Syntactic and Semantic Knowledge in the 
DELPHI Unification Grammar 
R. Bobrow 
Robert Ingria 
David Stallard 
BBN Systems and Technologies Inc. 
10 Moulton Street, Mailstop 6/4C 
Cambridge, MA 02138 
Abstract 
This paper presents recent natural language work on HARC, 
the BBN Spoken Language System. The HARC system in- 
corporates the Byblos system \[6\] as its speech recognition 
component and the natural language system Delphi, which 
consists of a bottom-up parser paired with an integrated syn- 
tax/semantics unification grammar, a discourse module, and 
a database question-answering backend. The paper focuses 
on the syntactic and semantic analyses made in the grammar. 
Introduction 
This paper discusses the unification-based grammar compo- 
nent of the BBN Delphi system, the natural language compo- 
nent of the BBN Spoken Language System. This grammar, 
previously discussed in \[4\]\[5\], is written in a variant of the 
Definite Clause Grammar formalism \[17\] and simultaneously 
assigns both syntactic structure and semantic interpretation 
to an utterance. The grammar comprises some 1300 rules 
(including those for terminal items), and has recently been 
evaluated on the ATIS air travel information domain with 
favorable results \[2\]. 
The paper has two main purposes. The first is to present 
this grammar's treatment of a number of syntactic and se- 
mantic phenonomena in the ATIS domain, in the belief that 
comparison of analyses are useful in and of themselves, par- 
ticularly in the context of a common evaluation. In particu- 
lar, we discuss the constraints imposed by subgrammars on 
conjunction, relaxation of subject verb agreement, optional 
argument subcategorization, and semantic interpretation of 
PPs and nominal compounds. 
The second purpose is to argue for the necessity of a de- 
vice which is frequently made use of Definite Clause Gram- 
mar work, but which has less often been utilized in the work 
on unification grammar that has appeared more recently (\[19\] 
\[14\]). This is the right-hand side "constraint relation" that 
does not derive any constituent of the utterance, but rather 
serves to constrain in various ways the feature assigments of 
those rule elements which do. Constraint relation elements 
are thus to be distinguished from other non-terminals which 
derive empty constituents, such as gaps or zero morphemes. 
While constraint relations have long been used in DCG- 
based workto treat, among other things, problems of quan- 
tifier scoping and the interaction of quanfifer scope and 
anaphora \[16\] \[18\] we argue that there are other, more low- 
level issues of lexical semantics and syntax for which con- 
straint relations are either conceptually useful or formally 
necessary, even in unification formalisms which allow full 
disjunction across features, such as \[10\] \[12\] \[11\] \[9\]. 
The remainder of the paper is divided into sections. In 
the next section, we first briefly review the formalism we 
use. In the two sections after that, we present syntactic 
analyses and semantic analyses made by the Delphi gram- 
mar, with emphasis placed on the use of constraint relation 
elements. Finally, in the last section we discuss the question 
of whether or not the constraint elements can be compiled 
out of grammar rules. 
Grammar Formalism 
The Delphi grammar formalism is a variant of Definite 
Clause Grammar and is discussed in more detail in \[4\]\[5\]. 
Left- and right-hand side rule elements have a functor (their 
major category) and zero or more features in a fixed-arity, 
positional order. Features are slots which are filled by terms. 
Terms can either be variables, which are atoms prefixed by 
colons ":", or functional terms consisting of a functor and 
zero or more features, again in fixed positional order, oc- 
cupied by other terms. Note that this means that constants 
in Delphi are just nullary functions. Disjunctions of purely 
atomic values are allowed as terms, with the functor ":OR". 
The following is an example role, much simplified for 
expository purposes, for handling NP conjunctions: 
(NP (AGR :P (PLURAL)) (REALNP :REALZ)) 
(NP (AGR :PERSONX :NU1VLX) (REALNP :REALX)) 
(CON J) 
(NP (AGR :PERSONY :NUMY) (REALNP :REALY)) 
(P-MIN :PERSONX :PERSONY :P) 
(NPTYPE-FILTER :REALX :REALY :REALZ) 
P-MIN and NPTYPE-FILTER are constraint relations whose 
function will be discussed in the next section. 
