A Simple Reconstruction of GPSG 
Stuart M. Shieber 
Artificial Intelligence Center 
SRI International 
and 
Center for the Study of Language and Information 
Stanford University 
Abstract 
Like most linguistic theories, the theory of generalized phrase 
structure grammar (GPSG) has described language axiomati- 
cally, that is, as a set of universal and language-specific con- 
attaints on the well-formedncss of linguistic elements of some sort. 
The coverage atttl detailed analysis of English grammar in the 
ambitious recent volume by Gazdar, Klein, Pullum, and Sag enti- 
tled Generalized Phrase Structure Grammar \[2\] are impressive, in 
part because of the complexity of the axiomatic system developed 
by the authors. In this paper, we examine the possibility that 
simpler descriptions of the same theory can be achieved through 
a slightly different, albeit still axiomatic, method. Rather than 
characterize the well-formed trees directly, we progress in two 
stages by procedurally characterizing the well-formedness axioms 
themselves, which in turn characterize the trees. 
1 Introduction I 
Like most llngafistic theories, the theory of generalized phrase 
structure grammar (GPSG) has described language axiomati- 
cally, that is, as a set of universal and language-specific con- 
straints on the we\[l-formedncss of linguistic elements of some 
sort. In the case of GPSG, these elements are trees whose nodes 
are themselves structured entltics from a domain of categories 
(a type of feature ~trueture \[6\]). The proposed axioms have be- 
come quite complex, culminating in the ambitious recent volume 
by Gazdar, Klein, Pullum, and Sag entitled Generalized Phrase 
Structure Grammar \[2\]. The coverage and detailed analysis of 
English grammar in this work are impressive, in part because of 
the complexity of the axiomatic system developed by the author. 
In this paper, we examine the possibility that simpler descrip- 
tions of the same theory can be achieved through a slightly dif- 
ferent, albeit still axiomatic, method. Rather than characterize 
the well-formed trees driectly, we progress in two stages by pro- 
cedurally characterizing tim well-formedaess axioms themselves, 
which in turn charaetei'ize the trees. In particular, we give a pro- 
cedure which converts GPSG gramma~ into gramma~ written 
lThls research was m~de possible by a gift. from the System Development 
Foundation. 
I am indebted to Lauri K~rttuncn and Ray Perrault for their eomrael~te 
on earlier drafts, and to Roger Evans, Gerald Gszdsr~ Ivan S~.$t ltenry 
Thompson, and members of the Foundations of Grammar project at the 
Center for the Study of Language and Information for their helpful dis- 
cussions during the development of this work. 
in a unification-b~qed formalism, the PATR-II formalism devel- 
oped at SRI International (henceforth PATR) \[5\], which h~s its 
own declarative semmltics, and which can therefore be viewed &s 
an axiomatization of string well-formedness constraints. 2 
The characterization of GPSG thus obtained is simpler and 
better defined than the version described by Gazdar et al. The 
semantics of the formalism is given directly through the reduction 
to PATR. Also, the PATR axiomatization has a clear construe- 
tire interpretation, unlike that used in Gazdar et al., thus mak- 
ing the system more amenable to computational implementation. 
Finally, the characteristics of the coml~ilation--the difficulty or 
ease with which the various devices can be encoded in PATR-- 
can provide a measure of the expressiveness and indispensability 
of these devices in GPSG. 
2 The GPSG Axioms 
2.1 A Summary of the Principles 
GPSG describes natural languages in terms of various types of 
constraints on local sets of nodes in trees. Pcrtlncnt to the ensu- 
ing discussion are the following: 
• ID (immediate dominance) rules, which state constraints of 
immediate dominance among categories; 
• metarules, which state generalizations coI~ccraing classes of 
ID rules; 
¢ LP (linear precedence) rules, which constrain the Ihwar or- 
der of sibling categories; 
• feature cooccurrencc restrictions (FCR), which constrain the 
feature structures as to which arc permissiHe categories; 
a feature specification defaults (FS1)), which provide values 
for features that are otherwise unspecified; 
and, most importantly, 
21towever, a caveat is \]n order th:~t the detailed ~u~alysis from this perspec- 
tive of the full range of GPSG devices (especially immediate dominance 
(ID) rules, and feature cooccurrence restrictions) is not discussed fillly 
here, nor do I completely understand them. (See Section 3.4.} And while 
in a confessional mood, I should add that the Msorlthm given here has not 
actually been implemented. 
