The Role of Intensional and Extensional Interpretation
in Semantic Representations The Intensional and
Preextensional Layers in MultiNet
Hermann Helbig and Ingo Glöckner
University at Hagen, Intelligent Information and Communication Systems, Germany
Abstract. Although it is well known that the full meaning of a concept includes
an intensional and an extensional aspect, the latter is neglected in almost all prac-
tically used knowledge representations and semantic formalisms, which consider
only the interrelationships between concepts but not their referential meaning. In
logically oriented representations with the usual model-theoretic interpretation,
the extensions of predicates or symbols of the language in general belong to a
metalevel (the model level) clearly distinguished from the logical language. In
this paper, we show in what way the extensional aspect is important (in addition
to the intensional aspect) to account for the full meaning of natural language ex-
pressions. The necessity of dealing with both types of meaning is illustrated by
means of semantic phenomena like factual and intensional negation, intensional
quantification and cardinalities, or by the meaning of prepositions describing set
relationships, and others. We will utilize the framework of Multilayered Extended
Semantic Networks (MultiNet) to discuss these issues. The MultiNet formalism
is successfully used in various NLP applications. Its explicit modeling of inten-
sional and preextensional layers offers an explanation of the interplay of inten-
sion and extension of conceptual entities in the overall process of constituting the
meaning representations of natural language expressions.
1 Introduction
At the latest since Carnap, it is well known that the full meaning of a concept is con-
stituted by two aspects, its intension and its extension [1]. The first part comprises the
embedding of a concept in the world of concepts as a whole, i.e. the totality of all re-
lations to other concepts. The second part establishes the referential meaning of the
concept, i.e. its counterpart in the real or in a possible world. The intension of the con-
cept Napoleon I, for instance, comprises the relations to the concepts France, emperor,
etc., while its extension is a concrete historical person. The concept emperor again is
related to government, autocracy, etc., while its extension is the set of all emperors of
this world. The aim of this paper is to show the necessity to deal with both aspects in a
knowledge representation and to discuss to what degree this can really be done.
Of course, it is impossible to cope with the full extensions of concepts on a com-
puter, since some concepts have an infinite extension (e.g. successor), some have a
fuzzy extension (e.g. hill, large), and some (like extension) arguably cannot be assigned
Helbig H. and Glöckner I. (2007).
The Role of Intensional and Extensional Interpretation in Semantic Representations The Intensional and Preextensional Layers in MultiNet.
In Proceedings of the 4th International Workshop on Natural Language Processing and Cognitive Science, pages 92-105
DOI: 10.5220/0002415900920105
an extension at all. These observations suggest that one should rather incorporate par-
tially described extensions in a KRS
, which represent only typical members or subsets
of the extension of the concept, or only the cardinalities of the corresponding sets. Thus,
we speak of a “preextensional” instead of an “extensional” interpretation. It is postu-
lated that the extensional meaning of a concept has to be modeled in the representational
formalism itself (not outside of it as in logic-oriented KRS with a model-theoretic se-
mantics). The role of intension and extension in the semantic interpretation of linguistic
expressions and even in coreference resolution, is illustrated by the following example:
“(A group of (four men)
found (many gems)
. Six of (them
had been stolen.
The example shows the following: Semantically, there is one group of men, not several
groups (as indicated by [CARD=1]), consisting of four men (indicated by [CARD=4]),
who discovered a rather underspecified set of gems. Nobody would figure out during
understanding of the first sentence how many gems there are (or any other details on the
extension of the concept described by many gems). But, when reading the second sen-
tence, it becomes clear from the partitive construction six of them that the pronoun them
cannot refer to the group of men (since there are only four) but must rather be linked to
the meaning of the phrase many gems, indicated by the index i. Moreover, the preposi-
tion of in the phrase four of them establishes a set inclusion between the extensions of
the conceptual entities denoted by many gems and the stolen objects. It becomes also
clear that the set underlying the intensional meaning of the quantificationally under-
specified phrase many gems must have a cardinality greater than 6. All this has to be
modeled in a full meaning representation (see Sect. 2.1); the semantic representation of
an analogous example is shown in Figure 4.
