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Concepts, Attributes, and Arbitrary Relations
Some Linguistic and Ontological Criteria
for Structuring Knowledge Bases
Nicola Guarino
Italian National Research Council,
Institute for Systems Dynamics and Bioengineering (LADSEB-CNR),
Corso Stati Uniti 4, I-35020 Padova, Italy
phone: +39 49 8295751, fax: +39 49 8295649, email: guarino@ladseb.pd.cnr.it
ABSTRACT
There is a subtle risk of ambiguity in the choice between concepts and roles forced by
current KL-ONE-like languages, since many roles may be concepts as well. In this paper we
explore the ontological foundations of the role/concept relationship, and analyze its implications
on the practice of knowledge engineering. We criticize the current interpretation of KL-ONE
roles as arbitrary relations, which vanishes their original meaning and makes them identical to
slots. We suggest to call attributes those concepts which actually act as conceptual components,
and propose a formal semantics which binds these concepts to their corresponding relations.
Keywords: knowledge representation, terminological logics, knowledge engineering,
knowledge acquisition, formal ontology, KL-ONE
Final Draft
To appear on Data and Knowledge Engineering 8 (1992)
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Concepts, Attributes, and Arbitrary Relations
Some Linguistic and Ontological Criteria
for Structuring Knowledge Bases
Nicola Guarino
Italian National Research Council,
Institute for Systems Dynamics and Bioengineering (LADSEB-CNR),
Corso Stati Uniti 4, I-35020 Padova, Italy
1 Introduction
In his seminal paper "On the epistemological status of semantic networks" Ron Brachman
gave the following definition of a role [4]:
The roles represent the various kinds of attributes, parts, etc, that things in the world are considered to
“have”. These include, for example, such things as parts (e.g., fingers of a hand), inherent attributes of
objects and substances (e.g. color), arguments of functions (e.g. multiplier and multiplicand of a
multiplication), and “cases” of verbs in sentences (e.g. “agent”). Any generalized attribute of this sort
has two important pieces (1) the particular entity that becomes the value for the attribute in an instance
of the Concept, and (2) the functional role which that entity fills in the conceptual complex. A Role is a
formal entity that captures both of these aspects in a structured way, by packaging up information about
both the role filler and the functional role itself.
Some years later, this definition changed slightly ([6], our italics):
(...) the Role is the primary component of a Concept. A Role acts like a generalized attribute
description, representing potential relationships between individuals of the type denoted by the Concept
and other individuals. In other words, Roles are the KL-ONE equivalent of two-place predicates.
Indeed, in current KL-ONE-style languages like CLASSIC [2,5], LOOM [15], BACK [17]
the semantics of a role is that of an arbitrary binary relation. John Sowa, however, introduces
the notion of role in a different context [21]:
Subtypes of ENTITY are of two kinds: natural types, which have no required set of linguistic
associations; and role types, which are subtypes of natural types in some particular pattern of
relationships. PERSON, for example, is a natural type, and TEACHER is a subtype of PERSON in the
role of teaching.
The difference is basically in the fact that a role, for Sowa, captures a particular pattern of
relationships, and not a single (arbitrary) relation as for Brachman. According to this view,
3
roles are associated to relationships, but are concepts, not relations. We may observe therefore
that Sowa's roles have almost nothing to do with KL-ONE roles; rather, we think that this
comparison sheds some light on the cognitive meaning of roles as important knowledge rep-
resentation primitives: there is a subtle, yet intimate connection between roles-as-concepts and
roles-as-relations. An evident sign of this connection is the fact that many commonly used KL-
ONE role names are actually common nouns like son or age, which may also be used as names
of concepts.
Yet, current systems force us to make a radical choice between roles and concepts, which
has a great influence on the knowledge engineering process of building a knowledge base. Once
we have split our domain into roles and concepts, we have only two possible choices. The first
is to definitely give up the possibility to capture the intrinsic meaning of our roles, using them
just as "flat" relations. Paradoxically, some roles have a meaning which is more defined than
that of the concepts they belong to: as noticed by Wilensky [23], age may have a well-defined
meaning, more so than does person. The second possibility is to create a number of concepts
which roughly parallel role names: for instance, has-age/age. Some systems like NIKL [16]
encourage this practice (which has been recently re-formulated by Brachman and colleagues [5])
by allowing a separate hierarchy of roles. As noticed again by Wilensky, although this choice
may improve the overall expressive adequacy, it leads to a duplication which does not account
in a systematic way of the a-priori relationship existing between roles and concepts, and leaves
the burden of its maintenance to the user. The dangerous effects of this duplication have been
noticed for instance by Haimowitz [13].