This formalism maintains the term unification practice of 
using functors with obligatory, positional arguments, rather 
than functorless feature structures with optional, labelled ar- 
guments, as in much recent work. There are several reasons 
for this. First of all, we find the functor very useful as a 
230 
way of indicating just what features are allowed in a given 
structure (and it is interesting to note attempts to restore it 
for just this purpose in \[13\].) Second, argument labels con- 
tribute their own clutter to the role. They would thus seem 
to be a notational win only if more than half the features of a 
given element are "don't-cares". In our grammar, however, 
we find on average that only about 3% of the feature slots 
in rules are "don't-cares". 
We should emphasize, however, that none of the work 
presented here hinges on these notational choices, and all 
the points made in subsequent sections carry over just as 
well to other unification notations. 
Syntactic Constraint Analyses 
Restrictions on agreement between features sometimes de- 
pend on the values of still other features. For example, 
English noun phrase conjunctions require that if one of the 
conjuncts belongs to a particular subgrammar (date, time 
etc.) then the other conjunct(s) must also belong to that 
subgrammar, but if neither of the conjuncts belongs to a 
subgrammar, there is no restriction. This can be done by 
including in the NP conjunction rule a constraint relation 
which provides a case-analyzing effect that could not be 
provided merely by unifying the variables ranging over the 
semantic type. This function is carried out by NPTYPE- 
FILTER, which we introduced above. This relation takes 
as its arguments the NPTYPE feature of the first conjunct, 
the NPTYPE of the second conjunct, and the NPTYPE fea- 
ture of the conjunction as a whole. This relation, then, can 
be thought of as constraining the possible triples of these 
values. 1 We present four instances of this rule for illustra- 
tion, where "~ 0" indicates production of the empty string. 
(NPTYPE-FILTER (NONUN1TNP 
(NONUNITNP 
(NONUN1TNP 
~O 
(NPTYPE-FILTER (NONUNITNP 
(NONUN1TNP 
(NONUNITNP ---+0 
(NPTYPE-FILTER (NONUNITNP 
(NONUNITNP 
(NONUN1TNP ~0 
(NPTYPE-FILTER (NONUNITNP 
(NONUNITNP 
(NONUNITNP 
~0 
(-PRO (TIMENP))) 
(-PRO (TIMENP))) 
(-PRO (TIMENP)))) 
(-PRO (DATENP))) 
(-PRO (DATENP))) 
(-PRO (DATENP)))) 
(-PRO (MISCNP))) 
(+PRO :PRO-TYPE)) 
(-PRO (MISCNP)))) 
(+PRO :PRO-TYPE)) 
(--PRO (MISCNP))) 
(-PRO (MISCNP)))) 
The first two rules require that if either of the conjuncts 
of a conjoined NP belongs to the TIMENP or DATENP 
subgrammar, than the other conjunct must belong to that 
subgrammar, as well. The last two rules allow ordinary 
pronominal and non-pronominal NPs to conjoin freely. 2 In 
lAltematively, it can be viewed as computing a value for the NPTYPE 
feature of the conjunction from the values of the individual conjuncts. 
2They also set the NPTYPE of the conjunction to being non-pronominal, 
since it cannot function as a pronoun. 
this example, note that while the first two rules could be 
collapsed into a single rule utilizing unifying variables, the 
third and fourth cannot. 
Another use of constraint relations is to "compute" a value 
from the feature values of the relevant consitutents, rather 
than requiring identity of features. For example, in NP con- 
junction with "and" in English, the person of the conjoined 
NP is first person if any of the conjuncts is first person, sec- 
ond person, if any of the conjuncts is second person and none 
is first person, and third person ff all the conjuncts are third 
person) This can be easily handled by the P-MIN constraint 
relation, which takes as its arguments the PERSON feature 
of the first conjunct, the PERSON of the second conjunct, 
and the PERSON feature of the conjunction as a whole. It 
has the following solutions: 
(P-MIN (1ST) :P (1ST)) .-4 0 
(P-MIN (3RD) :P :P) ---+ 0 
(P-MIN (2ND) (1ST) (1ST)) ~ 0 
(P-MIN (2ND) (3RD) (2ND)) ~ 0 
(P-MIN (2ND) (2ND) (2ND)) -4 0 
Still another case in which constraint relations provide a 
kind of flexibility greater than that available using standard 
unification is to allow the grammar to express "degrees of 
grammaticality". For example, in standard written English, 
it is common for a verb to agree in number with its subject. 4 
What do the restrictions represent? 
