Using Active Constraints to I)arse "")~'(' ',.:, \[ ,~ k,,<; 
Philipl)e I/la(:he 
lnstitut d'hffor,natiqu(~ 
Universit6 de NeuchateI (Suisse) 
e-mail: Blach e((~i,ffo, unine,ch 
Abstract 
Active constraints of tile CO,lslratnl higic program- 
in,rig paradigm allow (l) the reduction of the 
search space of progr~tms and (2) a very concise 
representation of the problcnls. These two l)rop 
erties are particuhtrly interesting for I)arsing prob- 
\[elns : they can hel I ) us to reduce non-determinisln 
and to use large coverage gramlnars. In this paper, 
we describe how to use Slleh constraints tot parsing 
ID/LP grammars and propose an inlplenlelmtl, iou 
in Prolog Ill. 
Keywords : constraints, syntax, ID/I,P formalism, 
bottom-up filtering, Prolog IlI 
1 Introduction 
Logic programming is one of the nlost useful tools 
in computational linguistics. These two domains 
are progressing very rapidly. The former with the 
emergence of the constraint paradignl and the lat- 
ter with the systematic use of well-formalized lin- 
guistic theories. In the l~st few years, natural lal> 
guage processing (hereafter NLP) and more pre 
cisely syntax have created tools allowing expression 
of general knowledge. 
Constraints simplify parsing problems to a con 
siderable extent, both in a formal and computa- 
tional way. From a formal point of view, we will 
see that they allow a very good adequacy between 
linguistic aim computational theories. We know 
that this prol)erty is essential to solve generality, 
reusability and coverage prolflems. On the otimr 
hal,d, from a computatiolml point of view, con 
straints set up a control of the I)rocesses which re- 
duces non-determmisnl m parsing. 
The question is to know whether it, is possible to 
illlph!tlleIlt a I)arsiag Illethod I)ased oil actllal eoil- 
straints. The answer depends on the choice of the 
grmmnatical formalism. We think thai the II)/LP 
formalism used lit (IPS(-I theory can bring a sohl 
tion to this I)roblem. 
In this paper, we will describe a parsing method 
based on \[D/LP formalism using boolean con- 
straints. We will show that this nlethod agrees 
with th( goals of generality and corm'el. 
2 Parsing and deduction 
IIoth for historical itllll \[orlilal reasolls, parsing turn 
ck)se relalions with logic The birth of Prolog, for 
example, w~s conditioimd by Ihat aud NLP was 
one of the early applications of this language. One 
of the re~molls, a.s shown in \[PereiraS,g\], is tiiat we 
('.all compare |)arsdlg and dednet, ion, More pre- 
cisely, it phrase- structure rule (hereafter PS-rule) 
can be interpreted its a Rmnula (an ilnplication), 
like a classical inDrenee rule. 
'\['hus, a PS-rule of the form : 
NX ~ ('~,...,C,, 
can be interpreted as the fl~llowmg implication : 
(,'1 A ... A (.',, D ,S'X 
the clausal form of which is : 
~Ci V , . • V ~(5',, V ,b'X 
Because of the ui,iquei~ess of the positive literal, 
we can interpret a PS-.rule as a Ilorn clause, with a 
direct translation into I'rolog. Thus, a context-free 
gr~unlnar, represenled by a set. of PS rule, corre- 
sponds to a set of clauses. To verify the grammat- 
icality of a sentence is tluls equivMent to proving 
the COllSiSteacy of a set of clauses. 
There is, howew,r, a restriction in the analogy 
hetwee\[l P~-rtlleS &lid claltses : a \[1111', detines all 
order on ils right-haI.l--side chunelltS, whereas a 
clause does not. This restriction has important 
coliseqllenct,s 011 tho generality of the lileChalliSlllS. 
hldeed, lhe noti(m of order iiivoIvi)s it multilllica 
tion of the rifles describing a giw~n phrase : we get 
as zn;nly rules as there are (:onfigural.ious. This is 
one of the limits of phrase structure gramlnars. 
ll)/l,l' formMism and boolean constraints will 
alk)w us to sMve this problem. "Ore will obtain 
a nearly perfect adequacy bet.weeIl I.h~ theoretical 
iiiode\] aiid its implementation. Within the classi 
fieation proposed m iF, van.s87\], it will be a strong 
direct interl)retation of the model. 
