HANDLING LINEAR PRECEDENCE CONSTRAINTS BY UNIFICATION 
Judith Engelkamp, Gregor Erbach and Hans Uszkoreit 
Universitfit des Saarlandes, Computational Linguistics, and 
Deutsches Forschungszentrum fiir Kiinstliche lntelligenz 
D-6600 Saarbriicken 11, Germany 
engelkamp@coli.uni-sb.de 
ABSTRACT 
Linear precedence (LP) rules are widely used for 
stating word order principles. They have been adopted 
as constraints by HPSG but no encoding in the 
formalism has been provided. Since they only order 
siblings, they are not quite adequate, at least not for 
German. We propose a notion of LP constraints that 
applies to linguistically motivated branching domains 
such as head domains. We show a type-based encoding 
in an HPSG-style formalism that supports processing. 
The encoding can be achieved by a compilation step. 
INTRODUCTION 
Most contemporary grammar models employed in 
computational linguistics separate statements about 
dominance from those that determine linear precedence. 
The approaches for encoding linear precedence (LP) 
statements differ along several dimensions. 
Depending on the underlying grammatical theory, 
different criteria are employed in formulating ordering 
statements. Ordering constraints may be expressed by 
referring to the category, grammatical function, 
discourse r61e, and many other syntactic, semantic, 
morphological or phonological features. 
Depending on the grammar formalism, different 
languages are used for stating the constraints on 
permissible linearizations. LP rules, first proposed by 
Gazdar and Pullum (1982) for GPSG, are used, in 
different guises, by several contemporary grammar 
formalisms. In Functional Unification Grammar (Kay 
1985) and implemented versions of Lexical Functional 
Grammar, pattern languages with the power of regular 
expressions have been utilized. 
Depending on the grammar model, LP statements 
apply within different ordering domains. In most 
frameworks, such as GPSG and HPSG, the ordering 
domains are local trees. Initial trees constitute the 
ordering domain in ID/LP TAGS (Joshi 1987). In 
current LFG (Kaplan & Zaenen 1988), functional 
precedence rules apply to functional domains. Reape 
Research for this paper was mainly carried out in 
the project LILOG supported by IBM Germany. Some 
of the research was performed in the project DISCO 
which is funded by the German Federal Ministry for 
Research and Technology under Grant-No.: ITW 9002. 
We wish to thank our colleagues in SaarbriJcken, three 
anonymous referees and especially Mark Hepple for 
their valuable comments and suggestions. 
(1989) constructs word order domains by means of a 
special union operation on embedded tree domains. 
It remains an open question which choices along 
these dimensions will turn out to be most adequate for 
the description of word order in natural language. 
In this paper we do not attempt to resolve the 
linguistic issue of the most adequate universal 
treatment of word order. However we will present a 
method for integrating word order constraints in a typed 
feature unification formalism without adding new 
formal devices. 
Although some proposals for the interaction 
between feature unification and LP constraints have 
been published (e.g. Seiffert 1991), no encoding has 
yet been shown that integrates LP constraints in the 
linguistic type system of a typed feature unification 
formalism. Linguistic processing with a head-driven 
phrase structure grammar (HPSG) containing LP 
constraints has not yet been described in the literature. 
Since no implemented NL system has been 
demonstrated so far that handles partially free word 
order of German and many other languages in a 
satisfactory way, we have made an attempt to utilize 
the formal apparatus of HPSG for a new approach to 
processing with LP constraints. However, our method 
is not bound to the formalism of HPSG. 
In this paper we will demonstrate how LP 
constraints can be incorporated into the linguistic type 
system of HPSG through the use of parametrized 
types. Neither additional operations nor any special 
provisions for linear precedence in the processing 
algorithm are required. LP constraints are applied 
through regular unification whenever the head 
combines with a complement or adjunct. 
Although we use certain LP-relevant features in 
our examples, our aproach does not hinge on the 
selection of specific linguistic criteria for constraining 
linear order. 
Since there is no conclusive evidence to the 
contrary, we assume the simplest constraint language 
for formulating LP statements, i.e., binary LP 
constraints. For computational purposes such 
constraints are compiled into the type definitions for 
grammatical categories. 
With respect to the ordering domain, our LP 
constraints differ from the LP constraints commonly 
assumed in HPSG (Pollard & Sag 1987) in that they 
201 
apply to nonsibling constituents in head domains. 
