Functional Constraints in Knowledge-Based 
Natural Language Understanding 
Lars AHRENBER(g 
Department of Computer and Information Science 
LinkSping University 
S-581 83 LinkSping, Sweden 
Telephone +46 13282422 
Internet: LAH~IDA.LIU.SE UUCP: {mcvax,mannari,annet}!enealliuidaIlah 
Abstract 
Many knowledge-based systems of semantic interpretation 
rely explicitly or implicitly on an assumption of structural 
isomorphy between syntaotic and semantic objects, handling 
exceptions by ad hoc measures. In this paper I argue that 
constraint equations of the kind used in the LFG- (or 
PATR-)formalisms provide a more general, and yet restricted 
formalism :in which not only isomorphic correspondences are 
expressible, but also many cases of non-isomorphic corre- 
spondences. I illustrate with treatments of idioms, speech act 
interpretation and discourse pragmatics. 
1. Background and purpose 
In knowledge-based natural language understanding systems 
the role of syntax is by no means self-evident. In the Yalean 
tradition /,~tchank & Riesbeck, 1981/ syntax has only played a 
minor role and whatever little syntactic information there is has 
been expressed in simple terms. Consequently, there is no 
grammar as such and syntactic conditions are freely intermixed 
with semantic conditions in the requests that drive the system 
forward/13irnbaum & Selfridge, 1981/. Similarly, in frame-based 
systems such as /Hayes, 1984/ the syntactic information is 
stated in ~:onjunction with all other information relevant for 
instances ot a frame. A justification for this approach, apart from 
transparency, is that it makes sense to say that part of our 
knowledge of a concept is knowledge about how it is communi- 
cated. 
A major disadvantage of this approach is of course its lack of 
generality. To overcome this problem we may extract general 
syntactic knowledge' and make use of it in a syntactic parser 
which works alongside with the semantic analyser. Examples of 
such systems are PSI-KLONE /Bobrow & Webber, 1980; 
Sondheimer et ah, 1984/ and MOPTRANS /Lytinen, 1986; 
1987/. The promise of these systems is that you get both 
modularity and integration, although there are many open 
questions about how the integration can best be achieved. 
Moreover, one would I!ke to put the integration of syntax and 
semantics, not just syntax and semantics per se, on a principled 
basis, i.e. we need a theory of how syntactic and semantic 
objects correspond. Linguistics and philosophy offer some 
guidelines here, such as compoeitionaiity, and a number of 
different theories, but a problem is that the semantic objects 
considered are usually not knowledge structures. /Hirst, 1987/, 
though, is an attempt at a principled, modular and integrated 
knowledge-based system where compositionality and a principle 
of strong typing provide the theoretical underpinnings. These 
principles teem to provide a tighter straight-jacket than one 
would really want, however, as indicated by the many structures 
that Hirst shows are problematic for his system. 
Another~ more recent approach is to capture correspondences 
between syntactic and semantic objects through constraints 
/Halvorsen~ 1983; 1987; Fenstad etal., 1985; Kaplan, 1987/. An 
essential feature of constraints is that they simultaneously 
characterize properties of a structural level and account for a 
correspondence between those properties and properties of 
another level, i.e. the level to which the constraint is attached. 
The correspondence may be between two different levels of 
syntactic structure, as in LFG, or between a syntactic structure 
and a semantic structure or conceivably between any two 
structural aspects that constrain each other. So far it seems that 
constraints have primarily been stated in the direction from form 
to meaning, where meaning has been regarded as inherent in 
linguistic expressions and thus derivable from an expression, 
given a grammar and a lexicon. 
In a working system, however, we are not merely interested in 
a decontextualised meaning of an expression, but in the content 
communicated in an utterance of an expression, which, as we 
know, depend on world knowledge and context in more or less 
subtle ways. A rather trivial fact is that we need to have an 
understanding of the context in order to find a referent for a 
referring expression. A more interesting fact is that we often 
need an understanding of context in order to get at the 
information which is relevant for determining the referent 
/Moore, 1981; Ahrenberg a 1987a,b; Pulman, 1987/. 
In a knowledge-based system, the knowledge-base provides an 
encoding of general world knowledge as well as a basis for 
keeping track of focal information in discourse. It seems a 
natural move to combine a knowledge-based semantics with the 
descriptive elegance and power of constraints, but as far as I 
know, not much work has been done in this area. /Tomita & 
Carbonell, 1986/presents a knowledge-based machine-translation 
system based on functional grammar and entity-oriented parsing. 