211 
® universal feature instantiation principles, which constrain 
the allowable local sets of nodes in trees; these feature in- 
stantiation principles include the head feature convention 
(HFC), the foot feature principle (FFP), and the control 
agreement principle (CAP). 
In GPSG all of these constraints are applied simultaneously. 
A local set of nodes in a tree is admissible under the constraints 
if mad only if there is some base or derived ID rule (which we 
will call tile licensing rule) for which the parent node's category 
is an extension of the left-hand-side category in the rule, and the 
children arc respective extensions of right-hand-side categories in 
the rule, and, in addition, the set of nodes simultaneously satis- 
fies all of the separate feature instantiation principles, ordering 
constraints, etc. By eztension, we mean that the constituent has 
all the feature values of the corresponding category in the licens- 
ing rule, and possibly some additional feature values. The former 
type of values are called inherited, the latter instantiated. 
The feature instantiation principles are typically of the follow- 
ing form: if a certain feature configuration holds of a local set 
of nodes, then some other configuration must also be present. 
For instance, the antecedent of the control agreement principle 
is stated in terms of the existence of a controller and eontrollee 
which notions are themselves defined in terms of feature configu- 
rations. The consequent concerns identity of agreement features. 
2.2 Interaction of Principles 
Much care is taken in the definitions of the feature instantia- 
tion principles (and their ancillary notions such as controller, 
eontrollee, fl'ce features, privileged features, etc.) to control the 
complex interaction of the various constraints. For instance, the 
FFP admits local sets of nodes with 8la~h feature values on parent 
and child where no such values occur in the licensing ID rule, i.e., 
it allows instantiation of slash features. But the CAP's above- 
mentioned definition of control is sensitive to the value of the 
slash feature associated with the various constituents. A simple 
definition of the CAP would ignore the source of the slash value, 
whether inherited, instantiatcd by the FFP, or instantlated in 
some other manner, llowevcr, the appropriate definition of con- 
trol needed for the CAP must ignore instantiated slash features, 
but not inherited ones. Say Gazdar et al.: 
We must modify the definition of control in such a way 
that it ignores perturbations of semantic type occa- 
sioned by the presence of instantiated FOOT features. 
12, p. 87\] 
Thus, the CAP is in some sense blind to the work of the PFP. 
As Gazdar ctal. note, this requirement makes stating the CAP 
a much more complex task. 
The increased complexity of the principles resulting from this 
need for tracking the origins of feature values is evident not only 
in the CAP, but in the other principles as well. The head feature 
convention requires identity of the head features of parent and 
!,,ad child. The features ayr and slash--features that can be 
itfimrited from an ID rule or instantiated by the CAP or FFP, 
respectively--are head features and therefore potentially subject 
to this identity condition. However, great care is taken to remove 
such instantiated head features from obligatory manipulation by 
the tIFC. This is accomplished by limiting the scope of the ItFC 
to the so-called free head features. 
Intuitively, the free feature specifications on a category 
\[the ones the HFC is to apply to\] is the set of feature 
specifications which can legitimately appear on exten- 
sions of that category: feature specifications which con- 
flict with what is already part of the category, either 
directly, or in virtue of the FCRs, FFP, or CAP, are 
not free on that category. \[2, p. 95\] 
That is, the FFP and CAP take precedence (intuitively viewed) 
over the ItFC. 
Finally, all three principles are seen to take precedence over 
feature specification defaults in the following quotation. 
In general, a feature is exempt from assuming its default 
specification if it has been assigned a different value 
in virtue of some ID rule or some principle of feature 
instantiation. \[2, p. 1001 
Qazdar et al. accomplish this by defining a class of privileged 
features and excluding such features from tile requirement that 
they take on their default value. Of course, instantiated head fea- 
tures, slash features, and so forth are all considered privileged. 