What does restriction VU/1 mean? 
What do the transport codes AL and R mean? 
However, in spoken English, conjoined noun phrases 
sometimes appear with singular agreement on the verb. 
What does RETURN ~ and RETURN MAX mean? 
What does class B and class Y mean? 
In still looser speech, agreement disappears even with 
non-conjoined subject noun phrases: 
List all the airlines that flies from Dallas to Boston nonstop. 
These facts can be handled by modifying the standard 
sentence rule: 
(ROOT-S :MOOD) 
(NP :AGR) 
(VP :AGR :MOOD) 
to the following: 
(ROOT-S :MOOD) 
(NP :AGR :CONJC) 
(VP :AGRX :MOOD) 
(SUBJECT-VERB-AGREEMENT :AGR :AGRX :CONJC) 
3Karttunen \[10\] handles such cases with a procees of generalization, 
rather than unification. 
4All of the examples in this discussion of subject-verb agreement are 
taken from the ATIS corpora collected by TI and distributed by NIST. 
231 
and adding the following solutions for SUBJECT-VERB- 
AGREEMENT. This is a constraint relation that takes as 
its arguments the agreement feature of the sentence's sub- 
ject NP, the agreement feature of the sentence's VP, and 
the conjunction feature of the subject NP which indicates 
whether it is a conjunction or not. 
(SUBJECT-VERB -AGREEMENT 
(SUBJECT-VERB-AGREEMENT 
(SUBJECT-VERB -AGREEMENT 
(SUBJECT-VERB -AGREEMENT 
(AGR :P :N) 
(AGR :P :N) 
:CON J) 
--~0 
(AGR :P (PLURAL)) 
(AGR :P (SINGULAR)) 
(+CONJ :CONJTYPE)) --~0 
(AGR :P (PLURAL)) 
(AGR :P (SINGULAR)) 
(-CON J)) 
~0 
(AGR :P (SINGULAR)) 
(AGR :P (PLURAL)) 
(-CON J)) 
---~0 
The first of these solutions enforces standard subject verb 
agreement: whether the subject NP is a conjunction or not, 
the agreement features of the subject and the VP must be 
the same. The second allows the VP to bear the singular 
feature when the subject is plural, just in case the subject is 
a conjunction. The last two rules allow the subject and the 
VP to disagree, when the NP is not a conjunction. The state- 
ment about the conjunction status of the subject is necessary 
in these last two solutions to make them orthogonal to the 
first two, so that a single structure will not be unnecessarily 
analyzed with more than one solution. 
This mechanism is superior to simply not requiring a VP 
to agree with its subject at all, by using distinct variables 
for the agreement features of the subject NP and the VP, 
since, given a large enough colpus, we can automatically 
associate different probabilities with the different solutions 
of this constraint relation. This is particularly useful in a 
spoken language system, since this will allow all the pos- 
sibilities, with some degree of probability, but will always 
prefer the most common solution and will only choose a less 
likely solution if a more common one is unavailable. 
Semantic Constraint Analyses 
The facility for case analysis is also used in semantic inter- 
pretafion, where the meaning representation of constructions 
are computed in terms of values of certain features which 
cannot always be known in advance. 
PP Interpretation 
Prepositional phrases, in both post-copular and post-nominal 
positions, are very common in the ATIS domain (and most 
other domains as well). Some examples: 
Which flights are on Delta Airlines 
Which flights are on Thursday 
Which flights are after 4 pm 
The role in our grammar which generates a post-copular 
PP is the following: 
(VP :SUBJ :WFF) 
(V (BE)) 
(PP :PP) 
(PREDICATIVE-PP :PP :SUBJ :WFF) 
PREDICATIVE-PP is the constraint relation in the role. It 
is responsible for specifying the formula meaning of the VP 
in terms of the translation of the PP (:PP) and the translation 
of the subject passed down from the clause (:SUB J). 