A possibility to account in some way for the role/concept connection has been explored in
the early KL-ONE networks, with the proposal of the so-called "QUA link" [9]. Its purpose
was to define a concept in terms of the RoleSet of another concept, but its semantics was never
completely clarified, and the construct has been now abandoned.
In the rest of this paper we shall try to explore the ontological foundations of the
role/concept relationship, and to analyze its implications on the current practice of knowledge
engineering. In the next section we propose to use the term "role" only in Sowa's sense;
bearing on Husserl's theory of foundation [18], we distinguish between roles and natural
concepts, and define a role as a concept which implies some particular "pattern of
relationships", but does not necessarily act as a conceptual component of something. In section
3 we define attributes as concepts having an associate relational interpretation, allowing them to
act as conceptual components as well as concepts on their own; we propose a formal semantics
which binds these concepts to their corresponding relations, and a linguistic criterion to
distinguish attributes from slots, i.e. from those relations which cannot be considered as
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conceptual components. Moreover, we show how the choice of considering attributes as
concepts enforces discipline in conceptual analysis as well as uniformity in knowledge
representation.
In section 4 we show that the set of roles and that of attributes, as defined above, do actually
have a large intersection, represented by all those concepts like mother which, besides implying
a pattern of relationships, act also as conceptual components. However, there are at the same
time examples of attributes which cannot easily be called roles: they are for instance qualities
like color and part-names like wheel. We propose a basic ontology of attributes, which uses the
ontological notions of foundedness and semantic rigidity as classification features.
Finally, in the discussion we propose a possible methodology to decide whether a given
name may actually be used as attribute of a certain object, which integrates the linguistic and
ontological considerations made in the paper.
2 Roles and concepts
Let us try first to propose a standard definition for the term "role". We take Sowa's
interpretation as a starting point, since it seems to fit well with the general meaning of the term.
For instance, Websters’ International Dictionary reports the following meanings for the word
"role":
•a character assigned to or assumed by someone
•a socially prescribed pattern of behaviour corresponding to an individual’s status in a particular society
•a part played by an actor
•a function performed by someone or something in a particular situation, process, or operation.
The proper meaning of a role is therefore that of a concept, whose instances are involved in
"some particular pattern of relationships". Sowa proposes a simple test to decide whether a
concept is a role [21]:
τ
is a role type if something can only be identified as type
τ
by
considering some other entity, action, or state. This test is however too vague to capture our
intended meaning. For instance, a car may be classified as a role since in order to recognize
something as a car somebody has to check whether it has (at least) an engine and some wheels.
2.1 The notion of foundation
In order to be able to propose a more adequate condition, we have first to introduce the
notion of foundation among concepts, typical of Husserl's ontology [20]. Foundation has been
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formalized in [18] by the modal formula below, where ε is the membership relation1, ≤ the part-
of relation and nec stands for the modal necessity (box) operator:
Definition 2.1 The concept α is founded on β (written α ⇓ β) if:
nec ∀x (x ε α ⊃ ∃y (y ε β ∧ x ≤/ y ∧ y ≤/ x)).
α is called founded (written α ⇓) if there exists a β such that α ⇓ β. α is called essentially
independent (written I(α)) if ¬ (α ⇓), and self-founding if α ⇓ α.
The meaning of the above definition is that, in order α to be founded on another concept β,
any instance x of α has to be necessarily associated to an instance y of β which is not related to
x by a part-of relation. In other words, the instances of α cannot exist as such except in a more
comprehensive unity where they are associated to some other object. For example, son is
founded since sons as such exist only within the framework of a family, where they are
associated to their parents. On the other side, car is essentially independent since, although the
existence of a car implies the existence of its engine, this engine does not necessarily belong to a
more comprehensive unity of which the car is a part, but is instead a part of the car. Finally,
spouse is an example of a self-founding concept.
2.2 Roles and natural concepts
The notion of foundation defined above seems to be very appealing in order to give a formal
definition to Sowa's roles: if we stipulate that a role is a founded concept, not only concepts
denoted by relational nouns like son or spouse [8] fall under this category, but also concepts
like pedestrian, exactly as argued by Sowa. Indeed, both categories are associated to some
"pattern of relationships": the association is explicit for the former and implicit for the latter.