There are few proposals to deal with this extensional dimension besides the inten-
sional aspect in a KRS, one early example is [2]. Elements of the extensional meaning
of concepts are also present in KL-ONE [3] and its successors, i.e. in several kinds of
Description Logics [4]. Here, we meet them in form of the cardinalities of roles. The
aspect of extensionality which traditionally raised most interest is that of characterizing
the real-world existence or facticity of entities mentioned in a discourse. Apart from
the vast literature on presuppositions, this topic has also been addressed in modal logics
[5] and in the context of knowledge representation [6–9].
In the paper, we discuss these issues from the perspective of Multilayered Extended
Semantic Networks (MultiNet), a KRS designed with a clear distinction of an inten-
sional layer and a preextensional layer in mind. The formalism, extensively docu-
mented in [10], is successfully used in large NLP applications, ranging from question
answering over natural language interfaces to electronic teaching (see Sect. 8). After
introducing the core concepts of MultiNet, we turn to the main topic, discussing sev-
eral phenomena of linguistic relevance whose treatment in a KRS calls for a model-
ing on a (pre)extensional level. We address the distinction of intensional quantification
vs. preextensional cardinality, the discernment of intensional and preextensional nega-
tion, treatment of existential presuppositions and of implicative or factive verbs, the
modeling of counterfactuals, and the modeling of set relationships implicit in partitive
constructions and quantification involving coordinations.
Knowledge Representation System(s)
2 Multilayered Extended Semantic Networks
2.1 The Main Characteristics
In designing a KRS, one should first specify a set of criteria to be satisfied by the en-
visioned knowledge representation. In our context, the most important of these criteria
are: 1) cognitive adequacy which to the very least means that the semantic represen-
tation should be concept-centered in the sense that every conceptual entity has a unique
representative; 2) homogeneity the descriptive means should be suitable for defining
the semantics of lexemes, the semantics of sentences or texts, and the axiomatic appa-
ratus and inference rules of the KRS as well; and 3) stratification it must be possible
to represent the different semantic aspects (like intensional vs. extensional aspects, or
immanent vs. situational aspects of meaning) in different layers of the KRS.
Like other semantic network formalisms, MultiNet represents conceptual entities
by nodes, while relations between concepts are represented as arcs between these nodes
(see Figure 4). However, MultiNet has several additional features:
1. The nodes of the SN are classified according to a predefined conceptual ontology,
i.e. by a sort assignment.
2. The nodes have a rich inner structure, i.e. the relevant classificatory dimensions of
conceptual entities are expressed by values of ‘layer attributes’ of each node.
3. The formalism commits to a fixed set of relations in order to provide a stable basis
for axiomatization and a platform for long-term projects like lexicon development.
4. The distinction of an intensional layer and a preextensional layer has already been
mentioned. Each layer comes with its own relations and functions and its own layer
attributes which refine the description of a node at the considered level.
5. We discern categorical knowledge about a concept (e.g. for the concept car: A car
has a motor”), prototypical knowledge about the concept which only holds by de-
fault (“A car typically has an airbag”) and finally so-called situational knowledge,
i.e. contingent knowledge about a concept which is irrelevant with respect to the
concept’s core meaning. For example, the introduction of a specific car in the sen-
tence Paul bought a car is situational with respect to the generic concept car and
has no effect on the meaning of car in general.
6. Axiomatic rules (meaning postulates) are employed for interrelating the meanings
of natural language expressions described in the lexicon. They also define the basic
relations and functions, which can be viewed as nodes at a metalevel.
For a complete documentation of the expressional means of MultiNet see [10].
2.2 Sorts and Features of Concepts
In MultiNet, every node is assigned a sort from a fixed sort hierarchy whose upper part
is shown in Figure 1. The primary purpose of these sorts is that of defining the signatures
(i.e. the domains and value restrictions) of the relations and functions provided by the
formalism. The restrictions imposed by the sorts on the use of relations and functions
or on the valency frames of verbs, nouns, and adjectives are automatically enforced by
the workbenches for the knowledge engineer [11] and for the computer lexicographer
Fig. 1. The Upper Part of the Hierarchy of MultiNet Sorts .