A(m{s 131! COLING 92, NAN'II~S, 23 28 ao(rr 1992 8 1 Pit<It. OF COLING 92, NANrES, AU<;. 23-28, 1992 
3 Constraints and linguistic theory 
The basic mechanism of constraint logic program- 
ming is the restriction of the search space, or the 
reduction of the domain-variables. Tiffs goal can 
be reached differently depending on the active or 
passive constraint type (ef \[Vanllentenryck89\]). In 
the classical logic programming framework, the ba- 
sic technique is that of generate-and-test. Iu this 
ease, the program generates values for the vari- 
ables before verifying some of their properties : the 
search space is reduced a posteriori. On the other 
hand, in the CLP paradigm, the use of constraints 
allows the reduction of this space a priori. More- 
over, the set of constraints forms a system which 
incorporates new constraints (luring the process, 
while the use of simple predicatcs verifying a prop- 
erty only has a local scope. 
This active/passive distinction can be useful for 
parsing, especially according to the type of knowl- 
edge that is constrained. Active constraints can 
easily be defined for syntactic structures and their 
formation. On the other hand, expressing rela- 
tions between these structures with this kind of 
constraint is not always possible. 
We will describe the principles governing the for- 
marion of the structures. A syntactic structure can 
be of two types : 
* simplestructures : lexical categories (e.g. Del, 
N,V...) 
• complex structures : phrases or propositions 
(e.g. NP, VP ... ) 
The formation of complex structures is governed 
by two types of knowledge : 
• internal : specific information within a struc- 
ture 
• external : relations between structures 
Internal knowledge concerns the structure com- 
position, independently of its context. For a 
phrase, it is the set of its constituents. External 
knowledge describes interactions between struc- 
tures. They concern on the one hand the order and 
on the other hand tile government (in the sense of 
phrase-structure grammars : selection, agreement 
...). 
ID/LP formalism uses such a distinction : it 
separates information about immediate dominance 
(i.e. the set of possible constituents of a phrase) 
from that on linear precedence (i.e. the partial or- 
der relation between these constituents). 
It is possible to consider these two types of 
knowledge as constraints (cf \[Saint-Dizier91\]). But 
it is important to distinguish their respective fune- 
tionings. We will illustrate this point by presenting 
principles for each type. 
o Internal knowledge 
Each complex structure must contain at least 
one particular element called the head. This cat- 
egory gives the phrase its type and its presence 
is compulsory. The other constituents are usually 
optional. We must specify that local constraints 
could require the presence of a particular category, 
but it is a sub-categorization aspect : it concerns 
relations between the sub-structures of the com- 
plex structure and is not specific to the structure 
itself. We will see that this distinction between 
optional and compulsory constituents can be rep- 
resented directly as an active constraint. 
o External knowledge 
In the case of ID/LP formalism, the order con- 
straints (i.e. linear precedence) cannot be easily 
used with an a priori reduction of the search space. 
Indeed, LP-rules define a partial order upon the set 
of categories. The LP-aeceptability relation uses 
this order and can be regarded as a constraint upon 
the domain-variables. It is a symbolic user- defined 
constraint. The use of this kind of constraint is 
possible in Chip (ef \[Dincbas88\]), but not in Pro- 
log III (cf \[ColmerauergO\]). 
tlowever, using this order relation as an ac- 
tual constraint allowing the reduction of domain- 
variables is difficult. In so far as it is a partial 
order, the LP notion cannot be used to predict the 
categories that can follow a constituent. It is used 
during the parse to verify the possibility for each 
new category to appear at a given place in the syn- 
tactic structure. 
Generally speaking, internal properties allow an 
easier use of active constraints than external ones. 
4 Constraints and ID/LP formalism 
As we have seen, ID-rules of ID/LP formalism only 
contain tile set of possible constituents (without 
any notion of order). Therefore, an ID-rule is 
strictly equivalent to a clause. 
