Notes.
Objects [o]: There are two types of objects, concrete objects, which can be sensually perceived, abstract objects, for which this is not true.
Concrete objects [co]: Among these we distinguish substances and discrete objects (things).
Substances [s]: These have a quasi-continuous extension; they are divisible but not countable.
Examples: milk, honey, iron, 300 g uranium .
Discrete objects [d]: These are countable but not divisible.
Examples: house, cherries, the Leaning Tower of Pisa
Abstract objects [ab]: They are products of human reasoning (of an abstracting thought process, to be exact). We distinguish between the following:
Situational objects [abs]: They represent situations elevated by abstraction to the cognitive status of objects. They are divided into
Abstractions from dynamic situations [ad] – race, robbery, integration, knowledge acquisition , movement, . . . Abstractions from static situations [as] – calmness, equilibrium, awareness, sleep, illness, . . .
Attributes [at]: Here, we have to distinguish between measurable, operationally definable attributes like height, weight, average, . . . (sort[oa]), and attributes for which this does not hold, like form, character
trait , flexibility, . . . (sort [na]).
Relationships [re]: causality, similarity, difference, relationship, synonymy, contradiction, . . .
Ideal objects [io]: religion, mercy, justice, criterion, category, . . . Abstract temporal objects [ta]: Renaissance, Middle Ages, Easter, holidays, Paleozoic Era , . . . Modalities [mo]: probability, necessity, intention, permission, . . .
Type of Extensionality (Attribute ETYPE)
In the same way as sorts and features are used in signatures to specify at the intensional level which MultiNet relations and functions can in principle describe certain relationships between conceptual representatives, a classification
of nodes is needed to achieve the analogue at the preextensional level. Thus, the element relation ELMT can hold only between an individual extensional which is not a set and a proper set, or between a set and a family of sets, and so on (see
the definition of the relation ELMT). Similarly, a subset relation can hold only between two sets of the same type (see the definition of the relation SUBM).
To formulate these regularities, the attribute type of extensionality ( ETYPE ) is used whose values are summarily described in the following ([ETYPE=nil] characterizes concepts like intention, religiosity, etc., which
have no extension):
Means for Expressing Classification and Stratification
0 – Representative of an elementary extensional which is itself not a set.
Examples: the extensionals of the house, Max, this school, . . .
1 – Set of elements of type 0
Examples: the extensionals of several children, three cars, the crew, a family, . . .
2 – Set of elements of type 1
Examples: the extensionals of three crews, many organizations, . . .
3 – Set of elements of type 2
Example: the extensional of two umbrella organizations, where umbrella organization is a concept already denoting a group of organizations (characterized by type 2).
It must be remarked with regard to cardinalities that the corresponding attribute CARD is not applicable to extensionals of type 0. For an extensional E of type n, the cardinality is the number of the elements of E with type (n-1).
17.2.4 Variability (Attribute VARIA)
Some differences in the readings of natural language expressions have to be represented by the distinction in whether a node at the preextensional level is considered a variable or a constant.
This distinction is specified by means of the attribute variability (or VARIA). Its values have the following meanings:
[VARIA = con] – The node represents a fixed element of the preextensional level that does not change depending on the variation of other conceptual representatives.
[VARIA = var] – The node represents an element of the preextensional level that has to be considered a variable (a so-called parameterized entity).
Such a node represents either every single element of a set (it runs, so to speak, over all elements of the set analogously to the interpretation of a universally quantified variable in logic), or the node represents an element of the set that
changes depending on the extensional interpretation of another concept (analogously to an existentially quantified variable in logic whose interpretation depends on that of a universally quantified variable).
[VARIA = varia] – In the lexicon, generic concepts obtain the value[VARIA = varia] as their primary specification (underspecification of the attribute). This value is preserved with a pure plural description of a generic concept
(line 7 in Table 17.2),
but is instantiated to [VARIA = con] when describing a prototypical element of the extension of a generic concept
(line 8 in Table 17.2).11
To illustrate the above definitions we consider the following sentences
(Figure 17.5 shows the corresponding semantic representations):
“There is a book [VARIA = con], which has been read by every student. [VARIA = var] ”
The extensional of the node k1 = a book in the representation of Sentence (17.16) is a fixed representative with [VARIA = con] which is independent of the student doing the reading.
“Every student [VARIA = var] bought a new suit.” [VARIA = var]
In contrast, the extensional of the node k2= every student is a parameterized individual running over the set of all students [VARIA = var], albeit independent of other nodes.
“Students [VARIA = varia] read books.” [VARIA = varia]
Compared to that, the extensional of the node k3 = a new suit depends on the student buying the suit. In addition to the value of variability, this dependence is expressed by the nonsymmetric relation DPND at the preextensional level of MultiNet.
Since every student buys another suit, the extensional of this concept (node k3 in Fig. 17.5) bears the attribute value [VARIA = var] and is connected by the DPND relation to the extensional of node k2 representing every single student.
17.2 Layers 425
To complete the illustration, the prototypical extensionals belonging to the generic concepts book, student, and suit are also represented in Fig. 17.5.
