 
locl=>locl:< 
cat=>cat:{ 
head=>prep:{ 
pform=>with}, 
subj=>\[\], 
comps=>\[synsom:{ 
locl=>locl:< 
cat:>cat:{ 
hoad=>noun:{caso=>acc}, 
subj=>\[\], 
comps:>\[\]}, 
content=>inst_paoa:{ 
rel=> Rol}}}\]}, 
con~ent=>ins~_psoa:{ 
rel => Rel, 
sem~constr => with_variant:{ 
arg2_stato=>loca~um, 
arg3_stato=>locum}}}}}}. 
4 Conclusion 
We have shown that horizontal redundancy is in- 
herent to a lexicon consisting of descriptions of 
fully formed objects. To eliminate horizontal re- 
dundancy, direct relations between descriptions of 
fully formed objects must be defined externally to 
the Typed Mulitple Inheritance Network or unin- 
tuitive solutions must be pursued. Available ira- 
plementations of horizontal relations fail to satisfy 
the reasons that dictate their implementation: the 
on-need generation of lexical entries and efficient 
parsing. Alternatively, we proposed that lexical 
entries are descriptions of objects which allow for 
further contextual specification of their properties 
on the basis of clearly defined constraints. We 
have shown that this is an easily implementable 
proposal even in environments with lean inference 
power and expressivity because it relies on very 
basic machinery which is available for independ- 
ent reasons. 
This approach can be adopted whenever inforru- 
a.tion can be distributed among independent sur- 
face strings. Under the light of this proposal, many 
of the phenomena which have been argued in (Pof 
lard & Sag 1987) to justify the horizontal related- 
ness approach can be viewed as different 'inter- 
pretations' of a 'core' lexical entry according to 
well-specified types of 'context'. tlowever, it must 
be noted here that this is not always a simple task. 
Roughly speaking, the less specific the contextual 
information is the more inference power and ex- 
pressivity is needed to retain the underspecifica- 
tion approach. 
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