However, a modification of these exemptions is necessary in the 
case of lexical defaults, i.e., default values instantiated on lexical 
constituents. We will not discuss here the rather idiosyncratic 
motivation for this distinction, bnt merely note that Icxical con- 
stituent defaults are to be insensitive to changes engendered by 
the HFC, as revealed in' this excerpt: 
ftowever, this simpler formulation is inadequate since 
it entails that lexical heads will always be exempt from 
defaults that relate to their ttEAD features .... Accord- 
ingly, tile final clause needs to distinguish lexical cate- 
gories, which become exempt from a default only if they 
covary with a sister, and nonlexieal categories, which 
become exempt from a default if they covary (in rele- 
vant respects) with any other category in the tree. \[2, 
p. 103\] 
Thus the interaction of these principles is controlled through 
complex definitions of the various classes of features they are 
applicable to. These definitions conspire to engender the fol- 
lowing implicit precedence ordering on tire principles, principles 
earlier in the ordering being blind to the instantiatlons from later 
principles, which are themselves sensitive to (and exempt from 
applying to) features instantlated by the earlier principles) 
CAP ~.4 FFP ~'- FSDuz ~ tlFC >- FSDno,a~ 
Of course, all ID rules, both base and derived arc subject to 
all these principles; yet met,rule application is not contingent on 
instantiations of the base ID rules. Conversely, LP constraints 
are sensitive to the full range of instantiatcd features. The prece- 
dence ordering can thus be extended as follows: 
SCurrent efforts by at least certain GPSG practitioners are placing the 
GPSG type of analysis directly in a PATR-like formalism. This formal- 
ism, Pollard's head-drlven phrase structure grammar (ltPSG) variant of 
GPSG, uses a run-time algorithm similar to the one described in this pa- 
per \[4\]. Highly suggestive is the fact that the \]IPSG run-time algorithm 
also happens to order the principles in substantially the same way. 
4We use the symbol ~- to denote one principle "taking precedence over" 
another. 
212 
META ~- CAP ~- FFP >- FSDttx 
~- ItFC >- FSDno,u~ ~" LP 
The existence of such an ordering on the priority of axioms is, 
of course, not a necessary condition for the coherence of such an 
aximaatic theory. Undoubtedly, this inherent ordering was not 
apparent to the developers of the theory, and may even be the 
source of some surprise to them. Yet, the fact that this ordering 
exists and is strict leads us to a substantial simplification of the 
system. Instead of applying all the constraints simultaneously, 
we might do so sequentially, so that the precedence ordering-- 
tile blindness of earlier principles in the ordering to the effects of 
later ones emerges simply because the later principles have not 
yet applied. 
This solution harkens back to earlier versions of GPSG in 
which the semantics of the formalism was given in terms of 
compilation of the various principles and constraints into pure 
context-free I~lles. This compilation process can be combinato- 
rially explosive, yielding vast numbers of context-free rules. In- 
deed, the whole point of the GI'SG decomposition is to succinctly 
express generalizations about tile possible phrasal combinations 
of natural languages, ltowever, by carefully choosing a system 
for stating constraints on local sets of nodes--a formalism more 
compact in its representation than context-free grammars--we 
call compile out the various principles and constraints without 
risking this explosion in practice. 
The GPSG principles are stated in terms of identities of fea- 
tures. What we need to avoid the combinatorial problems of pure 
CF rules is a formalism in which such equalities can be stated 
directly, without generating all the ground instances that satisfy 
the equalities. What is needed, in fact, is a unification-based 
grammar formalism \[6\]. We will use a variant of PATR \[5\] as 
the fi)rmalism into which (H)SG grammars are compiled. In par- 
tieular, we assume a version of PATR that has been extended 
by the familiar decomposition into an immediate-dominance and 
linear-precedence component. Ttfis will allow us to ignore the 
LP portion of GPSG for the nonce. 
PATR is ideal for two reasons. First, it is the simplest of the 
unification-based grammar formalisms, possessing only the appa- 
ratus that is needed for this exercise. Second, a semantics for the 
formalism has been provided, so that, by displaying this compi- 
lation, we implicitly provide a semantics for GPSG grammars as 
well. In the remainder of the paper, we will assume the reader's 
familiarity with the rudiments of the PATR formalism. 
3 The Compilation Algorithm 
We postpone for the time being discussion of the metarules, LP 
constraints, and feature eooccurrence restrictions, concentrat- 
ing instead on the central principles of GPSG, those relating to 
feature instantiation. The following nondeterministic algorithm 
generates well-formed PATR rules from GPSG ID rules. A GPSG 
grammar is compiled into the set of PATR rules generated by this 
algorithm. 
is written in unordered PATR as 
Xo~Xt, X2 
(Xo n) =- 
(Xo ~) =+ 
(Xo bar) = 2 (R~) 
(Xo s,,O) = + 
(Xl bar) = 2 
(x2 s.O) =- 
Note that abbreviations (like 5' for l-n, +v, bar2,-t.subj\]) have 
been mad(; explicit. 