In this paper I discuss the role of syntax in three general and 
related aspects of utterance interpretation: referent 
determination, classification, and role identification. A 
joint solution to these problems will fall out if we assume, as is 
often done, a simple, one-to-one structural (or categorial) 
correspondence between syntactic and semantic objects. This is 
done explicitly e.g. by /Danleli et ah, 1987/ and /Hirst, 1987/ 
and, so far as I can judge, implicitly in many other systems. 
However, the assumption is much too simplified and must be 
amended. I will illustrate some cases where the correspondences 
are more involved and argue that local constraints of the kind 
used in the LFG-formaiism /Kaplan & Bresnan, 1982/ are able 
to handle them in a fairly straight-forward way. Thus, instead of 
ad hoc-solutions the isomorphic cases will in this framework fall 
out as particularly simple instances of the general principles. 
2. A framework and a system 
I regard the process of interpretation as a process in which a 
given object, the utterance, is assigned a description, the 
analyMs. The description has different aspects, primary among 
them being 
13 
- a constituent structure, (c-structure) 
. a functional structure, (f-structure), 
a semantic structure, (d-structure) and 
• a content structure. 
I refer to these structural levels as aspects in order to 
emphasize the idea that they are all part of one and the same 
interpretation of the utterance. The c-structure and the 
f-structure are roughly as in LFG /Kaplan & Bresnan, 1982/, 
but with some important deviations. The functional structure is 
strictly syntactic. There are no semantic forms and hence no 
grammatical notions of coherence and completeness. Instead of 
the PRED-attribute, there is an attribute LEX whose value is a 
"lexeme", an abstract grammatical unit which in turn is 
associated with semantic objects: object types, semantic attri- 
butes, and so on. 
The semantic structure is a descriptor structure ('dag') just 
as the functional structure, but with descriptors pertaining to 
the discourse referents accessed or made available by the 
utterance. Thus, a constituent of the semantic structure consists 
of a description that potentially applies to an object in the 
universe of discourse. The content structure differs from the 
semantic structure mainly in that referents for descriptions have 
been identified (where possible). 
If a c-structure, an f-structure and a d-structure apply to an 
expression under a given interpretation they are said to 
correspond. If, similarly, a sub-expression of the input is 
associated with constituents at all three levels, these constituents 
are said to correspond. 
Correspondences between c-structure and f-structure are 
defined by an LFG-style grammar and a dictionary of stems and 
~. affixes. Correspondences between f-structure and d-structure are 
defined by the lexeme dictionary and information in the 
knowledge-base. Primary among the knowledge structures are 
types, attributes, and instances. Every type is associated with a 
prototype, a frame-like structure whlch'defines what attributes 
apply to instances of that type, as well as restrictions on their values. 
Prototypes are also associated with functional constraints, 
thus defining possible correspondences between d-structures and 
f-structures. For example, the attribute AGENT, beside other 
restrictions on its occurrence and values, may be assigned the 
canonical constraint (~ SUB J) = ~. The arrows in this schema 
have the same interpretation as in the grammar rules: i" points to 
the f-structure node corresponding to the description of which 
the attribute is part, ~ points to the f-structure node 
corresponding to its value. 
Semantic attributes may also be associated with contextual 
constraints. The context is represented by a special object, the 
discourse state (DS), the description of which encodes the 
contextual information that the system currently has available. 
In particular, this will include information about who is speaker 
and who is addressee. A simple contextual constraint can be 
stated as =(DS SPEAKER), which when associated with an 
attribute asserts, the identity between its value and the current 
speaker. 
The relations between different structural aspects and the 
knowledge sources that define and constrain them are illustrated 
in figure 1. 
In the process of interpretation the analysis is ideally 
constructed incrementally. When information is added to one 
structural aspect and there is a constraint associated with this 
information, we are justified in adding the information stated in 
the constraint to the structural aspect to which it relates. If this 
is not possible, e.g. due to the presence of contradicting 
information, the initial information can be rejected. 
14 
string 
c structure 
f structure 
d-structure 
content structure 
LEXICAL-FUNCTIONAL GRAMMAR 
MORPH DICTIONARY 
LEXEME \] DICTIONARY 
g 
PROTOTYPES ) 
DISCOURSE i STATE 
Figure 1: Structural aspects and their correspondencaL 
The ideas presented here have been partially implemented in 
a system called FALIN, which is developed as a precursor to an 
understanding component of a dialog system (Ahrenberg, 
1987a). 1 The world of FALIN is a drawing-pad and its 
knowledge cover simple geometrical objects that the user can 
draw and manipulate using natural language. FALIN's parser (a 
chart parser) is constructing a c-~tructure and an f-structure in 
tandem, hut hands f-structures over to another module which 
attempts to construct corresponding d-structures and content 
structures. The content structure is then evaluated against the 
knowledge-base. 