However, there is a class of relational nouns not mentioned by Sowa, which would fit very
hard with the natural meaning of "role" and still fit our definition of founded concepts. They
usually denote qualities like color, weight, velocity, or position. Take for instance color: if blue
is a color, then necessarily exists an object whose color is blue, which is not related to the
object blue by a part-of relation2. The concept color is therefore founded, but it does not seem
to fit the dictionary definition of a role reported above. The proper ontological classification of
these concepts will be given in section 4; for the time being, we simply want to exclude them
from being roles. We propose therefore to introduce a further condition, which, together with
1 It should better called predication relationship, but for our purposes may be equally intended as a membership.
2 Unless we accept the (somewhat unnatural) view that properties of an object like its color are also parts of that
object.
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foundedness, gives us a more adequate characterization of the meaning of roles, distinguishing
them from other kind of concepts.
Definition 2.2 A concept α is called semantically rigid (written R(α)) if
∀x (x ε α ⊃ nec (x ε α)).
Intuitively, we can think that a concept α is semantically rigid if it contributes to the very
identity of its instances, in such a way that, if x is an α in a particular situation, it has to keep to
be an α in any possible situation in order to keep its identity. For instance, an animal can cease
to be a pup while still being a dog: animal and dog are semantically rigid, pup is not.
Definition 2.3 A concept α is called a role if it is founded but not semantically rigid, that is,
α ⇓ ∧ ¬ R(α).
According to this definition, qualities cannot be roles, since they are semantically rigid: if
what is a color would (by absurd) cease to be a color, it would be something else. On the other
side, all the other concepts considered so far as plausible roles appear to be not semantically
rigid. We see therefore that two independent notions contribute to the meaning of a role: the
former is the notion of some "pattern of relationships" which defines the meaning of a role only
within a more general unity; the latter is bound to the Aristotelian distinction between substance
and accident, and guarantees that (using Sowa's words) this "pattern of relationships" is a
"particular" one.
The two notions of foundations and semantical rigidity can be used to introduce an
important set of concepts which is disjoint from that of roles and which is usually not formally
defined: the set of natural concepts.
Definition 2.4. A concept α is called a natural concept if it is essentially independent and
semantically rigid, that is, I(α) ∧ R(α).
Example 2.1 dog is an example of a natural concept. Observe that, according to the above
definitions, color is neither a role nor a natural concept, since it is semantically rigid but not
essentially independent. The same is true for pup or lame-dog, since they may be considered as
essentially independent but not semantically rigid.
3 Slots and attributes
After having re-established the natural meaning of the term “role”, we shall investigate in
this section on the relationship between this meaning and that of the entities called “roles” in
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KL-ONE. Provisionally, we shall call these entities “KL-ONE roles”.
The first observation is that the latter of Brachman’s definitions cited in the introduction is a
dangerous generalization of the former, since it presents a subtle internal contradiction3: if
something has to be a component of a concept it cannot be an arbitrary two-place predicate! To
see that, let us recall one of Woods’ examples [25]:
JOHN
HEIGHT: 6 FEET
HIT: MARY
Woods argues that, in this case, "no longer do the link names stand for attributes of a node,
but rather arbitrary relations between the node and other nodes", and suggests to use a different
notation for the two types of knowledge. The choice made with KL-ONE is in this direction;
however, as long as KL-ONE roles are arbitrary binary relations, there is no a priori criteria to
distinguish among the two different kinds of knowledge. For instance, Brachman ([3], p. 137)
tackles Woods’ example by conceptualizing the hit relation and therefore representing mary as
the filler of an object role for hit, but nothing in his formalism prevents the user from adopting
another formalization, by representing mary as the filler of the hit “role”. What we want to
stress is that hit should be forbidden to be a KL-ONE role: the intended meaning of KL-ONE
roles – as results from the former of the two definitions above – is something else. It is this
difference which should differentiate them from slots. We suggest to call attributes those KL-
ONE roles which capture the original intended meaning of conceptual components, while
adopting the term slot for generic equivalents of two-place predicates.
3.1 Woods' linguistic test
We think that we can find the right meaning of attributes by looking at the linguistic
interpretation suggested by Woods:
Y is a value of the attribute A of X if we can say that Y is a A of X (or the A of X).