While LP constraints control the order of nodes that are 
not siblings, information is accumulated in trees in 
such a way that it is always possible to detect a 
violation of an LP constraint locally by checking 
sibling nodes. 
This modification is necessary for the proper 
treatment of German word order. It is also needed by all 
grammar models that are on the one hand confined to 
binary branching structures such as nearly all versions 
of categorial grammar but that would, on the other 
hand, benefit from a notion of LP constraints. 
Our approach has been tested with small sets of 
LP constraints. The grammar was written and run in 
STUF, the typed unification formalism used in the 
project LILOG. 
LINGUISTIC MOTIVATION 
This section presents the linguistic motivation for 
our approach. LP statements in GPSG (Gazdar et al. 
1985) constrain the possibility of linearizing 
immediate dominance (ID) rules. By taking the right- 
hand sides of ID rules as their domain, they allow only 
the ordering of sibling constituents. Consequently, 
grammars must be designed in such a way that all 
constituents which are to be ordered by LP constraints 
must be dominated by one node in the tree, so that 
"flat" phrase structures result, as illustrated in figure 1. 
VmaX 
sollte V max 
should 
NP\[nom\] ADV NP\[dat\] NP\[acc\] V 0 
der Kurier nachher einem Spion den Brief zustecken 
the courier later a spy the letter slip 
The courier was later supposed to slip a spy the letter. 
Figure 1 
Uszkoreit (1986) argues that such flat structures 
are not well suited for the description of languages 
such as German and Dutch. The main reason 1 is so- 
called complex fronting, i.e., the fronting of a non- 
finite verb together with some of its complements and 
adjuncts as it is shown in (1). Since it is a well 
established fact that only one constituent can be 
fronted, the flat structure can account for the German 
examples in (1), but not for the ones in (2), 
(1) sollte der Kurier nachher einem Spion den Brief 
zustecken 
zustecken sollte der Kurier nachher einem 
Spion den Brief 
den Brief sollte der Kurier nachher einem 
Spion zustecken 
1Further reasons are discussed in Uszkoreit 
(1991b). 
einem Spion sollte der Kurier nachher den 
Brief zustecken 
naehher sollte der Kurier einem Spion den 
Brief zustecken 
tier Kurier sollte nachher einem Spion den 
Brief zustecken 
(2) den Brief znsteeken sollte der Kurier 
nachher einem Spion 
einem Spion den Brief zusteeken sollte 
der Kurier nachher 
naehher einem Spion den Brief 
znsteeken sollte der Kurier 
In the hierarchical tree structure in figure 2, the 
boxed constituents can be fronted, accounting for the 
examples in (1) and (2). 
V~aX 
I 
der Kurier \[\] 
! nachher 
Figure 2 
I I 
den Brief zustecken 
But with this tree structure, LP constraints can no 
longer be enforced over siblings. The new domain for 
linear order is a head domain, defined as follows: 
A head domain consists of the lexical head 
of a phrase, and its complements and adjuncts. 
LP constraints must be respected within a head 
domain. 
An LP-constraint is an ordered pair <A,B> 
of category descriptions, such that whenever a 
node cx subsumed by A and a node 13 subsumed 
by B occur within the domain of an LP-rule (in 
the case of GPSG a local tree, in our case a 
head domain), cz precedes 13. 
An LP constraint <A,B> is conventionally written 
as A < B. It follows from the definition that B can 
never precede A in an LP domain. In the next section, 
we will show how this property is exploited in our 
encoding of LP constraints. 
ENCODING OF LP CONSTRAINTS 
From a formal point of view, we want to encode 
LP constraints in such a way that 
202 
• violation of an LP constraint results in unification 
failure, and 
• LP constraints, which operate on head domains, 
can be enforced in local trees by checking sibling 
nodes. 
The last condition can be ensured if every node in 
a projection carries information about which con- 
stituents are contained in its head domain. 
An LP constraint A < B implies that it can never 
be the case that B precedes A. We make use of this 
fact by the following additions to the grammar: 
• Every category A carries the information that B 
must not occur to its left. 
• Every category B carries the information A must 
not occur to its right. 
This duplication of encoding is necessary because 
only the complements/adjuncts check whether the pro- 
jection with which they are combined contains some- 
thing that is incompatible with the LP constraints. A 
projection contains only information about which 
constituents are contained in its head domain, but no 
restrictions on its left and right context 2. 