3. Structural Isomorphy 
The semantic aspects that this paper considers are three very 
basic ones: (i) referent determination; to determine the set of 
discourse objects (referents) that a given utterance relates to; (ii) 
classification; for each of these referents to determine their type, 
and (iii) role identification; to determine the relations they 
contract with the other referents. From the first task I then 
exclude the problem of actual identification of referents, 
restricting myself to the task of deciding that there is a separate 
entity that some part of the utterance applies to. 
Now, we can formulate a general and practical principle, 
which is commonly used in semantic interpreters and which 
offers a solution to all three problems at once, namely a 
principle of structural isomorphy between syntactic and 
semantic structure. The basic tenet of this principle is that there 
exists a level of syntactic representation (which I will call fnnctional 
structure here, but which may be represented in 
various ways, e.g. as a dependency structure) such that (a) every 
referent is expressed by some major constituent of the functional 
structure; (b) the type of a referent is given, directly or 
implicitly, by (one sense of) the head of that constituent; and (c) 
two referents contract a role relationship iff their respective 
constituents contract a grammatical relation in the functional 
structure. These one-to-one correspondences between syntactic 
and semantic objects yield isomorphic syntactic and semantic 
structures as long as we only consider the three mentioned 
aspects of semantic interpretation, and hence the name 
"structural momorphmm. See figure 2 for a graphical 
illustration. 
1 FALIN can be read .~'st Attempt at LINkfping Natural Language 
~nterface. 
Thus, no claims are made for other aspects of semantic inter- 
pretation, such as quantification or modification. 
SyN~fAX 
l - o.Tto-o,;~ -\] ~EIV~AN'IICS 
Categore~natic Word1 ~ ................ ~ Referent Type1 ,.) 
Corl~,tituent 1\] ~ ...... ._> Referentl 
% : ........ Jza~ 
Constituent2 \] 
....... - 
Categorematic Word2 Referent Type2 
Figure 2: Correspondences of syntactic and semantic objects 
yielding structural isomorphism. 
It should t,e observed that the isomorphy principle allows for 
both lexical and structural ambiguity, i.e. it does not require 
~hat a given word, or grammatical relation can be interpreted in 
only one way. What it requires is a one-to-one correspondence of 
syntactic and semantic objects of the same interpretation. 
Moreover, structural isomorphy is riot the same as 
composition~,lity. In one sense compositionality is more 
restrictive since it applies to all ~mpects of semantic inter- 
pretation. On the other hand compositionality is less restrictive 
since it requites derivation trees to be i~omorphic, not consti- 
tuent structmea. Howe¢er, compositional systems too, e.g. /Hirst 
198'1/, oi°~en ~ssume structural isomorphism for the aspects of q 
col|tern here. ~ 
As an ilh~a~tration, consider (1). Here the speaker can be said 
to refer to hmr entities, a sale, a car and two male humans. The 
last three rdate to the first as, say, Goods, Provider and 
Receiver, re~pectively. Each of the referents corresponds to a 
major constituent, the whole sentence for the case of the sale and 
subject, direct object and indirect object for the others. Also, the 
head words as//, Jim, car and Englishman provide the type 
inibrmation ~ stipulated. 
(t) Jim sold the car to an Englishman. 
in the fi'aaaework used here we could have the following 
grammar rule, defining constraints on the functional structure: 
RI: S .... NP: (t SUBJ) = $ VP: T=$ 
R2: VP -~ FV: ~'::~ NP:(~ OBJ) =: ~ PP*: (t POBJ)9 
R3: Pl? ,-~ P: ~':::$ NP: i'==~ 
/I,4: NP -+ { (DET: ~:::~) N: ~::~ / PN: ~=:J. } 
3 h:~ tlirst's ~lm~em prepositions and "pseudo.prepositions" (named 
o°()t~3 , OBJ, INDOB3) are the rdevaat syntactic objects hlstead of 
i~r~mla~ical ~u actions. 