[12], which use MultiNet for representing knowledge and describing lexical semantics.
The sorts are crucial for the formal definition of the representational means, but also
an important source of information for disambiguation in the semantic interpretation
of linguistic constructs (e.g. prepositional phrases). However, the sorts alone are too
coarse to specify arbitrary selectional restrictions. For that one needs additional seman-
tic features (e.g. being animated or being an artifact) also offered by MultiNet [12].
2.3 Relations and Functions of MultiNet
The formal devices for interlinking the conceptual nodes of a semantic network are
relations and functions. MultiNet provides a fixed set of about 140 semantic relations
and functions which can roughly be classified into two main groups.
Firstly, there are relations and functions of the intensional level. They are used to
describe the inner structure of conceptual objects and situations as well as their rela-
tionships to other entities. Typical descriptions of objects involve the characterization
of their material structure (by the part-whole-relationship PARS), of their material ori-
gin (described by the ORIGM relation), or of their properties (using the PROP rela-
tion). Situational concepts like events or states, on the other hand, are typically defined
by specifying the participants involved in the situation and the semantic roles which
characterize the relationship between a situation and its participants. Typical examples
are deep case relations like AGT (agent), EXP (experiencer), or OBJ (neutral object).
Additionally, situations are characterized by their spatio-temporal embedding (e.g. lo-
cation LOC or temporal specification TEMP). See Table 1 for a brief description of the
relations on the intensional level referenced in this paper.
Second, there are also relations and functions of the preextensional level (see Table
2). They offer the descriptive means needed for modeling sets and other extensional
Table 1. Typical relations of the intensional layer. The notation ¨o requires an entity of sort o with
[ETYPE>0] (i.e. a plurality) while o or si require generic concepts with [GENER=ge].
Relation Signature Short Characteristics
AFF si × [o si] Affected object
AGT si × co Agent
ANTE [sit]×[si t] Temporal successorship
ASSOC ent × ent Association
ATTCH o × o Attachment of objects to objects
AVRT dy × o Aversion/Turning away
CAUS si × si Causality relation
COND si × si Conditional relation
EXP si × o Experiencer
HSIT si × si Composition of situations
LOC co × l Location of an object
MCONT si × [si o] Mental or informational content
MODL si × md Modal restriction
OBJ si × [o si] Neutral object
ORIGM co × co Relation of material origin
ORNT si × o Orientation towards something
PARS co × co Part-whole relation for concrete objects
PRED ¨o × o Specification of a plurality
POSS o × o Possession
PROP o × p Relation between object and property
SUB o ×
o Conceptual subordination (for objects)
SUBS si × si Conceptual subordination (for situations)
SUBST [o×o][si×si] Substitution/Replacement
TEMP si × [si t] Relation of temporal containment
representatives. Some rationale for introducing these constructs has already been given
in the introduction and the remainder of the paper will focus on these constructions.
Relations and functions are characterized by implicational axioms familiar from
first-order predicate logic. We discern two types of axioms: 1) B-axioms which interre-
late natural language concepts; and 2) R-axioms which connect relations and functions
of the formalism without reference to any lexicalized concept. The connection between
the concepts kill and die is a typical case of a B-axiom:
SUBS kill) (sv
AFF o) sv
SUBS die) (sv
AFF o)]
On the other hand, the relationship between causality and temporal order can be ex-
pressed by an R-axiom (s
) ¬(s
). For an overview of the dif-
ferent types of axioms used in MultiNet see [13].
2.4 Stratification of the Networks
The MultiNet formalism was designed such that qualitatively different aspects of mean-
ing will not be pressed into one flat structure. To this end, the nodes and arcs of MultiNet
are embedded in a multidimensional space of so-called layer attributes. The layer speci-
fications for arcs are defined by a K-TYPE attribute which assigns one of the knowledge
Table 2. Relations of preextensional layer. p(e)
denotes extensions of entities with [ETYPE=n].