In the following example, we assume the LP-rules 
A<B and B<C. The lexical head of the tree is X 0, and 
the projections are X, and X max. The complements 
are A, B and C. Each projection contains information 
about the constituents contained in it, and each 
complement contains information about what must 
not occur to its left and right. A complement is only 
combined with a projection if the projection does not 
contain any category that the complement prohibits on 
its right or left, depending on which side the 
projection is added. 
xmax 
{A, B, C} 
A X 
\[left: ~B\] {B, C} 
B -- 
\[left: ~C \] X 
Lright: --,AJ 
Figure 3 
{cl 
c x \[right:-- B\] \[ } 
Having now roughly sketched our approach, we 
will turn to the questions of how a violation of LP 
constraints results in unification failure, how the 
2Alternatively, the projections of the head could as 
well accumulate the ordering restrictions while the 
arguments and adjuncts only carry information about 
their own LP-relevant features. The choice between 
the alternatives has no linguistic implications since it 
only affects the grammar compiled for processing and 
not the one written by the linguist. 
information associated with the projections is built 
up, and what to do if LP constraints operate on feature 
structures rather than on atomic categories. 
VIOLATION OF LP-CONSTRAINTS 
AS UNIFICATION FAILURE 
As a conceptual starting point, we take a number 
of LP constraints. For the expository purposes of this 
paper, we oversimplifiy and assume just the following 
four LP constraints: 
nora < Oat (nominative case precedes 
dative case) 
nora < ace (nominative case precedes 
accusative case) 
Oat < ace (dative case precedes accusative 
case) 
3to < nonpro (pronominal NPs precede 
non-pronominal NPs) 
Figure 4 
Note that nora, Oat, ace, pro and nonpro are not 
syntactic categories, but rather values of syntactic 
features. A constituent, for example the pronoun ihn 
(him) may be both pronominal and in the accusative 
case. For each of the above values, we introduce an 
extra boolean feature, as illustrated in figure 5. 
NOM bool 1 DAT bool 
ACC boot 
PRO boot 
NON-PRO boo 
Figure 5 
Arguments encode in their feature structures what 
must not occur to their left and right sides. The dative NP einem Spion 
(a spy), for example, must not have 
any accusative constituent to its left, and no 
nominative or pronominal constituent to its right, as 
encoded in the following feature structure. The feature 
structures that constrain the left and right contexts of 
arguments only use '-' as a value for the LP-relevant 
features. 
FLE \[ACC-\] \] 
NOM - 
Figure 6: Feature $mJcture for einem Spion 
Lexical heads, and projections of the head contain a 
feature LP-STORE, which carries information about 
the LP-relevant information occuring within their 
head domain (figure 7). 
\]1 |DAT - LP-STORE |ACC - |PRO - t.NON-PRO - 
Figure 7: empty LP-STORE 
203 
In our example, where the verbal lexical head is 
not affected by any LP constraints, the LP-STORE 
contains the information that no LP-relevant features 
are present. 
For a projection like einen Brief zusteckt (a 
letter\[acc\] slips), we get the following LP-STORE. 
\[NOM- ÷1 |DAT - LP-STORE/ACC + 
\[PRO - 
L.NON-PRO 
Figure 8: LP-STORE of einen Briefzusteckt 
The NP einem Spion (figure 6) can be combined 
with the projection einen Brief zusteckt (figure 8) to 
form the projection einem Spion einen Brief zusteckt 
(a spy\[dat\] a letter\[acc\] slips) because the RIGHT 
feature of einera Spion and the LP-STORE of einen 
Brief zusteckt do not contain incompatible 
information, i.e., they can be unified. This is how 
violations of LP constraints are checked by 
unification. The projection einem Spion einen Brief 
zusteckt has the following LP-STORE. 
FNOM- 1 |DAT + 
LP-STORE |ACC ÷ 
/PRO - 
LNON-PRO + 
Figure 9: LP-STORE of einem Spion einen Brief zusteckt 
The constituent ihn zusteckt (figure 10) could not 
be combined with the non-pronominal NP einem 
Spion (figure 6). 
\[NOM- \]\] 
/DAT - || 
LP-STORE/ACC + II 
|PRO + \]l 
I_NON-PRO =ll 
Figure 10: LP-STORE of ihn zusteckt 
In this case, the value of the RIGHT feature of the 
argument einem Spion is not unifiable with the LP- 
STORE of the head projection ihn zusteckt because 
the feature PRO has two different atoms (+ and -) as 
its value. This is an example of a violation of an LP 
constraint leading to unification failure. 