In fact, we will make one change in tile structure of categories 
(to simplify our restatement of the HFC) by placing all head 
features under the single feature head in tile corresponding PATR 
rule. We do not, however, add an analogous fcature foot. s Tiros 
the preceding rule becomes 
Xo --* Xi, Xz 
(Xo head n) = .- 
(Xo head v) = -t- 
(xo head bar) = e (~) 
(Xo head subj) = + 
(Xt head bar) = 2 
(X2 head sub l) = - 
We use an operation addc (read "add conservatively') which 
adds an equation to a PATI~ rule conservatively, in Ihc sense 
that the equation is added only if thc equations arc not thereby 
rendered unsolvable. If addition would yield uosolvability, thcn a 
weaker set of unifications arc added (conserw~tively)instead, one 
for each feature in the domain of tile value being equated. For in- 
stance, suppose that the operation add~((Xo head) = (Xt head)) 
is called for, where the domain of the head feature wdues (i.e., 
the various head features) arc a, b, and c. If the equations in 
the rule already Sl)ccify that (X0 head a) # (X1 hc~,d a) then 
this operation would add only the two equations (X0 head b) = 
(Xl head b) and (Xo head c) = (Xt head c), sincc the addition 
of the given equation itself would cause rule failure. Thus the 
earlier constraint of values for the a feature is given precedence 
over the constraint to be added. 
In the description of the algorithm, a nonempty path p is said 
to be defined for a feature structure X if and only if p is a unit 
path (\]) and f ~ dora(X) or p = (h?) and p' is defined for 
X(f). Our notion of a feature's being defined for a constituent 
corresponds to the GPSG concepts of being instantiated or of 
covarying with some other feature. 
As in the previous definition, we will be quite lax with respcct 
to our notation for paths, using ((a b) c) and (a (b e) ) as 
synonymous with (ab c) . Also, we will eonsistcntly blur the 
distinction betwcen a set of equations and the fcaturc structure 
it determines. (Sce Shleber \[7\] for details of the mapping that 
makes this possible.) 
3.2 The Algorithm Itself 
Now our algorithm for compiling a G PSG grammar into a PATR 
grammar follows: 
3.1 Preliminaries 
We first observe that a GPSG ID rule is only notationally dis- 
tinct from an unordered PAI'R rule. Thus, the first step in the 
algorithm is trivial. For example, the ID rule 
,'~ -+ x ~, II\[- ,ub j\] ( RI ) 5But recall that dawh is a head feature and titus would fall tinder the p~th (head slash) . 
213 
For each ID rule of GPSG (basic or derived by metarule) X0 "--' 
X1,... ,X,,: 
CAP If Xi controls Xy (determined by Type(Xi) and Type(Xj)), 
then adde((Xl con) = (Xj con)) where 
(head slash) if (head slash) is defined for Xi 
con = (head acr) otherwise 
FFP For each foot feature path p (e.g., (head slash} ), ifp is not 
defined for Xo , then adde((Xi p) = (Xo p) ) for zero or more 
i such that 0 < i <_ n and such that p is not defined for X,'. 6 
FSDtez For all paths p with a default value, say, d, and for all i 
such that 0 < i < n, if (Xi bar) = 0 and p is not defined for 
Xi, then add,((X¢ 1) = d). 
HFC For X/the head of X0, add~((Xi head) = (Xo head)). 
FSDnont~z For all paths p with a default value, say, d, and for 
all i such that 0 < i _< n, if (Xi bar) # 0 and p is not defined 
for X¢, then add¢((X¢ J) = d). 
3.3 An Example 
Let us apply this algorithm to the prcceding rule RI. 7 We start 
with the PArR equivalent Rs. By checking the existing control 
relationships in this rule as currently instantiated, we conclude 
tbat the subject X1 controls the bead )(2. We conservatively add 
the unification (X2 head agr) = (XI). This can be safely added, 
and therefore is. 
Next, the FFP step in the algorithm can instantiate the rule 
further. Suppose we choose to instantiate a slash feature on X2. 
Then we add the equation (Xo head .dash) = (X2 head slash). 
Lexical default values rcqulre no new equations, since no con- 
stituents in the rule are given as 0 bar at this point. 
The tlFC conservatively adds the equation (X0 head) = 
(X2 head), as )(2 is the head of Xo. But this equation, as it 
stands, would lead to the entire set of equations being unsolv- 
able, since we already have conflicting values for the head feature 
subj. Thus the following set of unifications is added instead: s 
{X0 head n) = (X2 head n) 
(Xo head v) = (X2 head v) 
(Xo head bar) = (X2 head bar) 
{X0 head agr) = (X2 head agr) 
(Xo head ;nv) = (x2 head in,) 
6Several comments are pertinent to this portion of the algorithm. First, 
it is the FFP portion that is responsible for its nondeterminism. Second, 
the operation add¢ is actually superfluous here. The equation can simply 
be added directly, since we have already guaranteed that the pertinent 
features are not yet instantiated. By a similar argument, we can conclude 
that only the addc operations in the CAP and HFG are actually necessary. 
