A PROPOSAL FOR MODIFICATIONS IN THE FORMALISM OF GPSG 
James Kilbury 
Universit~t~Trier, FB II: LDV 
Postfach 3825, D-5500 Trier 
Fed. Rep. of Germany 
ABSTRACT 
Recent investigations show a remarkable conver- 
gence among contemporary unification-based formal- 
isms for syntactic description. This convergence 
is now itself becoming an object of study, and 
there is an increasing recognition of the need for 
explicit characterizations of the properties that 
relate and distinguish similar grammar formalisms. 
The paper proposes a series of changes in the for- 
malism of Generalized Phrase Structure Grammar that 
throw light on its relation to Functional Unifica- 
tion Grammar. 
The essential contribution is a generalization 
of cooccurrence restrictions, which become the 
principal and unifying device of GPSG. Introducing 
Category Cooccurrence Restrictions (CCRs) for lo- 
cal trees (in analogy to Feature Cooccurrence Re- 
strictions for categories) provides a genuine gain 
in expressiveness for the formalism. Other devices, 
such as Feature Instantiation Principles and Linear 
Precedence Statements can be regarded as special 
cases of CCRs. The proposals lead to a modified no- 
tion of unification itself. 
A PROPOSAL FOR MODIFICATIONS 
IN THE FORMALISM OF GPSG 
Recent investigations show a remarkable conver- 
gence among contemporary unification-based formal- 
isms for syntactic description (cf Shieber 1985). 
This convergence is now itself becoming an object 
of study, and there is an increasing recognition 
of the need for explicit characterizations of the 
properties that relate and distinguish similar 
grammar formalisms. For example, Shieber (1986) 
describes a compilation from Generalized Phrase 
Structure Grammar (GPSG; cf Gazdar et alii 1985, 
henceforth GKPS) to PATR-II. The compilation de- 
fines the semantics of GPSG by explicitly relating 
the two formalisms; at the same time, difficulties 
in specifying the compilation show that differ- 
ences between the formalisms transcend variety in 
notation. 
This paper is similar to Shieber's in its aim 
but differs in the approach. A series of changes 
in the formalism of GPSG will be proposed that 
make it look more like the "tool oriented" formal- 
ism of Functional Unification Grammar (FUG; cf Kay 
1984 and Shieber 1985). This notational transfor- 
mation has two consequences: the essential and 
nonessential differences between GPSG and FUG can 
be made more apparent, and the internal structure 
of GPSG itself becomes more homogeneous and trans- 
parent. 
The homogeneity of a formalism is desirable on 
methodological grounds that amount to Occam's 
principle of economy: entities should not be mul- 
tiplied. This is not to suggest that linguistic 
formalisms can be simplified at our will; on the 
contrary, they must be complex and expressive 
enough to capture the complexities inherent in 
language itself. The burden of proof, however, 
falls on those who choose more complicated and 
heterogeneous notational devices. 
Despite its restrictiveness in comparison with 
current transformational theory, GPSG in the GKPS 
version offers a rich palette of formal devices. 
It introduces Feature Cooccurrence Restrictions 
(FCRs) to state Boolean restrictions on the co- 
occurrence of feature specifications within cate- 
gories but does not explore the use of analogous 
restrictions in other parts of the formalism. Im- 
mediate Dominance rules, metarules, and lexical 
rules are clearly distinguished in their form but 
all serve to capture the phenomenon of subcategor- 
ization. 
This paper proposes the extension of cooccur- 
rence restrictions in GPSG to express constraints 
on the cooccurrence of categories within local 
trees. While presented in Kilbury (1986) as a new 
descriptive device, such Category Cooccurrence 
Restrictions (CCRs) are in fact simply a general- 
ization of principles fundamental to GKPS. 
The motivation for CCRs is analogous to that 
for distinguishing Immediate Dominance (IO) and 
Linear Precedence (LP) rules in GPSG (cf GKPS, 
pp. 44-50). A context free rule binds information 
of two kinds in a single statement. By separating 
this information in ID and LP rules, GPSG is able 
to state generalizations of the sort "A precedes 
B in every local tree which contains both as 
daughters," which cannot be captured in a context 
free grammar. 
Just as ID and LP rules capture generalizations 
about sets of context free rules (or equivalently, 
about local trees), CCRs can be seen as stating 
more abstract generalizations about ID rules, 
which in turn are equivalent to generalizations of 
the following sort about local trees: 
156 
(I) Any local tree with S as its root must have 
A as a daughter. 
(2) No local tree with C as a daughter also has 
D as a daughter. 
We can state CCRs as expressions of first order 
predicate logic using two primitive predicates, 
R(~, t) '~ is the root of local tree t' and 
D(~, t) '~ is a daughter in local tree t'. 