The PREDICATIVE-PP solution for the "flight-on-airline" 
sense is as follows: 
(PREDICATIVE-PP (PP-SEM (:OR (ON)(ABOARD) 
(ONBOARD)) 
(:NP AIRLINE)) 
(:SUBJ FLIGHT) 
(EQUAL (FLIGHT-AIRLINE-OF :SUBJ) 
:NP)) 
The first occurences of the variables :NP and :SUBJ above 
are paired with semantic types AIRLINE and FLIGHT; this 
is shorthand for me actual state of affairs in which a term 
representing a package of information (including encoding of 
semantic type) appears in the slots of the role these variables 
occur in. This term carries quantification and semantic type 
information, as below: 
(Q-TE/~w (QUmCrn~ER) (VARIABLE) 
(NOM (PARAMETER) (SET) (SORT))) 
This structure is so constructed as to not unify with another 
such structure if its semantic type is disjoint, using a method 
for encoding semantic types as terms described in \[20\]. 
The PP translation is also a package with the functor PP- 
SEM, containing the preposition and the translation of the 
NP object of the PP. No local attempt is made to translate 
the preposition. 
When parsing with the above predicate PP role, the system 
searches through a database of PREDICATIVE-PP solutions 
like the above, much as a PROLOG-based system would. 
If a solution succesfully unifies, the formula is passed up as 
the translation of the VP. Recursion is allowed, as in: 
(PREDICATIVE-PP (PP-SEM :PREP (:NP TIME)) 
(:SUBJ FLIGHT) 
:WFF) 
(PREDICATIVE-PP (PP-SEM :PREP (:NP TIME)) 
(DEPARTURE-TIME-OF :SUB J) 
:WFF) 
This rule says that any PP relating a flight to a time should 
be translated as if it related the departure time of the flight to 
that time. In this way, a common system of PREDICATIVE- 
PP solutions stipulating the meanings of various preposi- 
tional comparisons between times ("after", "before", "on", 
232 
"during") can be specitied just once, and used in multiple 
contexts. 
Such a method for interpreting PPs can be compared to 
one that uses unification over features of constituent ele- 
ments instead of constraint relations, such as proposed in 
\[13\] and \[8\]. There, the multiple meanings of a preposition 
are enumerated locally as a semantic feature of the preposi- 
tion, using a form of full-scale disjunction. Type constraints 
filter out those which are not meaningful in the given con- 
text, just as in our work. 
We claim, however, that the constraint relation method is 
superior exactly in view of its recursive power as described 
above. In order to handle such constructions as "flight after 
4pm", "flight before 4 pm" etc. a strictly unification-based 
approach would have to compile out all the possibilities for 
the type of the clause subject (TIME, FLIGHT etc.) and 
store them as disjunctive values of the translation feature 
on the given preposition. Thus in the ATIS domain there 
would be (at least) two senses of the preposition "after", 
both expressing the "time-after" relation. Clearly such an 
approach would not capture the general relations on times 
that these prepositions express. 
Subcategorization 
One of the devices used by the DELPHI grammar for en- 
coding subcategofization is derived from GPSG \[7\]. This 
is to place a feature for subcategofization on the rule for a 
given verb, and key all VP rules off this feature: 
(VP :SUBJ :WFF) ;for "John kicked Mary" 
------k 
(V (TRANSITIVE :WFF :SUBJ :OBJ)) 
(hiP :OBJ) 
The semantics of the subject of the sentence is passed down 
through the :SUBJ variable to the V, along with the seman- 
tics of the complements. The V in turn passed back up the 
formula representing the semantics of the whole sentence, 
through the :WFF variable. 
Of course this mechanism requires one VP rule for every 
subcategorization frame one wants to handle, and this can 
mn to many rules (about 60 in the DELPHI grammar). A 
more serious problem, however, arises in the case of optional 
complements to verbs, as seen in the following actual ATIS 
training sentences that use the verb "arrive": 
Show me all flights from Boston to Denver that arrive 
before 5 PM 
Show me flights ... that arrive in Baltimore before noon 
Show me all the nonstop flights arriving from Dallas 
to Boston by 10 PM ... 