We will use adds, however, for uniformity. Finally~ we assume that an FSD 
will place the value ~ on any remaining constituents unmarked for foot 
features. 
7We do not include here the effect of the rule on every feature postulated 
by Gazdar etal. but only a representative sample. 
8A more efficient representation of such sets could be achieved by the intro- 
duction of nonmonotonic operations such as overwriting or priority union. 
But such considerations need not concern us here. 
214 
Finally, nonlexieal defmdts are introduced for features not in 
the domains of constituents2 Since the path (head inv) is de- 
fined for the constituents X0 and X2, l° the defanlt value (i.e., 
'-' according to FSD 1 of Gazdar et al.) is not instantiated on 
either constituent. Similarly, the case default value (ace, FSD 
10) is not instantiated on tile subject NP. But the conj feature 
default tt ('~') will be instantiated on all three constituents with 
the equations 
(Xo eo.~,) = ~ 
(xl conj) = ~ 
(xz eonj) = ~ 
The (partial) generated rule is the following: 
Xs -* X~, Xz 
(Xo head n) = - 
(Xo head v) = + 
(Xo head bar} = 2 
(Xo head subl) = + 
(X1 head bar) = 2 
(X2 head subl) = - 
(X2 head agr) = (X1) 
(Xo head slash) = (Xz head slash) 
(xo head .) = (xz head .) 
(Xo head v) = (X2 head v) 
(Xo head ~ar) = (xz head bar) 
(Xo head aor) = (X~ head a~r) 
(Xo head inv) = (-)(2 head inv) 
(x 0 co@ = ~ 
(X, co@ = ~ 
(X2 so.j) = ~ 
3.4 Problems and Extensions 
Several problems have been glossed over in tile previous discns- 
sion. First, we have not mentioned the role of LP rules. Two 
possibilities are available for their interpretation: a "rtm-time" 
and a "eompile-tlme" interpretation. We can augment tile PATR 
formalism with I,P rules in tbe same way as Gazdar et al., pro- 
viding for local sets of nodes to satisfy an unordered PATR rule 
if and only if the nodes are extensions of elements in the ID rule 
such that the LP rules are all satisfied. Alteruatively, we can 
generate at compile time all possible orderlngs of tile unordered 
rules compatible with ttle LP statements, but this leads us into 
the problem of interpreting LP statements relative to partially 
instantiated categories, an issue beyond the scope of tiffs paper. 
Second, feature eooeeurrenee restrictions were ignored in the 
previous discussion. Again, we will limit ourselves to a brief dis- 
eussion of the possibilities. One alternative is to modify the lat- 
OWe have made the simplifying assumption that feature specification de- 
faults are stated in terms of simple default values for features, rather than 
the more complex boolean conditions used in the Gazdar et al. text. 
The modifications to allow the more complex FSDs may or may net be 
straightforward. 
t°The value of the feature head on the constituent Xo has the feature inv in 
its domain because the unification (Xo head iuv} = (X2 head inv) gives 
as value to (Xo head inv} a variable, the same variable as the value for 
(X2 head ins) . Thus the path (head lay} is defined for Xo and, similarly, 
for X:. 
IIWe assume here, contra Gazdar et al., that '~' is a fnll-fledged value in 
its own right, at least as interpreted in this compilation. Since this value 
fails to unify with any other value, e.g., '+' or '-', it has exactly the 
behavior desired, namely, that the feature is prohibited from taking any 
of its standard values. 
tice of categories relative to which unification is defined tz in such 
a way that all categories violating the FCILs are simply removed. 
Then unification over this revised lattice will be used instead 
of the simpler w!rsion and FCRs will automatically always be 
obeyed. Unfortunately, tire possibility exists that unification over 
tile revised lattice may not bear the same ordcr-in(lependence 
properties that characterize unification over the freely-generated 
lattice.. Of course, if this turns out to be the ease, it c~,~ts doubt 
on the well-fomMedness of the original Gazdar et al. interpre: 
tation of FCRs as well, apd tlms is an interesting question to 
pursue. 