In the next section, we show how LP-STOREs 
are manipulated. 
MANIPULATION OF THE LP-STORE 
Since information about constituents is added to 
the LP-STORE, it would be tempting to add this 
information by unification, and to leave the initial LP- 
STORE unspecified for all features. This is not 
possible because violation of LP constraints is also 
checked by unification. In the process of this 
unification, values for features are added that may lead 
to unwanted unification failure when information 
about a constituent is added higher up in the tree. 
Instead, the relation between the LP-STORE of a 
projection and the LP-STORE of its mother node is 
encoded in the argument that is added to the projection. 
In this way, the argument "changes" the LP-STORE 
by "adding information about itselff. Arguments there- 
fore have the additional features LP-IN and LP-OUT. 
When an argument is combined with a projection, the 
projection's LP-STORE is unified with the argument's 
LP-IN, and the argument's LP-OUT is the mother 
node's LP-STORE. The relation between LP-IN and 
LP-OUT is specified in the feature structure of the 
argument, as illustrated in figure 11 for the accusative 
pronoun ihn, which is responsible for changing figure 
7 into figure 10. No matter what the value for the 
features ACC and PRO may be in the projection that 
the argument combines with, it is '+' for both features 
in the mother node. All other features are left 
unchanged 3. 
\[NOM ~\] \] /DARN / / 
t'P- N/ACCt\] / / 
IPRO \[ \] / / LNON-PRO ~\]J / 
\[NOM \[i\] \]1 |DAT~\] 
11 
LP-OUT/ACC + II 
/PRO + II LNON-PRO / 
Figure 11 
Note that only a %' is added as value for LP- 
relevant features in LP-OUT, never a '-'. In this way, 
only positive information is accumulated, while 
negative information is "removed". Positive 
information is never "removed". 
Even though an argument or adjunct constituent 
may have an LP-STORE, resulting from LP 
constraints that are relevant within the constituent, it 
is ignored when the constituent becomes argument or 
adjunct to some head. Our encoding ensures that LP 
constraints apply to all head domains in a given 
sentence, but not across head domains. 
It still remains to be explained how complex 
phrases that become arguments receive their LP-IN, 
LP-OUT, RIGHT and LEFT features. These are 
specified in the lexical entry of the head of the phrase, 
but they are ignored until the maximal projection of 
the head becomes argument or adjunct to some other 
head. They must, however, be passed on unchanged 
from the lexical head to its maximal projection. When 
3Coreference variables are indicated by boxed 
numbers. \[ \] is the feature structure that contains no 
information (TOP) and can be unified with any other 
feature structure. 
204 
the maximal projection becomes an argument/adjunct, 
they are used to check LP constrains and "change" the 
LP-STORE of the head's projection. 
Our method also allows for the description of head- 
initial and head-final constructions. In German, for 
example, we find prepositions (e.g. far), postpositions 
(e.g. halber) and some words that can be both pre- and 
postpostions (e.g. wegen). 
The LP-rules would state that a postposition 
follows everything else, and that a preposition precedes 
everything else. 
\[PRE +\] < \[\] 
\[ \] < \[POST +\] 
Figure 12 
The information about whether something is a 
preposition or a postposition is encoded in the lexical 
entry of the preposition or postposition. In the 
following figure, the LP-STORE of the lexical head 
contains also positive values. 
Figure 13: part of the lexical entry of a postposition 
\[LP-STORE \[pP~REST+\]\] 
Figure 14: part of the lexical entry of a preposition 
A word that can be both a preposition and a 
postposition is given a disjunction of the two lexical 
entries: 
POST - 
LP-STO   \[POST ÷Ill 
/LPRE - .ILl 
Figure 15 
All complements and adjuncts encode the fact that 
there must be no preposition to their right, and no 
postposition to their left. 
LEFT \[POST 
Figure 16 
The manipulation of the LP-STORE by the 
features LP-IN and LP-OUT works as usual. 
The above example illustrates that our method of 
encoding LP constraints works not only for verbal 
domains, but for any projection of a lexical head. The 
order of quantifiers and adjectives in a noun phrase can 
be described by LP constraints. 