Example : 
N P "-'*id Del, N, AP ~ N P V ~De~ V ~N V ~AP 
This equivalence is the basis of the conciseness 
and generality properties of GPSG. But it is diffi- 
cult to represent. As we have seen, logic program- 
ming cannot directly represent the non-ordered as- 
pect of a clause. Ilowever, it is possible to repre- 
sent this kind of information as active constraints. 
These must allow the expression of tile simple fact 
that a phrase is well-formed if it is at least com- 
posed of the constituents Ct,..., C,. Other rela- 
tions between the structures (like order or selec- 
tion) will only be verified if this constraint is sat- 
isfied. 
ACT~.S DE COLING-92, NANTES, 23-28 AOt~rr 1992 8 2 PROC. OF COLING-92, NANTES, AUG. 23-28, 1992 
Practically, each rule descrihing a phrase cor: 
responds to a clause whose literals represent cat- 
egories. An ID-rule is thus translated into a 
boolean formula where each category corresponds 
to a boolean. The semantics of this representatiou 
is the following : 
A literal is true if it corresponds to a well-formed 
structure. A structure is well- formed if it corre- 
sponds to a le~cical category (simple structure) or 
to a well- formed phrase (compler structure). 
Thus, the boolean value of a complex structure is 
the interpretation of this formula, and so depends 
on the value of its constituents. 
Ezample : 
Given the following set of ID-rules de- 
scribing a NP : 
N P --q~ DeC N 
NP ~i,* N 
NP -old DeC AP, PP, N 
NP ~ia Det, AP, N 
NP --qa Det, PP, N 
This set of rules corresponds to the fol- 
lowing fornmla : 
(1)el A N)V 
(N)V 
(Det A AP A PP A N)V 
(Dot A AP A N)V 
(Det A PPA N) D NP 
It is interesting to note that the ID/LP formal- 
ism strongly reduces the problem of PS-rules mul- 
tiplication inherent in phrase-structure grammars, 
tlowever, as we have seen in tile previous example, 
there is still a redundancy in the information. In- 
deed, a set of rules describing a phrase allows us 
to distinguish between two types of constituents 
according to their ot)tional or eomtmlsory aspect. 
Hence, for each phrase we can define a minimal 
set of compulsory constituents (generally limited 
to the head of the phrase), which we call the min- 
imal set of a phrase. 
Ezample : 
In the previous example, the minimal set 
of the NP is {N}. 
We introduce an additional restriction prevent- 
ing the repetition of an identical category within a 
phr,~se. This restriction is very strong and has to 
be relaxed for some categories (such as PP). But it 
remains a general principle : most of the categories 
should not be repeated. 
We then construct a principle defining tile well- 
formedness of complex structures. 't'his principle 
only concerns internal knowledge : 
A phrase is well-formed iff it respects the follow- 
ing properties : 
m it contains at least one head 
• no constituent is repeated 
~, all its embedded phrases are well-formed 
In the logical paradigm (equivalence between a 
role and a clause), we say that a literal is true ~ it 
corresponds to a lexieal category of the parsed sen- 
tence or if it correslmnds to a well-formed phrase. 
This formation rule allows its to simplify the ver- 
itication of the grammatieality of a sentence. We 
simply need to verify the presence of the minimal 
set of compulsory constituents to indicate the well- 
formedness of a phrase. The boolean value of the 
complete structure is then evaluated recursively. If 
all the intermediate structures are true, the com- 
plete structure is also true and corresponds to a 
gralomatical sentence. 
We will call realization the actual presence of a 
category in tile syntactic structure corresponding 
to a sentence. The verification process of the well- 
fornmdness of a phrase follows these steps 
1. verifieatmn of the realizatiou of the minimal 
set 
2. verification of the membershil) of the realized 
constituents within the minimal set 
3. verification of the uniqueness of the con- 
stituents in a pllr,'~se 
4~ verification of the well4ormedness of embed- 
ded phrases 
In an active constraint, we replace the set of 
clauses describing all the possible constructions 
with a system <)f constraints S defining the set of 
l)ossihle constituents and the condition of realiza- 
tion for the minitelal set. We can represent it as 
follow : 
Let G' he the set of possible constituents of a 
phrase XP, let X t>e the head of XI', let M be the 
minimal set such xs M = {X}UC' (where C' C C), 
and let zX be the disjtmction of the literals of M. 