Relation Signature Short Characteristics
*DIFF p(e)
Set difference (of extensions)
DPND p(e) × p(e) Dependency (of extensions)
ELMT p(e)
× p(e)
Membership (of extensions)
EXT ent × p(e) Extension
SUBM p(e)
× p(e)
Subsumption (inclusion of extensions)
*UNION p(e)
Set-theoretic union (of extensions)
types mentioned in point 5, Section 2.1 to each argument of the edge. For nodes, the
layer specification comprises a whole set of so-called layer attributes (see Figure 2).
The following layer attributes describe a conceptual entity at the intensional level:
GENER: The degree of generality indicates whether a conceptual entity is generic
(value: ge) or specific (value: sp). Example: A lion [GENER=ge] is dangerous.
vs. (This lion) [GENER=sp] is dangerous.
QUANT: The intensional quantification represents the quantitative aspect of a con-
ceptual entity, i.e. whether it is a singleton (value: one) or a multitude (values: two,
several, many, all etc). Within the set of values characterizing multitudes, we dis-
cern between fuzzy quantifiers like several, many, most with value [QUANT=fquant]
and non-fuzzy quantifiers like two, three, all with value [QUANT=nfquant]. Exam-
ple: (Two dogs) [QUANT=nfquant, CARD=2] barked.
A bundle of four additional layer features is concerned with the extensional aspect:
ETYPE: This attribute characterizes the type of extensionality of an entity with
values: nil no extension (e.g. intension), 0 individual that is not a set (e.g.
Napoleon I ), 1 entity with a set of elements from type [ETYPE=0] as extension
(e.g. hmany emperorsi, hthe dynastyi), 2 entity with a set of elements from type
[ETYPE=1] as extension (e.g. hmany dynastiesi), etc.
FACT: The facticity attribute, to be discussed in greater detail in Section 5, discerns
actually existing objects and situations [FACT=real] from non-existing objects or
situations [FACT=nonreal] and hypothetically assumed objects or situations which
are labeled [FACT=hypo]. Example: (The girl) [FACT=real] dreamed that (she
was crying) [FACT=hypo].
REFER: This attribute specifies the determination of reference, i.e. whether there
is a determined object of reference (value: det) or not (value: indet). The REFER
attribute is especially important for guiding coreference resolution in a discourse
processing or ‘assimilation’ stage which constructs an integral representation of a
whole text from the representations of individual sentences [14].
Example: (The boy) [REFER=det] bought (a toy) [REFER=indet].
CARD: We have already met this cardinality attribute in the introduction. As op-
posed to the intensional quantification expressed by QUANT, the CARD attribute
specifies the actual cardinality of the extension of a node.
VARIA: The variability indicates whether an object is conceptually varying (value:
var) i.e. it is a ‘parameterized object’ or if it is a fixed constant (value: con). Ex-
ample: (The teacher) [VARIA=con] looked at (every homework) [VARIA=var].
Fig. 2. The multidimensional space of layer attributes.
The idea of layers is motivated by an analogy to the mathematics of an n-dimensional
space. If one fixes a value along one of the axes of an n-dimensional coordinate system,
one gets a (n 1)-dimensional hyperplane. In the same way, if one is fixing one value
of a layer attribute (let us assume [GENER=ge] or [FACT=hypo]), then one gets a
special layer or stratum (in this case the layer of all generic concepts or the layer of
all hypothetical entities, respectively). The interplay of these layer attributes becomes
visible in the representations of the following two sentences (see Figure 3):
(E1) All students own bicycles. (E2) Every student owns a bicycle.
In Figure 3, the first statement is represented by the POSS arc labeled with (1) and
the second by the POSS arc labeled with (2). As shown in the figure, the extension of
node n
(representing the concept hevery studenti) is a varying individual p
within the
set p
of all students. The abbreviations hall i and heveryi stand for a whole bundle of
layer attributes and their values shown in Table 3. [ETYPE=+k] in this table means that
the extension type of a concept characterized with every/all is incremented by k com-
pared to the ETYPE of the basic concept found in the lexicon. The counterpart p
at the
preextensional level of node n
at the intensional level (a varying, parameterized, and
individual bicycle) is connected by the dependency relation DPND with the extensional
representative p
of n
. This, together with the layer information of n
, gives a special
reading to sentence (E2) saying that every single student owns exactly one bicycle de-
Fig. 3. Sample network with intensional and preextensional layers.