These nodes (like the extensionals of the nodes k1 , k2 , and k3 ) are elements of the set of all books, all students, or all suits, respectively. In contrast to the nodes k1 , k2 , and k3 , however, they bear the attribute value [VARIA = varia].
17.2.5 Facticity (Attribute FACT)
In natural language, one can explicitly or implicitly refer to the truth of states of affairs or to the existence of objects and thus also to the extensional interpretation of concepts or states of affairs in the philosophical sense. Since the content of a sentence may directly or indirectly refer to the real world or to possible worlds, this relationship must be taken into account in the knowledge representation itself (not outside of it, but at the preextensional level). For this end, a further attribute, the facticity (abbreviation FACT), has been introduced.
In the area of conceptual objects, existential statements like there is a(n) ,there is possibly a(n) , there is no , etc. require representational means such as those provided by the facticity attribute of MultiNet. Also the state of our world knowledge demands expressional means to distinguish objects by the information about whether they really exist ( Peter’s car , the Eiffel Tower , New York , . . . ), whether they are hypothetically assumed (quarks, black holes , . . . ), or whether they are nonexisting imaginary objects (yetis, unicorns, . . . ); this can be expressed with the facticity attribute by selecting the following values: [FACT = real], [FACT = hypo], and [FACT = nonreal], respectively (the last is also written as [FACT = non]).12
The facticity attribute is also relevant to the treatment of existential presuppositions (implicit existential statements).13 To elucidate, the following example sentences are used
(17.19) “The boy has got a new bicycle.”
(17.20) “The tourist claimed that he had seen a UFO.”
The first sentence contains implicitly the statements (i.e. they can be derived) that the concepts the boy as well as a new bicycle correspond to existing
12
We do not comment here on the existence of yetis. It is only shown in the examples that if yetis are taken as nonexistent objects or quarks as hypothetical ones, then this has to be represented in a MultiNet knowledge base by [FACT = non] or [FACT = hypo], respectively. The use of only three values for the attribute FACT, where distinctions are made between a real, a possible, and a nonexisting world, is of course a simplification. In general, this attribute could be used to distinguish and to index arbitrarily many possible worlds.
13
A presupposition of a sentence S is a statement not explicitly expressed in S but following from S as well as from the negation of S.
426 17. Means for Expressing Classification and Stratification objects.
Both concepts obtain the values [FACT = real] in a MultiNet representation. Similar considerations apply to the concept the tourist in the second sentence. The situation is entirely different for the concept a UFO , however, which is embedded in a modal context “the tourist claimed” (a so-called opaque context). From Sentence (17.20) one cannot conclude without further
information that the UFO really exists (the tourist may lie or err). For this reason, this concept is assigned the attribute value [FACT = hypo], provided there is no additional knowledge source justifying the specification [FACT = non]
or [FACT = real]. The attribute values real, hypo, and nonreal (abbreviated non) correspond respectively to the truth values true, unknown, and false of a three-valued logic. They characterize not only the existence or nonexistence
of objects, but also the status of situations in general.14
Analogously to the existence of objects, natural language sentences also convey information about the validity or nonvalidity of arbitrary states of affairs (“it holds”, “it does not hold”, etc.). There are also means to express directly or indirectly that a situation is only imagined, only hypothetically assumed, or merely alleged, which suggests to the hearer/reader that the validity of the corresponding statement is at least uncertain (“it is possibly the case that”, “it is assumed that”, etc.). This information must also be reflected in the meaning representation of the corresponding sentences, thus requiring a
characteristic like the attribute of facticity.
The attribute FACT is also important for the semantic representation of whole situations, such as those described by Sentences (17.19) and (17.20).
While the representatives of the main clauses have to be characterized by [FACT = real] in both cases15 , the subordinate clause of Sentence (17.20), “the tourist had seen a UFO”, must be assigned the attribute value [FACT = hypo].
This is justified by the observation that the content of an indirect propositional sentence generally has to be assigned an uncertain truth value in the absence of further information (cf. the relation MCONT). The semantic representation of
conditional sentences or counterfactuals, which is also important for automatic language processing, can be adequately described only by explicitly including the attribute of facticity (see Sect. 11.2.3 and the relation COND).
Strictly speaking, the attribute FACT should be related not only to the real world and to that what is classified in this world as being valid/true, hypotheti-
14
Although there seems to be a difference between the layer specification [FACT = hypo] and
the truth value “unknown” from an epistemological point of view, the two characterizations
are equivalent from the perspective of a language game. Thus, if we ask for the truth of a state
of affairs whose specification is used to describe the premise of a condition (characterized
by [FACT = hypo] in MultiNet), then the proper answer should be UNKNOWN.
15
At least if one assumes that the speaker is telling the truth.
17.2 Layers 427
cally assumed, or invalid/not true following the common knowledge about the general state of affairs (at least for a certain moment). In a more general approach, one should rather specify with each fact or conceptual object in what
world (in the real world or in the mental worlds of speakers A1 , . . . , An ) this fact or this conceptual object is assigned a certain degree of facticity (according to the conception of possible worlds in modal logic [146]). For such a
fine-differentiation, the relation MCONT is provided in MultiNet, permittingthe specification of different epistemic contexts.