The well-formedness constraint is : 
s = {A 7) xl,} 
Example : 
The well-formedness constraint for a Nt' 
is: {NDNI'} 
The well:formedness constraint for a PP 
is : { f'rel> A N P D I' P } 
ACIES DE COLING-92, NAIqrES, 23-28 ^o~r 1992 8 3 PROC. OF COL1NG-92, NANTES, AUG. 23-28, 1992 
It is interesting to note that the implication cor- 
responding to the set of rules describing the NP in 
the previous example forms a system of constraints 
that can be simplified to {N D NP}. This prop- 
erty is verified for all phrases : 
Given a grammar G, VXP such that Xf' E G, 
lel A be the disjunction of the liter'Ms of the min- 
imal set of XP, then the formula corresponding ~o 
the rules describing XP is simplified to {A D XP}. 
We thns have both a linguistic and a h)rmaljns- 
tit|cation of tile active constraint used to verify tile 
well formedness of a phrase. 
5 Implementation in Prolog III 
We will now describe the parsing strategy and its 
implementation. 
5.1 Bottom-up filtering 
Our parsing strategy relies on tile concept of left 
boundary of a phrase. It is an improvement of 
the left-corner strategy (cf \[Rosenkrantz70\]) called 
bottom-up filtering (ef \[maehe90\]). It consists 
in using tile information extracted from 1,P con- 
straints to determine all the left-bounds of the 
phrases from the list of lexieal categories corre- 
sponding to a sentence. This process, unlike the 
left-corner one, relies on a distributional analysis 
of the categories and the verification of some prop- 
erties. 
We define the following flmctions which allow 
the initialization of the left boundaries. 
o First-legal daughters (noted I"LD(P)) : this 
function defines for each phrase P the set of cate- 
gories that can appear as left boudaries. It is de 
tined ,as follows ( LP relation between sets is noted 
with ~:) : 
Let P be a phrase, ga such that f' -~ c~ then 
FLD, the set of first legal daughters, is defined ,'~s 
R)llows: 
m,D(P) = {e E ~ such that e -< ,, - {e} } 
<, Immediate precedence (noted ll',,(c)) : this 
fimetlon defines for each FLI) c of a phrase P the 
set of categories that can precede e in P. It is de- 
fined as follows : 
Let P be a phrase, V(* such that P --÷ o, let x be 
a non-terminal, let c E FLD(P), then IPv(e), the 
set of immediate precedence of c for P, is defined 
as follows: 
IPp(c) = { ..... h that (x -4 c) or (,c E ....... l 
neither x -< c nor e -< z ea:ist)} 
o Iu'tialize : this flmction verifies whether a 
category c is the actual left boundary of a phrase 
P. It is defined ms follow : 
Let I be a string, let C be tile list of lexical 
categories of I, Ve E C, c' G N (set of non4erminal 
symbols) such that c' precedes c in C ; 
c initializes S life E FLI)(S) anti e' ¢ IPs(e) 
The syntactic structure of the sentence is built 
from a list of partially evaluated structures. The 
process consists in determining all the h.'ft bounds 
and, from this structure, in completing tire par- 
tial structures by an analysis of the other con- 
stituents of the phrase. This is done by verifying 
whether the current category can or cannot belong 
to the cnrrent phrase.We have at our disposal the 
set of possible constituents for each phrase, the LP 
constraints and the other instant|at|on principles 
of the GPS(\] theory. After these verifications, if 
tile current category cannot belong to the current 
phrase, then we have reached the right boundary 
of the current ptm~se. 
Example : 
Input sentence : 
7'he old man sings. 
Categorization : 
Det.Adl.N. V 
Partial structure : 
S.(NP, Det).(AP, Adj).N.(VP, V) 
Complete structure : 
(S,(NP, Det,(AP, Adj),N),(VP, !7)) 
This strategy allows a reduction of the search 
space. Parsing becomes a simple membership test 
of a category within a set. 