Show me flights departing Atlanta arriving San Francisco 
by 5 PM 
Show me flights arriving into Atlanta by 10 PM from Dallas 
We see here that, in addition to the temporal PP that always 
accompanies it, "arrive" can be followed by (1) nothing else, 
(2) a PP with "in", (3) a "from"-PP and a "to"-PP, (4) a 
bare noun phrase, or (5) an "into"-PP and a "from"-PP. The 
principle pattern that emerges is one of complete optionality 
and independence of order. Indeed, in the fifth example, the 
temporal PP, which might be more traditionally regarded as 
an adjunct rather than a complement, and thus as one of 
the siblings of the VP rather than one of its constituents, is 
instead interposed between two PPs complements, making 
the adjunct analysis rather problematic, s 
The only way the subcategorization scheme presented 
above could deal with these variations would be to enu- 
merate them all in separate roles. But this would clearly be 
infeasible. The solution we have adopted constructs a right- 
branching tree of verbal complements, where the particular 
constituents admitted to this tree are controlled by constraint 
relations keying off the lexical head of the verb. There are 
two main rules: 
(VP :SUBJ (AND :INITIAL-WFF :COMP-WFF)) 
(V :LEX (INTRANSOPTCOMPS :SUBJ 
:INITIAL-WFF)) 
(OPTCOMPS :LEX :SUBJ (DUMMY) :COMP-WFF) 
and 
(VP :SUBJ (AND :INIIIAL-WFF :COMP-WFF)) 
(V :LEX (TRANSITIVEOPTCOMPS :SUBJ 
:OBJ 
:INITIAL-WFF)) 
(NP :OBJ) 
(OPTCOMPS :LEX :SUBJ :OBJ :COMP-WFF) 
The category OPTCOMPS generates the fight-branching tree 
of optional complements. It has the rules 
(OPTCOMPS :LEX :SUBJ :OBJ (AND :WFF1 :WFF2)) 
(PP :PP) 
(OPTCOMPS :LEX :SUBJ :OBJ :WFF1) 
(OPTCOMP-PP :LEX :SUBJ :OBJ :PP :WFF2) 
and 
(OPTCOMPS :LEX :SUBJ :OBJ (TRUE)) ~ 0 
The OPTCOMP-PP is the constraint relation; it keys off 
the lexical head of the verb (the variable :LEX) and com- 
bines the subject, object, and PP complement translations to 
produce the contribution of the PP complement to the final 
formula that represents the sentence meaning. An arbitrary 
number of PP complements are provided for by the recursion 
of the first role above, which bottoms out in the case of the 
second role when there are no more complements. Phrasal 
types other than PPs are accomodated by similar mles. 
The solution for PP complements to "arrive" such as "in 
Atlanta", "into Baltimore .... at Denver" etc. follows: 
5To see that these PPs are truly associated with the verb rather than 
somehow modifying the subject flight-NP, one need only replace the subject 
with the pronoun "it". 
233 
(OPTCOMPS (ARRIVE) 
(:SUBJ type FLIGHT) :ANY 
(EQUAL (DESTINATION-CITY :SUB J) :NP)) 
(PP (PP-SEM (:OR (INTO) (IN) (AT)) (:NP type CITY))) 
(N-BAR :NOM3) 
(N-BAR :NOM1) 
(N :NOM2) 
(NOM-COMP-READING :NOM1 :NOM2 :NOM3) 
This rule says that for a flight to "arrive" INTO, IN or 
AT a city means that the city equals the value of the flight's 
DESTINATION-CITY attribute. Semantic type information 
is here notated with a shorthand keyword "type"; in the ac- 
tual system a partially-specified term that packages semantic 
type information in a specific slot is unified into such vari- 
ables as :SUBJ, :OBJ and :NP. Note also the use of disjunc- 
tion (the :OR) to combine different prepositions together. 