Another alternative involves checking the FCRs at every point 
in the algorithm, throwing out any rules which violate them at 
any point. In addition, FCRs would be required to be checked 
during rau-time as well. This alternative, though more direct, 
violates the spMt of the enterprise of giving a compilation from 
the eoml>lex Gazdar et al. formulation to n simpler system. 
A final problenl concerns the ordering of the III"C and the 
(JAIL The definitions of eontroller and controllee necessary for 
stating ttw CAP depend on the assigmnent of semantic types tr) 
constitncnts, which in turn deltend on the configuration of fea- 
tures in {;he categorical. We have ah'eady noted that the features 
pertinent to tit(! definition of sen(antic type (and hence control) 
do not include instantiatcd fi)ot featttrcs. Indeed, Gazdar et al. 
claim that "it is just IlEAl) feature specifications (other than 
those which are also I?OOT feature specifications) and inherited 
FOOT fl,aturc specifications that determitre the semantic types 
relevant to the definition of control." \[2, p. 87\] Unfortunately, 
the orderiug we have giveu lu'ecludes instantiated head features 
from participating in the definition of semantic type and hence 
the CAI)) "~ It seems that the III"C nmst apply before che CAP 
lot the (Mini\[ion of semantic type, but after the CAP so that the 
CAI' instantiatlons of head features take ln,eeedence. Tbus, our 
earlier claim of strict ordering may be falsified by this case. 
Of com-se, the :~et of features neeessat T for type determination 
and the :act; instantiated by tile CAP may be disjoint. In this 
case, we can merely split the application of the IIFC in two, in- 
start\[taring the flu'met' class beibre the CAP and tile latter class 
after the FFP ms originally described. Alternatively, it might be 
possible to notate head features on the head constituent rather 
than tim l)arent as is conventlally dtate. In this case, tile infor- 
mation needed by tile CAP is inherited, (tot instantiated, head 
feature wdues, atnl titus not subject to the ordering problem. 
On the other hand, if the sets are nondisjoint, this presents a 
problem not only for our algorithmic analysis, but for the deti- 
nltion of GI'SG given by Gazdar et al. Suppose that the IlFC 
determines types in such a way that the CAP is required to ap- 
ply and instantiates head features thereby overriding the original 
values (since the CAP takes preeedence) attd changing the type 
determination so that the CAP does not apply. We wouhl thus 
require the CAP to apply if and only if it does not apply. This 
paradox :qtpears as an ordcring cych: in our algorithm; in the 
declarative detinition of Gazdar et al., it would be manifested 
in the inadmissability of all local set.~ of nodes 11\], at( equally 
unattractive effect. We leave the resolution of this problem open 
for the time being, merely noting that it is a di|fieulty for GPSG 
iu general, and not only for our characterization. 
l~For the technicM background of st\[d\[ a move, see the discussion of PATR 
semantics \[3\]. 
~uI am indt:bted to Roger Evens and William Keller for pointing this problem 
out, to me and for helpful discussion of solution alternatives. 
4 Conclusion 
The axiomatic formulation of generalized phrase structure gram° 
mar by Gazdar et al. is a quite subtle and complex system. Yet, 
as we have qhown, GPSG grammars cm~ be substantially con- 
verted to grammars in a simpler, attd constructive, axiomatic 
system through a straightforward (albeit procedural) mapping. 
Intrinsic iu this conversion is the use of a unification-based gram- 
mar formalism, so that axioms can be stated schematically, with- 
out enumerating all nf their possible instantiations. In fact, we 
wouhl contend that defining the semantics of a GI)SG grammar 
in this way yields a much simpler fornmlation. The need for such 
a reconstruetinn is evident to anyone who has studied tit\[: C;azdar 
et al. text. 
Of course, even if certain parts of the GPSG for'realism not 
discussed fully here, i.e., FCRs att(I l,l ) constraints, arc found not 
to be reducible to PATR, this in itself wouhl be an interesti,g 
fact. It wouhl slmw that exactly those porticos of the formalism 
were truly essential for stating certain analyses, i.e., that analyses 
using those formal devices do so necessarily. 
We find a hopefid sign in the recent work in (\]PSG that is pro-. 
ceeding iu the direction of using unilication directly in the rules, 
in addition to its implicit m~e iu featuce instantiation principles. 
Wc hope that this paper has provided evidence that such a sys- 
tem may be able to more simply state the kiuds of generalizations 
that linguists claim, and has pointed out I)oth the possibilities 
and difllcultics inherent in these tcehniques. 
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