Advantages of CCRs are discussed in Kilbury 
(1986): The metarules of GPSG can be eliminated as 
an extra device of the formalism. As noted above, 
generalizations can be captured that elude the ex- 
pressive capabilities of GPSG. Moreover, CCRs ren- 
der the GPSG formalism more homogeneous and estab- 
lish a parallelism that can be expressed in the 
traditional notation ~ of an analogy: 
(3) FCR : category :: CCR : local tree 
Linguistic items (categories and local trees) 
and restrictions on such items make up the terms 
of the above analogy. GPSG chooses to represent 
the items and restrictions as different kinds of 
object, whereas FUG has only one kind of object, 
the functional description (FD), which Kay (1984: 
76) defines as "a Boolean expression over fea- 
tures" \[i.e. GPSG feature specifications\]. Thus, 
a homogeneous formalism for GPSG is easily 
achieved: just like cooccurrencerestrictions, lin- 
guistic items can be represented as Boolean ex- 
pressions, namely, as conjunctions of atomic as- 
sertions. 
We shall henceforth regard a GPSG category as a 
conjunction of assertions about the values as- 
signed to features \[i.e. FUG attributes\]; the as- 
sertions assigning these values constitute feature 
specifications. Unlike FUG, which always allows 
more information to be added to FDs and hence has 
no notion of a complete description, GPSG has ful- 
ly specified categories in which every feature 
possible for the category is assigned a value. 
Excluding certain extensions to GPSG for non-con- 
text-free phenomena (cf Gazdar and Pullum 1985), 
GPSG allows only a finite number of categories for 
a language, while FUG permits infinitely many FDs. 
Like FDs, GPSG categories do not have a fixed term 
structure, but this property is nonessential for 
GPSG while being essential for FUG. It may be 
added that the modifications to GPSG proposed here 
leave it nonfunctional in Kay's sense. 
FUG as described in Kay (1984) provides for 
conjunction and disjunction but not for negation 
in FDs. Karttunen (1984), however, argues for the 
use of both disjunction and negation in unifica- 
tion-grammar formalisms. GPSG has the full set of 
logical connectives in FCRs, which are arbitrary 
Boolean conditions on the cooccurrence of feature 
specifications within categories; categories them- 
selves, however, are restricted in form to con- 
junctions of feature specifications. If the formal 
distinction of GPSG between linguistic items and 
linguistic restrictions is abandoned in favor of a 
uniform representation for both as Boolean expres- 
sions, we then can in effect use disjunction and 
negation in the categories as well. Conversely, we 
may view FCRs as partially instantiated catego- 
ries, and CCRs correspondingly as partially in- 
stantiated local trees. 
All Boolean expressions can be written in con- 
junctive normal form ,£NF), i.e. as a conjunction 
of disjunctions of li~erals (positive or negated 
atomic expressions). Expressions in CNF are in 
turn equivalent to clause sets, i.e. sets of such 
disjunctions. Given this uniform representation 
for linguistic items and grammatical statements, 
it should come as no surprise to see unification, 
the principal operation of unification grammar, be 
closely identified with resolution as introduced 
by Robinson (1965) for automatic theorem proving. 
Nevertheless, no previous version of unification 
grammar has to my knowledge taken just this step. 
The proposed operation differs somewhat from 
resolution. While the resolution of the clause 
sets {P} and {~P v Q} yields the resolvent 
( Q~, their unification in this sense produces 
( P, Q \]. Some examples of such resolution-based 
unification will be useful at this point: 
(4) C I = {f1:vl, (--f2:v2 v f3:v3) ) 
c2: {f2:v2} 
c a : {fa:va } 
C 4 = {f2:v2 w f4:v4~; 
: {f2:v4 } 
c I U c 2 : { fl 
= {fl 
c I U c 3 : {fl 
= {fl 
:v I, f2:v2, (,,true v f3:v3)} 
:v I, f2:v2, f3:v3 } 
:v I, f3:v3, (~f2:v2 v true)} 
:v I, f3:v3 } 
C I U C 4 = {f1:vl, (f3:v3v f4:v4)} 
Note that for any two atomic values a I and a 2, 
the unification a I U a 2 succeeds iff a I : a2. 
Given (4) above, if v 2 II v 4 succeeds (whether v 2 
and v 4 are atomic or complex), then the unifica- 
tion C 2 U c 5 : {f2:(v2 U v 4)} succeeds; if 
v 2 U v 4 fails, then C 2 Ll c 5 also fails. The uni- 
fication C I U C 5 has three cases: 
(5) C I U C 5 = {f1:vl, f2:v4, (~,true v f3:v3)} 
= ~f1:vl, f2:v4, f3:v3 
if v 2 II v 4 succeeds and v 4 is an 
extension of v 2 
C I U C 5 = { f1:vl, f2:v4, (,~f2:v2 v f3:v3)} 
if v 2 U v 4 succeeds and v 4 is not 
an extension of v 2 
157 
C I U C 5 : {f1:vl, f2:v4, (~-false vf3:v3)} 
: {f1:Vl, f2:v4 } 
if v 2 U v 4 fails 
FUG employs two special values, ANY and NONE, 
which unify with any and no other value, respec- 
tively. With the adoption of negation in the form- 
alism, ANY and NONE emerge in the following dual 
relationship: 
(6) ~f: ANY ~ f: NONE (Def.) 