Other devices for encoding subcategorization have been 
proposed. One, made use of in PATR-II and described in 
\[19\] encodes subcategorization infomaation as a list of the 
complement patterns that are required to follow the verb, 
and generates a right-branching tree of VPs, each absorbing 
one of the complements in the list until no more are left. 
The difference between the PATR-II scheme and the one 
way presented here is that the complements in PATR-II are 
required and must follow one another in a predetermined 
order. The only obvious way it could handle the optionality 
and order independence seen in the "arrive" examples is 
just the same brute-force method of enumerating possiblities, 
using lists of differing order and length. 
Using Unification to Encode Semantic Con- 
straints beyond Semantic Type 
Not all constraints on meaningfulness are strictly reflections 
of the semantic type of phrase denotations. Consider the 
lexical item "L" in the ATIS training set. Seen in a number 
of different database fields, it can variously denote limousine 
availablity, lunch service, or other classes of service avail- 
able on a flight. Yet in the following example it is clear that 
its usage is relevant to just the first of these: 
What is transport code L? 
Our claim is that not just the referent of "L"--limolasine 
service for ground transportation--that plays a role here, but 
also the means by which it gets to that referent: namely, by 
being an abbreviation or code rather than a name. That is, 
"transport code L" is a meaningful compound, while "trans- 
port code limousine" would not be. The lexical entry for 
abbreviation terms like "L" reflects this by taking the form 
of an inverse function application: the referent of the lexical 
item "L" is the ground transportation type that has the string 
"L" as its abbreviation: 
(INVERSE-VAL* (ABBREV-OF) "L" 
(GROUND -TRANSPORTATION)) 
While this has the same referent as the lexical entry for 
"limousine" it has a different form, one which the role ana- 
lyzing the construction above makes use of. 
Nominal compounds in the DELPHI system are generated 
by the following rule: 
in which the constraint relation NOM-COMP-READING 
computes the semantics of the whole conslruction from the 
semantics of the head houn and the nominal modifier. NOM- 
COMP-READING has different solutions for different se- 
mantic types of noun translation. The relevant one here is: 
(NOM-COMP-READING 
(NOM (CONS-P (REL1) 
(:ARG type :ARG-SORT) 
:PARS2) 
(R.EL-APPLY* :FUNCTION :NP) 
:VAL-SORT) 
(NOM :PARS1 (INVERSE-VAL* :FUNCTION 
:TERM1 :SET) 
:ARG-SORT) 
(NOM :PARS1 (INVERSE-VAL* :FUNCTION 
:TERM1 :SET) 
:ARG-SORT)) ~ 0 
The first slot of the NOM terms above encodes the argument- 
taking property of relational nouns such as "code", "salary" 
or "speed", and has been described in an earlier paper \[20\]. 
The rule states that an inverted attribute reference (here, 
"L") preceded by a relational noun (here, "code") for that 
same attribute (here, "ABBREV-OF') simply refers to that 
inverted attribute reference. 
Our view is that the preceding nominal modifier essen- 
fiaUy performs a function of disambiguation: it serves to 
distinguish the desired sense of the head from any other pos- 
sible one. This is reinforced when the whole compound-- 
"transport code L" is considered. Another NOM-COMP- 
READING role is responsible for combining "code" with 
"transport": 
(NOM-COMP-READING 
(NOM :PARS1 :ARG-SET :ARG-SORT) 
(NOM (CONS-P (REL1) 
(:ARG type :ARG-SORT) 
:PARS2) 
(REL-APPLY* :FUNCTION :NP) 
:VAL-SORT) 
(NOM (CONS-P (REL1) 
:ARG 
:PARS2) 
(REL-APPLY* (F-RESTRICT :FUNCTION 
:ARG-SET) 
:NP) 
:VAL-SORT)) ~ 0 
This constrains the domain of the relational noun it modifies 
to be just the set that is the translation of the modifying noun. 
The semantic type of the modifying noun must be unifiable 
with the argument type of the head relational noun. After 
this unification fomas the translation of the compound "trans- 
port code", the resulting type constraints serve to distinguish 
234 
the correct sense of "L"--that of ground transportation-- 
from the meal service and other senses. 