INTEGRATION INTO HPSG 
In this section, our encoding of LP constraints is 
incorporated into HPSG (Pollard & Sag 1987). We 
deviate from the standard HPSG grammar in the 
following respects: 
• The features mentioned above for the encoding of 
LP-constraints are added. 
• Only binary branching grammar rules are used. 
• Two new principles for handling LP-constraints are 
added to the grammar. 
Further we shall assume a set-valued SUBCAT 
feature as introduced by Pollard (1990) for the 
description of German. Using sets instead of lists as 
the values of SUBCAT ensures that the order of the 
complements is only constrained by LP-statements. 
In the following figure, the attributes needed for 
the handling of LP-constraints are assigned their place 
in the HPSG feature system. 
I- ,..,:,-,i,,,ti Ill cP-otrr\[ I/l/ 
SVNSEM, LOC / L FTC \] /// / 
.RIGHT\[\] all 
LLP-STORE \[ \] J\] 
Figure 17 
The paths SYNSEMILOCIHEADI{LP-IN,LP- 
OUT,RIGHT,LEFT} contain information that is 
relevant when the constituents becomes an 
argument/adjunct. They are HEAD features so that 
they can be specified in the lexical head of the 
constituent and are percolated via the Head Feature 
Principle to the maximal projection. The path 
SYNSEMILOCILP-STORE contains information 
about LP-relevant features contained in the projection 
dominated by the node described by the feature 
structure. LP-STORE can obviously not be a head 
feature because it is "changed" when an argument or 
adjunct is added to the projection. 
In figures 18 and 19, the principles that enforce 
LP-constraints are given 4. Depending on whether the 
head is to the right or to the left of the comple- 
ment/adjunct, two versions of the principle are dis- 
tinguished. This distinction is necessary because linear 
order is crucial. Note that neither the HEAD features 
of the head are used in checking LP constraints, nor 
the LP-STORE of the complement or adjunct. 
PHON append(N, l; 
... \[LP-STORE ~\]\] 
T \[PHON ~l FLEFTFil ll 
H 
l"" LP'sT~LPE?7 \[~J 
Head Complement/Adjunct 
Figure 18: Left-Head LP-Prineiple 
4The dots (...) abbreviate the path SYNSEMILOCAL 
205 
PHON append(~\],~)\] 
... \[LP-STORE ~\] J ( 
PHON \[~\] \[R~ 
HEAD |LP-IN ri\] III I 
• .. \[LP-Otrr ~ll \[PHON ~-\] \] u>-s+oREt\] JJ \[... \[L~-STORENJ 
Complement/Adjunct Head 
Figure 19: Right-Head LP-Prineiple 
In the following examples, we make use of the 
parametrized type notation used in the grammar 
formalism STUF (D6rre 1991). A parametrized type 
has one or more parameters instantiated with feature 
structures. The name of the type (with its parameters) 
is given to the left of the := sign, the feature structure 
to the right. 
In the following we define the parametrized types 
nom(X,Y), dat(X,Y), pro(X,Y), and non-pro(X,Y), 
where X is the incoming LP-STORE and Y is the 
outgoinl LP-STORE. 
"NOM \[ \] \] "NOM + "\] DAT\[\] / DAT\[\] / ) 
nom ACC\[\] /, ACC\[\] / := PROlT1 / PROr~ / 
NON-PRO~I\] ~ON+RO711 
CASE nom rs~s~l,..ocri.~.~r rDA T 1\]\]\] 
t L t L~-'r \[ACC-IIII 
Figure 20 
/I-NoM\[\] \] rNo~rri -I //DAT \[\] / IDAT+ J 
dai\[/ACC~I l,l~+cm |\[PROlTI I \[PROITI 
X LNON-PRO ~ t.NON-PRO 
I" rCASEd~ SYNSEMILOC \[HEAD \[LEFT I 
ACC- 
L \[RIGHT I NOM - 
Figure 21 
@w 
/I-NoMrrl -II-NoMIrl -IX //OATI'7"I / /DAT \[\] / / 
proll ACC \[\] l,l~m II:= 
l IPRO \[ \] I IPRO + I | LNON+RO ml LNO~*"O IZll / 
\[SYNSEmILOC \[HEAO \[LEEr I NON-PRO -\]\]\] 
Figure 22 
/\[NOMI'7"I \] I-NOMI'rl \]\ 
/|DAT~ J |DAT ~ // non-prol/ACC \[\] ,/ACC~ //:= 
| \[PRO I'a"l |PRO\[\] // 
tLNON-PRO\[ \] LNON-PRO+J \] 
\[SYNSEMII£)C \[HEAD\[RIGHT I PRO -\]\]\] 
Figure 23 
The above type definitions can be used in the 
definition of lexical entries. Since the word ihm, 
whose lexical entry 5 is given in figure 24, is both 
dative case and pronominal, it must contain both 
types. While the restrictions on the left and right 
context invoked by dat/2 and pro/2 can be unified 6, 
matters are not that simple for the LP-IN and LP-OUT 
features. Since their purpose is to "change" rather than 
to "add" information, simple unification is not 
possible. Instead, LP-IN of ihm becomes the in- 
coming LP-STORE of dat/2, the outgoing LP- 
STORE of daft2 becomes the incoming LP-STORE of 
pro/2, and the outgoing LP-STORE of pro/2 becomes 
LP-OUT of ihm, such that the effect of both changes 
is accumulated. 