Table 3. Detail from the description of quantificators by means of layer attributes.
hall i all card con det +1
heveryi one 1 var det +0
pending on this student. Note that according to Table 3, n
has a non-varying collection
with determined reference as its extension, while n
and n
have varying extensions
with determined and indetermined references, respectively.
3 Intensional Quantification and Preextensional Cardinality
The interplay of the intensional and extensional aspects of meaning becomes visible in
the linguistic phenomenon of intensional quantification (carried by quantificators
several”, most”) and their extensional counterparts, the cardinalities of sets.
For the semantic representation of expressions containing these quantificators the
combination between the intensional and preextensional layer is needed (see motivating
example in introduction). Here we consider a similar case which demonstrates how the
example sentences are analyzed on the intensional and preextensional levels:
(S1) Peter sent his mother many letters. (Node sv
(S2) Fife of them were lost. (Arc sv
The MultiNet represented in Figure 4 reveals that sentence (S1) is indeed represented
on the intensional level only. The partitive construction in the second sentence, however,
requires a shift to the preextensional level. The representation of (S2) on the right-hand
side of the figure asserts that there is a conceptual node on the intensional level which
represents a plurality of lost letters. The extension of this node has cardinality 5. Since
the partitive five of them rather than all of them was used, we know that a proper
subset relationship holds between the set of lost letters and the letters Peter had sent to
his mother. We conclude that the set of sent letters has indeed more than 5 elements,
which conforms to the intuitive expectations.
To distinguish these constructs from the existential quantifier and the universal quantifier
in logics, we deliberately coined the term quantificator”.
Fig. 4. Intensional quantificators vs. cardinalities on the preextensional level.
4 Different Types of Negation
The proper modeling of negation in a KRS is a difficult task, since the usual negation
of first-order logic does not cover all aspects of linguistic negation. Let us consider the
following example:
(N1) The concert was not unpleasant.
If we assume a constant c for the concrete concert and a unary predicate PLEASANT
for the meaning of the adjective pleasant”, the typical way of expressing the meaning
of the above proposition in FOL would be: ¬¬PLEASANT(c), which is equivalent to
PLEASANT(c). However, PLEASANT(c) is clearly not the meaning of (N1), which
demonstrates that the law of double negation does not hold for this kind of negated
gradable properties. Notice that a degree-based modeling along the lines of [15] might
solve this problem on the theoretical side but only at the price of a very complicated
representation which is hardly suited for knowledge processing.
MultiNet offers two types of negation to deal with negated sentences. An intensional
negation of a state of affairs sv is expressed by a modal restriction (sv MODL *NON)
which corresponds to the negation contained in the sentence itself. But there is also
the preextensional negation of sv expressed by the layer attribute [FACT(sv)=nonreal]
saying that sv does not hold in reality. To see the rationale for discerning these two
kinds of negation, consider the problem of interpreting subordinated sentences intro-
duced by the conjunction instead of in the case that the subordinated sentence again
involves negation. An example is Instead of taking nothing from the table, the guest ate
everything up which contains an intensional negation within the subordinated clause
by the negator nothing”. This negation expressed by (sv
MODL *NON) in Figure 5
is the basis for answering a question aiming at the expectations of the dialogue partners
(“What did you expect? That he took nothing!”) However the conjunction instead
of introduces a second negation as a presupposition, which has to be represented by
[FACT=nonreal] with sv
, stating that the state of affairs which had been expected does
not hold in reality. If we mingled these two types of negation (intensional vs. preexten-
Fig. 5. The two types of negation in subordinated sentences.
sional) or even deleted both of them on the basis of a wrongly applied law of double
negation we could not answer the question asking for an expectation. However, the two
types of negation may obviously cancel out under certain circumstances. This would
be the case for questions with a purely factual character (“Did he take something from
the table? Answer: Yes!”). In order to account for these effects, application of the
law of double negation (combining factual or preextensional negation with intensional
negation) should depend on the type of the question.