Our technique of allowing roles to impose restrictions on 
the forms of semantic translations themselves, rather than 
merely on the semantic types of this translations, bears some 
discussion because it differs from proposals made by others, 
such as \[14\]. In that work, the position is taken that in- 
specting or restricting the structure of a logical form is inad- 
missible on theoretical grounds, in that it violates or makes 
unenforceable the principle of compo@tionality. As far as 
theoretical matters go, we believe that the principle of com- 
positionality is open to many interpretations (for example, 
see \[15\]) and that its most general interpretation does not 
exclude techniques such as ours. 
A more practical concem, and one which may well un- 
derly or justify the theoretical qualm, is that rules based on 
the structure of logical form may not succeed if that structure 
happens to be transformed (say through wrapping with an- 
other structure) into some syntactically different form which 
cannot be recognized as one which the role should allow. 
This is not a problem for the rules presented in this sec- 
tion, since the operation of nominal compounding is so 
tightly localized, operating in a function-argument fashion 
that gets to the noun meaning "first", before other modifica- 
tions such as postnominal adjuncts. Ultimately, though, we 
feel that the real solution must lie in a different approach to 
meaning representation, one in which non-denotational prop- 
erties of the utterance meaning are encoded or highlighted 
in a way that stands above the variances of syntactic logical 
form. But this is a matter for future research. 
Can Constraint Relations be Compiled 
out of Rules? 
A natural question to ask is whether or not constraint rela- 
tions can be compiled out of grammar rules, turning them 
into unifications like any other over the features of "real" 
constituent elements. 
One technique for this kind of compilation is certainly 
well-known in logic programming: the method of partial 
execution \[16\] in which the constraint relation is solved for 
at the time the rule is read in, not when it is used. The solu- 
tion(s) so obtained are simply unified back into the remainder 
of the rule to create the compiled version. If the constraint 
relation is non-deterministic there will be more than one so- 
lution and hence more than one compiled version of the mle. 
This is certainly undesirable computationally, since multiple 
variants of the the same grammar rule will cause a parser to 
do redundant matching. On the other hand, if the unifica- 
tion method used permits full disjunction the variation can 
be kept "factored", and the redundant matching avoided. 
Such a compilation will be possible, obviously, only if 
the constraint relation can be guaranteed to have finite num- 
ber of solutions, given the degree of instantiation in which 
it appears in the role. But this is actually a rather strong 
condition to place on constraint relations, particularly on 
those which participate in semantic interpretation. Semantic 
strategies which defer part of the semantic computation for 
a constituent can have a problem with this condition, since 
there is no bound (given conjunction) on the size of most 
types of constituents. An example in our work would be the 
treatment of PP semantics outlined earlier, in which the PP 
is not fully translated at its own level, but instead passed up 
as a package of preposition and NP translation. The obvious 
extension for a conjoined PP would be as list of such struc- 
tures. But since there is no limit to the number of PPs that 
can be conjoined, there is no limit to the length of the list, 
and thus there can be no limit to the number of solutions for 
the attachment constraint. 
Even ff a finite number of solutions can be guaranteed, 
however, there are still reasons why one might not want 
to compile constraint conditions out of the grammar. One 
reason is that leaving them in allows one to add solutions 
to a constraint condition without re-compiling all the gram- 
mar mles and other constraint rules which use it (a situation 
exactly analogous to the macro/function distinction in Lisp 
programming). Another is that distinguishing certain con- 
straints from the rest of the unifications of the grammar mle 
enables us to intervene in the search with specific indexing 
methods (say on semantic type). This is discussed in \[3\]. 
And a final benefit of distinguishing constraint conditions 
from other unifications is that relative frequency counts can 
more easily be made of their different solutions, just as can 
be made on semantic senses of lexical items. This is dis- 
cussed in \[1\]. 
Acknowledgements 
The work reported here was supported by the Advanced Re- 
search Projects Agency and was monitored by the Office 
of Naval Research under Contract No. N00014-89-C-0008. 
The views and conclusions contained in this document are 
those of the authors and should not be interpreted as neces- 
sarily representing the official policies, either expressed or 
implied, of the Defense Advanced Research Projects Agency 
or the United States Government. 
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