The morph dictionary associates functional constraints with 
stems and affixes as in the following illustrations. Stems are also 
associated with lexemes~ but affixes and function words are not. 4 
LI: cat'; N, (i" LEX) = !CAR, (T NUMB) = SING 
1,2: sold; FV, (j" LEX) = !SELL, (T TENSE) = PAST 
L3: the; DET, -~ , (1" SPEC) = DEF 
L4: to; P, -- , (~" PCASE) = TO 
In the 
appropriate 
lexeme dictionary lexemes are associated with 
semantic objects. This association may be 
one-to-many, but only one of the alternatives can be involved in 
an analysis, thus making the correspondence between head words 
and types one-t(r.one. It may also involve object descriptions 
rather than objects. For instance, a proper name lexeme, such as 
!JIM, can have associations with known instances as well as with 
a description that can be used in the construction of a new 
instance. 
!SELL: { &Selll / &Sell2 / ... } 
!CAR: { &Carl / &Car2 / ... } 
!JIM: { Person67 / Person83 / Name18 / 
(TYPE=&Person, SEX=Male, NAME=NamelS) } 
Finally, the association between grammatical functions and 
semantic roles is captured in the definition of the latter. As attri- 
butes can be differentiated in very much the same way as object 
types, these correspondences can be stated at an appropriate 
level of generality. For instance, Provider may be analysed as a 
differentiation of Agent and inherit its association with the 
Subject function from that attribute, it is also possible to have 
these associations stated at the level of individual action types. If 
we want to express the difference between sell and buy as a 
difference in the role&ruction associations of Provider and 
Receiver~ we state the associations ii1 the definition of the two 
action types. In any case the prototype of &Sell\] will turn out to 
bear the following inibrmation: 
(2) _ &Selll 
Type; 
Provider; 
Receiver; 
Goods; 
Price; 
(T LEX) = !SELL 
(T SUBJ) = 
(t OBJ) = 
(T POBJ)~ 
(i PCASE) = TO 
(~ POBJ)-B 
($ PCASE) = FOR 
Here the associations are not just simply stated as a function 
label associated with the role attribute, but corresponding 
functional descriptions are explicitly represented. This is so 
because more than a mere function label may be involved and, as 
will be shown below, the correspondences may be more complex 
than this. 
The correspondences in a prototype should be read as a set of 
canonical correspondences. Alternative correspondences can be 
obtained from lexieal rules just as in LFG-theory /Bresnan, 
1982a; cf. also Halvorsen, 1987/. Applying the Passive lexical 
rule to (2) we obtain an alternative set of constraints, namely (2'). 
4 Lexemc labels are indicatied by an hLitial exclamation mark. Object 
types are indicated by an initial '&'. 
15 
(2') __ &Selll 
Type; (1" LEX) = tSELL 
(T ACT/PASS) = PASSIVE 
Provider; /I POBJ)~ ~ 
" PCASE) = BY 
Goods; (T SUB J) = 
Receiver; II POBJ)3 ~ 
PCASE) = TO 
Price; (1" POBJ)~ J. 
(I PCASE) = FOR 
There are some reasons for stating the role-function corre- 
spondences as functional constraints induced by the semantics 
rather than the other way round. For one thing, definitions of 
types and attributes are needed for independent reasons and the 
introduction of the functional constraints is merely a way of 
encoding knowledge that pertains to them, i.e. knowledge of how 
they are communicated. Moreover, subcategorization properties 
are semantically grounded, even if not absolutely predictable. 
4. Cases of non-lsomorphtsm. 
4.1 Non-isomorphic constructions. There are certain 
linguistic construction-types that, at least on the surface~ 
contradict the isomorphism principle, such as Equi, Raising, 
Longdistance dependencies and Gapping constructions. However, 
in most cases it seems possible to eliminate the problems posed 
by these constructions already in the grammar and thus have 
appropriate functions assigned to constituents at functional 
structure. 
4.2 Flexible idioms. For simplicity we may characterize a 
flexible idiom as a complex expression with a definte meaning 
whose parts may undergo variation and occur in non-adjacent 
positions. Fixed idioms, such as at once, back and forth, first of 
all do not pose the same problems as they can be taken care of 
already at the c-structure level. Most flexible idioms in English 
seem to involve a verb, such as make fun of, break someone's 
heart, or make up one's mind. Consider (3). 
(3) He broke their hearts completely. 