5 Existential Presuppositions and Counterfactuals
Another aspect of reference that must be captured by a KRS is concerned with the fac-
ticity of the entities of interest. In natural language we can discuss the existence or non-
existence of objects of a certain kind like ghosts, aliens or black holes. It is also pos-
sible to talk about situations or events regardless of facticity. Consequently, [6, 7] em-
phasize the importance of modeling non-existing objects for knowledge representation.
In predicate logic, however, there is an inherent existence assumption for all individuals
(i.e. individual constants) because the model-theoretic semantics demands that all con-
stants denote in the universe. This is why we introduced the attribute FACT to express
the facticity of a considered entity. As opposed to certain dialects of modal predicate
logic which use an existence predicate to tell existing objects from non-existing ones
[5], we discern three possible cases, viz the real, nonreal and hypo as mentioned above.
The third value hypo is needed, for instance, to describe states of affairs in conditionals
or in opaque contexts. [8] argues that seven ways of existing should be distinguished,
which could easily be accomplished by extending the set of facticity values.
Table 4 shows some basic axioms related to facticity, which also express some of
the existential presuppositions made while uttering a factual statement. Axiom (a) states
that the agent or experiencer of a factual event/state must really exist. For example, Peter
can only know something if he is a real person. The same can also be said about LOC
and TEMP, i.e. a real situation takes place at a real location and has a temporal extent in
the real world. An exception to Axiom (a) is the MCONT role which expresses mental
content or modal embedding. Here, somebody’s belief in the existence of the Yeti is
classified hypo by axiom (b). However, as shown by (c), there are special cases (e.g.
knowing something) which license the conclusion that the second argument of MCONT
Table 4. Selected axioms related to facticity. Axioms marked by must be considered defaults.
(a) (x R x
) [FACT(x)=real] [FACT(x
where R {AFF, AGT, EXP, OBJ, . . . } (valid for most argument roles)
(x MCONT x
) [FACT(x
(c) (s SUBS know) (s MCONT s
) [FACT(s)=real] [FACT(s
(d) (x R x
) [FACT(x)=real] [FACT(x
where R {PARS, ELMT, HSIT} (for all meronymy relations)
(e) (s COND s
) [FACT(s)=hypo] [FACT(s
is factual as well. For that reason (b) was marked as default knowledge. Axiom (d) states
that a real aggregate can only be composed of real parts. Finally, Axiom (e) expresses
the observation that if-then-relationships involve hypothetical situations. Consider the
following example: If John returns late, he will be tired. In this case, there is obviously
no commitment as to the facticity of premise and conclusion, which are thus tagged
It should be pointed out that the FACT attribute allows us to model all types of
implicative verbs, factive verbs and counterfactive verbs as listed in the classification of
[16]. We will pick two examples to demonstrate how to accomplish this.
The verb forget to is a so-called two-way implicative whose facticity pattern can
be described by the following two axioms:
(s SUBS hforget toi) (s MCONT m) [FACT(s)=real] [FACT(m)=nonreal]
(s SUBS hforget toi) (s MCONT m) [FACT(s)=nonreal] [FACT(m)=real] .
In other words, if Ed forgets to close the door, then Ed does not close the door; and if
Ed does not forget to close the door, then he actually closes the door.
Our second example is forget that ”, a factive verb with a positive existential pre-
supposition. Here we only need one additional axiom to describe the facticity pattern:
(s SUBS hforget thati) (s OBJ m) [FACT(s)=nonreal] [FACT(m)=real] .
Thus, if Ed does not forget that he closed the door, then Ed closed the door. Due to the
use of the OBJ role, the above axiom (a) already captures the opposite case, i.e. if Ed
forgets that he closed the door, we may conclude that Ed closed the door.
In practice, the entailments are expressed by axiom schemes for all verbs of the
considered type. In this way, all facticity patterns of [16] can be captured.
Counterfactuals are among the most prominent semantic phenomena where the
combination of intensional modality and preextensional facticity is needed to repre-
sent the full meaning. Figure 6 shows the proposed representation of the sentence: If
the boy had come yesterday, he would have got the toy”. Our analysis of counterfactuals
introduces two pairs of situations which correspond to the upper and lower half of the
depicted MultiNet. There are two hypothetical situations ˜sv
and ˜sv
linked by a con-
ditional, expressing If the boy came yesterday, he got the toy”. Moreover there is a pair
of negated factive situations with a causal relationship which roughly express The boy
did not get the toy because he did not come yesterday. These negated factive situations
and their causal link are implicit in the counterfactual statement.
