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4

Relationships with other Formalisms

Ulrike Sattler

Diego Calvanese

Ralf Molitor

Abstract

In this chapter, we are concerned with the relationship between Description Log-

ics and other formalisms, regardless of whether they were designed for knowledge

representation issues or not. We concentrated on those representation formalisms

[

1973

since we believe that their relationship with Description Logics is too weak.

In artificial intelligence (AI), various “non-logical” knowledge representation for-

malisms were developed, motivated by the belief that classical logic is inadequate

for knowledge representation in AI applications. This belief was mainly based upon

cognitive experiments carried out with human beings and the wish to have repre-

sentational formalisms that are close to the representations in human brains. In this

4.1.1 Semantic networks

Semantic networks originate in Quillian’s

[

Quillian, 1967

]

,

a graphical formalism designed to represent “word concepts” in a definitorial way,

i.e., similar to the one that can be found in an encyclopedia definition. This for-

malism is based on labelled graphs with different kinds of edges and nodes. Besides

others, Quillian’s networks allow for subclass/superclass edges, for and- and or

Brachman,

1979

generic nodes

class/superclass edges and property edges. Using subclass/superclass links, concepts

can be organised in a specialisation hierarchy. Using property edges, properties can

be associated to concepts, that is, to the individuals belonging to the concept the

properties are associated with. Figure 4.1 contains a hierarchy of animals, birds,

fishes, etc. Interestingly, the cognitive adequacy of this approach was proven em-

birds are equipped with skin because animals are equipped with skin, and birds

Fig. 4.1. A semantic network describing animals.

144 U. Sattler, D. Calvanese, R. Molitor

inherit this property because of the subclass/superclass edge between birds and

animals. In contrast, although ostriches are birds, they do not inherit the property

“can fly” from birds because this property is “modified” for ostriches.

]

, the above translation is not always intended. Sub-

class/superclass edges can also be read as

primitive

concept definitions, that is,

they impose only necessary properties but not sufficient ones. Hence the above

translation might better be

Due to the lack of a precise semantics, there are even more readings of subclass/su-

is the “right” one (see also Chapter 6).

As a consequence of this ambiguity, new formalisms mainly evolved along two

lines: (1) To capture inheritance by default, various non-monotonic inheritance sys-

tems, respectively various ways of reasoning in non-monotonic inheritance systems,

were investigated

[

Touretzky et al.

, 1987; 1991; Selman and Levesque, 1993

]

. (2) To

capture the monotonic aspects of semantic networks, a new graphical formalism,

structured inheritance networks

in conflicting situations. Brachman and Schmolze

]

argue that Kl-One does

not allow for cancellation or inheritance by default because such mechanisms would

make taxonomies meaningless. Indeed, all properties of a given concept could be

cancelled, so that it would fit everywhere in the taxonomy. Their proposition is to

make a strict separation of default assertions and conceptual descriptions.

Brachman and Schmolze

[

1985

]

, b esides pointing out the computation of the

Later

[

Levesque and Brachman, 1987

]

was provided with a well-defined

“Tarski-style” semantics which fixed the precise meaning of its graphical constructs

and led to the definition of the first Description Logic

Levesque and Brachman,

1987

146 U. Sattler, D. Calvanese, R. Molitor

based knowledge base can be translated into an

Calvanese et al.,

1994

Since there is no standard syntax for frame systems, we have chosen to use

basically the notation adopted by Fikes and Kehler

, which is used also in the

system.

a university. Cardinality restrictions are used to impose a minimum and maximum

number of students that may be enrolled in a course, and to express that each

course is taught by exactly one individual. The frame AdvCourse

which enroll only graduate students, i.e., students who already have a degree. Basic

courses, on the other hand, may be taught only by professors.

Hayes

[

]

Not only the translation but also the example are by Calvanese et al.

1994

.

is a trademark of Intellicorp. Note that a Kee user does not directly specify her knowledge base in

this notation, but is allowed to define frames interactively via the graphical system interface.