5.2 Implementation 
The following implementation considers only the 
ID/LP formalism (instead of the entire GPSG the- 
ory). We will not speak here about the other 
GPSG principles, bnt their insertion in the ID/LP 
module is very shnple. 
The parsing mechanism consists in assigning 
the value true l.o the boo\]eans corresponding to 
the categories a~s and when they appear. If the 
structure is simple (i.e. a lexical category), the 
LP-aeeeplability of this category in the phrase is 
checked and tire corresponding boolean is a.ssigned 
AC.I'ES DE COLING-92, NANTES, 23-28 AO(;F 1992 8 4 PROC. OV COLING-92, NANTES, At;c;. 23-28, 1992 
tile vMue true. In the case where the l)otton> 
up tiltering detects a left-bound, tile correspond- 
ing boolean of tile current category is mssigned tile 
value true and tile embedded phrase is parsed be- 
fore coming back to tile construction of tim cur- 
rent phrase. When we reach the right boundary, 
the well-forme(lness of tim embedded structures is 
checked (i.e. all the corresponding booleans must 
be true). If this is tile case, the corresponding 
boolean value is that of tile disjunction A of tile 
literals corresponding to the minimal set. 
The representation of tile categories and their 
associated Iiooleans will be done through two par- 
allel lists which will be examined simultaneously 
during an affectation (or any other operation). 
A l)hrase is described l)y the set. of its possil)le 
constituents, t,he set of its optional categories ~uld 
~ forlnuls, using its tniniLnal set. '\['lie two sets are 
represented by lists and the R)rmula is an imldiCa - 
don of the form {A D XP}. This inlbrm~ttion is 
collected into a systenl of constraints ehar;teteriz- 
ing each phra.se. 
Here is a simplilied version of our parsing prc~ 
cess. The following predicates allow the parsing of 
a Ithrase and its simple or complex constituents. 
It c;m be noted that tile gramnm.tieal knowl- 
edge is lmshed at it low level. It is repn:sented 
by the set of constraints ~ssoeiated to each phrase. 
Moreover, at this level we do not use the notion of 
sub-eategorizatioil, but only rules concerning the 
general structure. We grill idSO notice the concise- 
hess of this representation with reg;~rd to eh~ssical 
phra.se--strueture formalisms. 
Deseril)tion of the. implementation 
Let G be the following ll)/l,P grammar : 
NP-qa 1)el, N 
NP-'ia N 
NP ~ia Del, A P, I'P, N 
NP-q,t Det, Al', N 
NP-+ia Det, PP, N 
NP .'ia Det, Al', PP, N, l'Rcl 
Nt'-+ia Det, A 1', N, PRel 
NP ~id Det, PP, N, PRel 
NP-qd Det, N, PRel 
NP-~La N, t'Rel 
VI' ~id V 
VP--,i,t V, NP, PP 
Vl>-+id V, N} ) 
VP ~ia V, 1'1' 
AP--'L,L Adj 
I'P-'i,t l'ret', NP 
PRel-'id l'ro, NP, VP 
q}lm lbllowing predicates correspond to the heart 
of the parser for the grammar G : 
APhrase (<S (c) >. i ,12, Cat, Bool ,'r) , 
Coilst fluent (S, Cat, Bool ) 
Lphccept able (S ,Cat, Bool) 
hngmbeddedPhrae e (<S, c>. 1, ll. 
Cat,Bool,hl) 
APhrase (i i ,12, Cat, gool, A2) 
Tree(<S \[<c>. All >. A2,T) ; 
APhras e (<c>. i, 11, Cat, Bool, <c>. A) -+ 
LpAcceptable (c, Cat, Boo\].) 
lltstallciat e (e ,Cat, Bool) 
APhrase(l ,it ,Cat,Boo\].,A) ; 
Th( APhrase rllh! takes as illpllt ihe list Of par- 
tial structures returned by bottum-up filtering. It 
distinguishes between (we (:~ua.s aceor<ling to the 
type of the current structure : complex (rule ~1) 
or simple (rule #2). In the first c~use, the following 
processes arc eMlcd : 
® veritication of the mend)ership of the current 
structure within the set of the pnssibb con- 
sl.it)lel/ts el the curreltt phrmse (Constituent 
rule} 
o verifi<'ation of the l,l ) acceptability 
(LpAcceptabl e r,lle) 
~, parse of the elnbedded COlllplex structure 
(AnEmbeddedPhrase rule) 
tmrse of the rest cd" the phr;Lse (APhraee rule) 
construction and w'rilicatiou of the syntactic 
tree (Tree rub) 
In the case of simple structures, afl;er checking 
tim l,P-aeceptalfility, the correslmndiug boolean is 
assigned tile value true (Instanciate rule) and tile 
parse of the current phrase is pursued. 