Fig. 6. Representation of a counterfactual.
6 The Role of Extension Types in Semantic Representations
The extension type of concepts, introduced in Sect. 2.4 and represented by the layer
attribute ETYPE, is not only important for defining the signatures of relations and
functions at the preextensional level (cf. Table 2). Combined with other expressional
means, it also explains the difference between quantified concepts as all children
with [ETYPE=1] and every child with [ETYPE=0] (cf. Figure 3). While expressions
of the first type, when used in a sentence like All children bought a gift”, allow for a
cumulative and a distributive reading (and, thus, need background knowledge for a fur-
ther interpretation), this is not the case for expressions with [ETYPE=0], as in Every
child bought a gift”. The latter allows only for a distributive reading.
An effect seldom properly taken into account is the influence of the extension type
on the specification of lexical meanings, especially in connection with the selectional
restrictions of verbs. Concepts underlying verbs like die out or verbal constructs like
be at odds with each other can only be used either in connection with concepts of
[ETYPE1] or possibly with generic concepts. Examples: (The Miller clan)
died out. (The Blue Whale)
has almost died out.
7 Partitive and Coordinating Quantification
The last phenomenon to be discussed is the semantic interpretation of partitive and co-
ordinating quantifiers whose semantic representation requires the expressional means
of the preextensional layer. Partitive quantifications are typically expressed by prepo-
sitions like beside/except”, apart from”, without”, and some uses of the preposition
of ”. However, also coordinations building pluralities like Some teachers and all stu-
dents must refer to operations on sets which belong to the preextensional level. The
following example comprises typical effects in one sentence (N2):
Many students and all teachers of the school except the director cleaned the room.
Though such examples are routinely treated in the Theory of Generalized Quantifiers
[17], they are not visible in state-of-the art KRS. MultiNet, however, offers a corre-
sponding representation shown in Figure 7: To represent the meaning of sentence (N2)
and especially of the phrase Many students and all teachers of the school except the
Fig. 7. The construction of pluralities by means of prepositions.
director ”, a concept c at the intensional level and its representative p(c) at the preexten-
sional level have to be created, which are related by (c EXT p(c)). For specifying p(c),
at first a set difference is constructed using *DIFF to capture the meaning of except”.
After that the union of the result with the set of many students has to be built using the
function *UNION to capture the effect of and on the coordinating quantification.
8 Conclusion
We have argued that a comprehensive meaning representation for natural language ex-
pressions must combine the intensional and extensional aspects of semantic descrip-
tion. Since the full extension of a natural language concept is typically out of reach,
a preextensional layer was introduced which allows to deal with partially described
extensions or ‘preextensions’. Using Multilayered Extended Semantic Networks for se-
mantic representation, we discussed several linguistic phenomena whose interpretation
arguably involves the extensional aspect. We then explained how to handle theses cases
by combining the intensional and preextensional descriptive means of the framework.
Obviously there is specialized research into most of these issues (like handling par-
titive and coordinating quantifications or modeling facticity). However, none of these
approaches provides an integrated solution which has made its way into a working KRS.
The MultiNet approach, by contrast, has been used as a meaning representation formal-
ism in several projects (e.g. VirWiss [18]). It is also the semantic interlingua for repre-
senting user queries in natural language interfaces to internet information providers and
to local databases [19, 20]. Corresponding transformation modules exist which translate
MultiNet representations of questions into various target formats like Z39.50 and SQL.
The inference system of MultiNet and its axiom system are used in question answer-
ing (QA) systems [21, 22], in the natural language interfaces mentioned above, and in
the virtual electronic laboratory VILAB [23]. The use of MultiNet in the QA systems
InSicht and IRSAW is continually evaluated in the CLEF QA track (see [21, 22]) as
well as in the answer-validating system MAVE (AVE-track of CLEF [24]). In all CLEF
competitions from 2004 to 2006 these systems ranked among the best three for German.
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