At the c-structure and f-structure levels it is analysed in the 
same way as any other sentence. In particular, each constituent 
will have its own LEX-dsecriptor: 
(4) -LEX IBREAK 
TENSE PAST 
SUBJ \[LEX 
OBJ ~LEX 
|NUMB 
POSS 
IHE\] 
IHEART \]~ 
PL \[LEX ITHEY 
Object types for both ordinary breaking and heart-breaking 
are associated with IBREAK in the lexeme dictionary. The 
object type for heart-breaking also involve a reference to the 
lexeme tHEART, however. The object type &Break- 
someone's-heart carries the following information associated with 
the attributes of its prototype: 
16 
(5) __ &Break-someone's-heart: 
Type; II LEX) ---- 'BREAK / -~\] 
OBJ LEX)= 'HEART I 
\[ Cause; (T SUBJ)----- ~ L 
~patient; (1- OBJ POSS) = £ _~ 
This means that while there is a simple one-to-one 
correspondence between Subject and the role of Cause, the other 
function-role correspondences involve structural distortions. 
They are still expressible by local constraints, however, and this 
holds for any flexible verbal idiom where the fixed parts have a 
grammatical relation to the verb, or to some complement of the 
verb, i.e. for the great majority of verbal idioms in the language. 
In some cases a part of the idiom may play a double role. On 
the one hand it is part of the expression of the idiom and on the 
other hand it brings with it a referent of its own. Consider the 
following discourse: 
(6) A: He hasn't shown his face here for the last couple of 
weeks, has he? 
B: Who wants to see it anyway? 
To describe the fact that the phrase hie face can express a 
referent we may allow for this possibility in the statement of 
correspondences in the protytype for the action. 
(7) __ &Show-one's-face: 
Type; 
Agent; 
Object; 
Location; 
Ii LEX) = ISHOW 
oBJ LEX) = ~FACE 
OBJ POSS LEX) = IREFL 
(T SUB J) = 
(~ OnJ) = 
I~ ADV)~ 
PCASE) = LOC 
4.3 Constituted discourse objects. An utterance is itself a 
discourse object, i.e. it may be referred to in the discourse that 
follows. When this happens the utterance will be classified one 
way or the other, as in utterances of the following sort: 
81 That is a difficult question to answer. 
I think your statement needs clarification. 
Except for performative utterances there is no head word in the 
utterance that can be used to for its classification, however. 
Instead the classification will have to rely on other information, 
such as clause-structure and punctuation. 
Speech-act interpretation is often regarded as something 
entirely different from semantic interpretation proper. This, I 
would argue, is a mistake. Illocutionary categorization is 
constrained by words and world knowledge in very much the 
same way as categorization of other referents? The essential 
difference between the illocutionary act as a referent and other 
referents is that the illocutionary act come into being with the 
utterance of the words, whereas the other referents exist 
independently. This means that we can postulate (at least) two 
ways in which an uttered expression relates to discourse 
referents, first, it relates to referents described by the utterance, 
and second, to referents constituted by the utterance, in 
particular the illocutionary act. The analysis of an utterance 
would be incomplete if it does not include a classification of the 
utterance, as well as the discourse objects that fulfils the roles of 
Speaker and Addressee. 
(10) Show me the files. 
5 Similar problems arise with sentences each as The question is why he 
did it, The fact is that he did i~ where the subjects are not 
interchangeable: *The fact is why he did it. 
Consider now how (I0) may be analysed. Let us classify it by 
meaus of the object type &Directive which we assume to be 
supertype for commands, orders, directions and similar ~Jpeech 
acts. The prototype for this type may be assigned the following 
set of constraints (as one alternative): 
(11) __ &Directive 
Type; 
Speaker; 
I Addressee; 
lAction; 
(~ MOOD) = IMPERATIVE- 
=(DS SPEAKER) 
=(DS ADDRESSEE) 
~=~ 
In order to distinguish objects being described from objects being 
constituted w~ distinguish two modes of correspondence. The 
~-arrow indic~..tes" an f-structure node corresponding in consti- 
tutive mode. 6 The schema associated with the Action attribute 
says that the f-structure node corresponding to the d-structure 
node for the directive in constitutive mode actually coincides 
with the f-str~mture node describing the action being directed, 
thus encoding the one-to-two relation between the utterance and 
the discourse objects it relates to. 
4.4 Implied referents a~d types. As is well known, in 
situated discol~rse we regularly do not give explicit expression of 
the referents being talked about as such information can be 
inferred from the context. Obvious illustrations are given by 
short answers to questions as in (12). Similarly, we may suppress 
head words if t~hey are inferrable, as in (13). 