If the APhrase r,de fails, the right-bound of the 
phrase is reached and die parse is pursued at a 
superior level. 
AnEmbeddadPhr as e (<S, c>. l, 11, gag, Bool, A ) -, 
Constraints (S, C,B ,R,S' ) 
Instanciat e(c,C,B) 
APhrase(l, ii ,C,B,A) 
CorrectConstituent s (R, r) 
Valid(r,S,S' ,Cat,Boo\]) ; 
rFhe AilFanbeddedPhrase rule allows the parse of 
& ll(!W COIUptex Btriicttli'e. It begins with tile sys- 
tem of ins{ailing constraints describing this struc- 
tur~ (Coilstraints rule). TI,e wllidity of the con 
stituents is clmcked (CorrectConstituents and 
Valid rtdes) Before rettlrlling the boolean wthic of 
the parse for this phrg~se (variable S'). 
Constraints (NP,C,B, R,N P) , 
{ C - <Dot,Nm,AP,PP,PlteI>, 
B e <I)_ot,N,A.P,P P,P Rel>, 
R : <A~,P P,P_ReI>, 
N => N1 ~ }; 
Acri!s I)E COLING-92, NANIES, 23-28 AO\[a 1992 8 5 I)ROC. OF COIANG 92, NANTES, AtX;. 23-28, 1992 
Conatraints(VP,C,B,R,VA ~) -~ 
{ C = <Vb,IP,PP>, 
B = <V,IIA~,P-P>, 
R = <I_P,P_P> 
V ::~. V-P }; 
Constraints (AP, C,B, R,A~) -~ 
{ C = <Adj>. 
B = <aAj>, 
R = <>. 
AAj ~ A_P }; 
Constraints (PP, C,B, R, P-P) -~ 
{ C = <Prep,NP>, 
B = <P-top,IrA°>, 
R = <I_P>, 
(P_rep a IIJ ~) =;~ PA: }; 
Constraint a (PRel, C, B, R, P~Rel) ---* 
{ C = <Pro,NP,VP>, 
B = <P_ro,Ii_P,V_P>, 
R = <NA~.V-P>º 
(P2co & V~) :~ P_Kel }; 
We can notice that in this representation, sub- 
categorization consists in verifying the boolean val- 
ues corresponding to the categories concerned. 
6 Conclusion 
The ID/LP formalism distinguishes between inter- 
nal and external knowledge about syntactic struc- 
tures. This characteristic allows the expression of 
parsing mechanisms at a very high level of gener- 
ality. We can represent the description of a phrase 
in an extremely concise way with a rule clustering 
operation. These properties allow the use of ac- 
tive constraints. The result is an implementation 
in agreement with the theoretical nmdel respecting 
in particularl the generality and conciseness prop- 
erties of GPSG. Moreover, active constraints ef- 
ficiently control the progress of the processes and 
limit non-determinism of parsing. This last charac- 
teristic is very important for the ID/LP formalism 
which uses non-ordered rules implying an increase 
of the search space. 
We have shown in this paper how to use ac- 
tive constraints for ID/LP formalism. We can ap- 
ply the same approach to the entire GPSG theory 
interpreting features structures and instaneiation 
principles as formulas (cf \[Blache92\]). 
The implementation presented here has been 
done in Prolog III on a Macintosh. From a cover- 
age point of view, we can indicate that the rules in 
the grammatical formalism presented in our exam- 
ple roughly amounts to twenty standard ID-rules. 
ACTES DE COLING-92, NANTES, 23-28 nOt~r 1992 8 6 PROC. OF COLING-92, NANTES, AUG. 23-28, 1992 

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