ihm := 
LP-IN ri\] \[SYNSEMILOC \[HEAD \[LP_OUT ~ ^ 
~fi\],~b ^ p,o~,~ 
Figure 24: lexical entry for ihm 
After expansion of the types, the following feature 
structure results. Exactly the same feature structure had 
been resulted if dat/2 and pro/2 would have been 
exchanged in the above lexical entry 
I"! I'-'1 I'11"1 
(go(W, 2\[~) A dat(121, 3\[~) ), because the effect of both is 
to instantiate a '+' in LP-OUT. 
- - - I-~o~iri I--- 
IDAT II / 
LP-IN/ACC \[~ \[ 
/PRO \[ \] / L~oN-PRol3I i 
1 |DAT + / 
SYNSEMILOC HEAD I..P-OUTiACC~\] \] 
\[PRO + / LNON-PRoITll 
I \]~lTr \[ACC - -\] / ~" LNON-PRO 
Riol-rr INOM -\] 
- - -CASE dat 
Figure 25: expanded lexical entry for ihm 
5Only the information which is relevant for the 
processing of LP constraints is included in this lexical 
entry. 
6dat/2 means the type dat with two parameters. 
206 
The next figure shows the lexical entry for a non- 
pronominal NP, with a disjunction of three cases. 
Peter := 
\[SYNSEMILOC \[HEAD \[LP'IN \[~ \]\]1 LLP-OUTNJJ ^ 
(nom(~,~\]) v dat~,~\]) v acc(\[~,\[~))^ non-pro(\[2~,\[3-b 
Figure 26 
COMPILATION OF THE ENCODING 
As the encoding of LP constraints presented above 
is intended for processing rather than grammar writing, 
a compilation step will initialize the lexical entries 
automatically according to a given grammar including 
a separated list of LP-constraints. Consequently the 
violation of LP-constraints results in unification 
failure. For reasons of space we only present the basic 
idea. 
The compilation step is based on the assumption 
that the features of the LP-constraints are 
morphologically motivated, i.e. appear in the lexicon. 
If this is not the case (for example for focus, thematic 
roles) we introduce the feature with a disjunction of its 
possible values. This drawback we hope to overcome 
by employing functional dependencies instead of LP-IN 
and LP-OUT features. 
For each side of an LP-constraint we introduce 
boolean features. For example for \[A: v\] < \[B: w\] we 
introduce the features a_v and b_w. This works also for 
LP-constraints involving more than one feature such as 
\[,>.o + 1 r,>.o %3 CASE accJ < LCASE 
For encoding the possible combinations of values 
for the participating features, we introduce binary 
auxiliary features such as pro_plus_case_acc, because 
we need to encode that there is at least a single 
constituent which is both pronominal and accusative. 
Each lexical entry has to be modified as follows: 
1. A lexical entry that can serve as the head of a 
phrase receives the additional feature LP-STORE. 
2. An entry that can serve as the head of a phrase 
and bears LP-relevant information, i.e. a projection of 
it is subsumed by one side of some LP-constraint, has 
to be extended by the features LP-IN, LP-OUT, LEFT, 
RIGHT. 
3. The remaining entries percolate the LP 
information unchanged by passing through the 
information via LP-IN and LP-OUT. 
The values of the features LEFT and RIGHT 
follow from the LP-constraints and the LP-relevant 
information of the considered lexical entry. 