(12) - Who is the manager of the sales department? 
- Jim l~mith. 
(13) I've go~ many more at home. 
There are ~wo ways to react in the face of such "elliptic" 
utterances. One way is to say that they require special pragmatic 
heuristics which are independent of the principle of structural 
isomorphism (and vice versa) and thus simply regard them as 
irrelevant. However, this makes the principle limited in 
application. It would be better to have more general principles of 
utterance intelpretation that together covers both elliptical and 
non-elliptical utterances. Again, contextual constraints in 
conjunction with ordinary functional constraints can do part of 
the job ibr us. 
A phrase such as Jim Smith in itself does not give much 
information of course. However, when it is uttered in reply to a 
question, as in (12), it will have quite a well-defined meaning. In 
the definition of tiJe utterance type &Answer, we may thus 
include, beside attributes for Speaker and Addressee, also an 
attribute indiq',ating what question is being answered. This 
question can be retrieved from the discourse state, where it was 
put when it was raised and kept until it is answered or dropped. 
(14) __ _ &Answer 
Type; (~ MOOD) = DECL 
~peaker; = (DS SPEAKER) 
Addressee; : (DS ADDRESSEE) 
Question; e (DS QUESTIONS) 
_Answer; ~ = 1 
6 This use of the symbol '1~' should \]Lot be confused with its use in 
Bresnau (1982a}~ where it is part of the description of long-distance 
dependencies. 
5. Restrictiona on proper correspondence 
It would be premature to attempt an explicit characterization 
of the correspondence relations between the structural aspects of 
an analysis, especially as important aspects of semantic inter- 
pretation have not even been considered. In this final section I 
therefore only summarize the general ideas, pointing out how 
they differ from structural isomorphism and state a few 
necessary conditions on the correspondence between f-structure 
and d-structure. 
The referent descriptions conveyed by an utterance are 
constrained by linguistic form (functional structure) as well as 
by conceptual knowledge (prototypes) and context-of-utterance 
(discourse state). A referent need be given no overt expression in 
the utterance if it is inferable from a prototype and/or from the 
context. 
The constraints themselves need not be one-to-one, contrary 
to the principle of structural isomorphy, but they are local in the 
sense that they can only refer to (i) structures corresponding to 
either (a) the object that induces them, (b) the object of which 
that object is an immediate part, or (c) other dependents of that 
dominating object, or (ii) objects of the discourse state. 
To capture speech-act interpretation we recognize two modes 
of correspondence, one based on the relation descrip- 
tion-described object, and the other on the relation utterance~ 
constituted act. 
The f-structure is a syntactic structure, which means that it 
must be a minimal structure satisfying the constraints induced 
by the c-structure. However, it must also correspond properly 
with the d-structure. To account for this correspondence we 
must first realize that not all functional attributes need be 
semantically relevant e.g. those indicating grammatical gender. If 
¢ is an f-structure, ¢8 will indicate an f-structure obtained 
m . . from ¢ by subtraction o~ semantmally irrelevant paths. 
Thus, we get the following conditions on proper corre- 
spondence between d-structures and f-structures: 
(1) A d-structure, 6, and an f-structure, ¢, are corresponding 
properly in descriptive mode, only if 
(a) 6(Type)~ g(¢(LEX)), where g is the function defined by 
the lexeme dictionary; 
(b) There is a prototype, /'/, for 6(Type) such that (i) 6 
satisfies the conditions'' of //, and (ii) Cesta is a minimalHfo 
structure satisfying all functional constraints reduced by r 
the role attributes at top level of 6. 
(e) For any sub-structure~ 6', of 6, there is a sub-structure, ¢', 
of ~, such that 6' and ¢' correspond properly in descriptive 
mode. 
(2) A d-structure, 6, and an f-structure, ¢, are corresponding 
properly in constitutive mode, only if 
(a) There is an utterance-type, D, and a prototype, IID, for/2, 
such that 6 satisfies the conditions of//_. IJ 
(b) ~b is a minimal structure satisfying all functional 
constr~nmts induced by //~ for the role attributes at top level 
of ~. 
(c) as l(c). 
6. Acknowledgements 
This research has been supported by the Swedish National Board 
for Technical Development. I am indebted to Magnus Merkel 
and the other members of the Natural Language Processing 
Laboratory at Link6ping university, Mats Wirdn, Arne J6nsson 
and Nils Dahlbllck for valuable discussion of these topics. 
17 

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