-~f: NONE ~ f: ANY (Def.) 
ANY and NONE may be used in GPSG to express the 
condition that a feature must or may not receive a 
value. Shieber (1985: 32) notes that ANY consti- 
tutes a nonmonotonic device in the formalism, 
since final representations must not contain occur- 
rences of ANY. In our terms, final representations 
must not contain negation or disjunction, i.e., 
they must be sets of unit clauses, each of which 
is a nonnegated literal. Since the logic upon 
which this formalism is based is monotonic, how- 
ever, the essential monotonicity of the formalism 
is preserved. 
GPSG goes a step further and introduces Feature 
Specification Defaults (FSDs), which are a patent- 
ly nonmonotonic device based on default logic. 
This paper proposes banning them from the formal- 
ism for the time being. Some of the particular 
FSDs formulated in GKPS for English appear ques- 
tionable under different analyses (cf Kilbury 
1986). This is notto deny that default statements 
may capture significant generalizations about lan- 
guage. But why, then, should defaults be confined 
to the statement of restrictions on categories? 
It may be methodologically advantageous to first 
develop a more homogeneous and coherent formalism 
for GPSG without strongly nonmonotonic devices. 
If default logic later still appears desirable on 
theoretical linguistic grounds, then it can be re- 
introduced in a more principled fashion allowing 
default statements at all levels of linguistic 
description where it is useful. 
The position of Linear Precedence (LP) state- 
ments in this formalism must now be clarified. It 
was stated above that CCRs are formulated using 
the two primitive predicates R(~, t) '~ is the 
root of local tree t' and D(~, t) '~ is a daugh- 
ter in local tree t'. This is not quite adequate 
since different daughters in a local tree may be 
tokens of the same category. Let us replace 
0(~, t) with 0(~, i, t), interpreted as '~t is the 
i-th daughter in local tree t'. A local tree t 
with VP as root and V, NP, and NP as daughters (in 
that order) can now be represented with the fol- 
lowing set of unit clauses: 
(7) {R(VP,t), D(V,I,t), D(NP,2,t), D(NP,3,t)} 
Likewise, the LP statement ,t < S '~ may not 
precede ~ in any local tree t' (where '<' denotes 
the LP relationship) may be reformulated in a log- 
ical expression (using '(' for arithmetic compari- 
son) as follows: 
(8) Vt: ( 0(~., i, t) ^ D(B, j, t)) ~ i<j 
This, in turn, can be represented as a set con- 
taining one clause: 
(g) i, t) v ~D(a, j, t) v (i<j))} 
If arithmetic comparison '(' is now added to 
the primitive predicates allowed in CCRs, then LP 
statements become simply a special case of CCRs; 
they are applied to local trees by resolution- 
based unification with the representations of the 
latter. 
The principle of cooccurrence restrictions can 
be further generalized in a final step. GPSG de- 
scribes linguistic items and their distributions. 
Local trees are arrangements of categories, which 
in turn are arrangements of feature specifica- 
tions; the latter are themselves items consisting 
of a feature name and a feature value in an ar- 
rangement. The formal devices already introduced 
allow us to state cooccurrence restrictions gov- 
erning the combination of features and values in 
feature specifications; the definition of the 
value range of a feature can thus be regarded as 
another special case of cooccurrence restriction. 
In summary, the essential contribution of this 
paper lies in its generalization of the notion of 
cooccurrence restriction. Many of the distinct 
formal devices of GPSG as presented in GKPS can be 
eliminated without an apparent loss of expressive 
power, and the resulting formalism gains both in 
simplicity and homogeneity while preserving essen- 
tial properties of the GKPS formalism. Likewise, 
the uniform representation of cooccurrence re- 
strictions and linguistic items allows a new in- 
terpretation of unification which is promising in 
its own right and which should facilitate the com- 
parison of GPSG with other unification-based gram- 
mar formalisms. Parallels to other linguistic ap- 
proaches, both more and less distant, should be 
evident. Similarities to American structuralism 
are neither accidental nor unintentional. In re- 
gard to his own proposals for unification, 
Karttunen (1984: 31) remarks that "the problems 
that arise in this connection are very similar to 
those that come up in logic programming." Indeed, 
many questions involving the equivalence of nota- 
tions and of computational problems are raised 
that must be addressed in future studies. 
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159 