The values of LP-STORE, LP-IN and LP-OUT 
depend on whether the considered lexical entry bears the 
information that is represented by the boolean feature 
(attribute A with value v for boolean feature a_v). 
entry bears the entry doesn't bear 
information the information 
LP-STORE + 
LP-IN TOP new variable x 
LP-OUT + coreference to x 
CONCLUSION 
We have presented a formal method for the 
treatment of LP constraints, which requires no addition 
to standard feature unification formalisms. It should 
be emphasized that our encoding only affects the 
compiled grammar used for the processing. The 
linguist does not lose any of the descriptive means nor 
the conceptual clarity that an ID/LP formalism offers. 
Yet he gains an adequate computational interpretation 
of LP constraints. 
Because of the declarative specification of LP con- 
straints, this encoding is neutral with respect to pro- 
cessing direction (parsing-generation). It does not 
depend on specific strategies (top-down vs. bottom-up) 
although, as usual, some combinations are more 
efficient than others. This is an advantage over the 
formalization of unification ID/LP grammars in 
Seiffert (1991) and the approach by Erbach (1991). 
Seiffert's approach, in which LP constraints operate 
over siblings, requires an addition to the parsing algo- 
rithm, by which LP constraints are checked during 
processing to detect violations as early as possible, 
and again after processing, in case LP-relevant infor- 
mation has been added later by unification. Erbach's 
approach can handle LP constraints in head domains 
by building up a list of constituents over which the 
LP constraints are enforced, but also requires an 
addition to the parsing algorithm for checking LP 
constraints during as well as after processing. 
Our encoding of LP constraints does not require 
any particular format of the grammar, such as left- or 
right-branching structures. Therefore it can be 
incorporated into a variety of linguistic analyses. 
There is no need to work out the formal semantics of 
LP constraints because feature unification formalisms 
already have a well-defined formal semantics. 
Reape (1989) proposes a different strategy for 
treating partially free word order. His approach also 
permits the application of LP constraints across local 
trees. This is achieved by separating word order 
variation from the problem of building a semantically 
motivated phrase structure. Permutation across 
constituents can be described by merging the fringes 
(terminal yields) of the constituents using the 
operation of sequence union. All orderings imposed on 
the two merged fringes by LP constraints are preserved 
in the merged fringe. 
Reape treats clause union and scrambling as 
permutation that does not affect constituent structure. 
Although we are intrigued by the elegance and 
descriptive power of Reape's approach, we keep our 
bets with our more conservative proposal. The main 
problem we see with Reape's strategy is the additional 
207 
burden for the LP component of the grammar. For 
every single constituent that is scrambled out of some 
clause into a higher clause, the two clauses need to be 
sequence-unioned. A new type of LP constraints that 
refer to the position of the constituents in the phrase or 
dependency structure is employed for ensuring that the 
two clauses are not completely interleaved. Hopefully 
future research will enable us to arrive at better 
judgements on the adequacy of the different approaches. 
Pollard (1990) proposes an HPSG solution to 
German word order that lets the main verb first 
combine with some of its arguments and adjuncts in a 
local tree. The resulting constituent can be fronted. 
The remaining arguments and adjuncts are raised to the 
subcategorization list 7 of the auxiliary verb above the 
main verb. Yet, even if a flat structure is assumed for 
both the fronted part of the clause and the part 
remaining in situ as in (Pollard 1990), LP constraints 
have to order major constituents across the two parts. 
For a discussion, see Uszkoreit (1991b). 
Uszkoreit (1991b) applies LP principles to head 
domains but employs a finite-state automaton for the 
encoding of LP constraints. We are currently still 
investigating the differences between this approach and 
the one presented here. 
Just as most other formal appraoches to linear pre- 
cedence, we treat LP-rules as absolute constraints 
whose violation makes a string unacceptable. Sketchy 
as the data may be, they suggest that violation of 
certain LP-eonstraints merely makes a sentence less 
acceptable. Degrees of acceptability are not easily 
captured in feature structures as they are viewed today. 
In terms of our theory, we must ensure that the 
unification of the complement's or adjunct's left or 
right context restriction with the head's LP-STORE 
does not fail in case of a value clash, but rather results 
in a feature structure with lower acceptability than the 
structure in which there is no feature clash. But until 
we have developed a well-founded theory of degrees of 
acceptability, and explored appropriate formal means 
such as weighted feature structures, as proposed in 
(Uszkoreit 1991a), we will either have to ignore order- 
ing principles or treat them as absolute constraints. 

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