If we cannot find a Y that fits this expression, A cannot be an attribute. There is a simple
constraint that must be satisfied in order to fit the above interpretation: an attribute name has to
denote a concept (that is, it has to be a noun). It is here that we face the connection between
concepts and binary relations we have mentioned above: the kind of relations we would like to
3 There is another serious problem in this definition, namely that the intensionality present in the functional
meaning of roles cited in the former definition has disappeared. We discuss of the intensionality of KL-ONE roles
elsewhere [11].
8
use as conceptual components of an object have names which may easily be names of concepts.
3.2Attributes as concepts
The solution we propose is to represent attributes as concepts, i.e. unary relations, which
have an associated binary relation. We call this binary relation the relational interpretation of the
attribute. The two kinds of relations can be easily distinguished at the syntactic level on the
basis of their different arity, and therefore they can have the same functor name; the implicit
connection between them can be accounted by an enforced semantics. This choice will be
clearer while considering the following (super-simplified) assertional language AL:
Definition 3.1 The alphabet of AL consists of the following disjoint sets of symbols:
(a) a set O of objects;
(b) a set C of concepts, with a distinguished subset A of attributes.
Definition 3.2 An atomic formula of AL is defined as follows:
<atomic_formula> ::= <object_description> | <relation_description>
<object_description> ::= ( concept object ).
<relation_description> ::= ( attribute object object ).
Non-atomic formulas of AL are defined as usual.
Notice that, since attributes are concepts, there may exist some relation descriptions which
have the same functor of object descriptions.
Definition 3.3 An interpretation of AL is an ordered tuple I = <U, δ, ρ>, where:
(a) U is an arbitrary set called the universe of discourse;
(b) δ is a function from O ∪ C into U ∪ 2U called denotation function, such that for each x
∈ O and α ∈ C, δ(x) ∈ U and δ(α) ∈ 2U;
(c) ρ a function from A into 2UxU called relational interpretation function, such that, for
each attribute α and each <x, y> ∈ ρ(α), y ∈ δ(α).
Definition 3.4 An atomic formula φ of AL is satisfied by an interpretation I (written Ι |= φ) iff
it satisfies one of the following conditions:
(a) I |= (α x) iff δ(x) ∈ δ(α);
(b) I |= (α x1 x2) iff <δ(x1), δ(x2)> ∈ ρ(α).
9
We see that the denotation of a given attribute α is still unique and identical to that of a
concept, while the interpretation of a relation description with functor α is made with the help of
the auxiliary function ρ, which gives the relation associated to α. The connection existing
between the two meanings is expressed by the constraint which forces the range of ρ(α) to be
included in δ(α). This semantic constraint corresponds, at the syntactic level, to the following
(second-order)
Axiom 3.5 (Attribute Consistency Postulate). Any value of an attribute is also an instance of
the concept corresponding to that attribute. In AL, this means that ∀α∈A ∀x,y∈O (α x y) ⊃ (α
y).
In conclusion, we can formulate the following general definition:
Definition 3.6. An attribute is a concept which, in the domain of interest, has a unique
relational interpretation, satisfying the Attribute Consistency Postulate.
Let us assume, for the time being, that this relational interpretation is given by the user, as
we have seen for the language AL. We shall remove this assumption in the next section,
discussing the ontological status of attributes. First, we would like to discuss the implications
of the choice we have made. With the uniformity between attributes and concepts, we eliminate
a source of confusion and redundancy within current applications of frame-based languages.
Separate attribute hierarchies are no more necessary, and range declarations like (all age Age)
become superfluous. Moreover, we capture Brachman’s original intuition (abandoned in
subsequent formalizations) on the “abstract commonality” among KL-ONE roles with the same
name ([3], p. 141, our italics)
(...) while these roles [i.e., those with the same name] on the surface appear disparate, there is a strong
common sense between them. (...) While I do not as yet have a proposal on how this might be done, it
does appear to be a fruitful research area. (...) The abstraction of the commonalities between locally
defined roles separates this notation from one which uses role names merely as convenient names for
slots.
We see that it is exactly this "abstract commonality" which should account for the difference
between KL-ONE roles and ordinary slots. But current terminological languages do not exhibit
this conceptual distinction as far as their "roles" are interpreted as arbitrary binary relations.
Only the entities we have called attributes are really different from slots.
10
3.3. Naming discipline
We have seen that, in order to suit our interpretation, attribute names have to pass "Woods'
linguistic test". The first consequence of this is the necessity of a strong discipline in choosing
attribute names. For instance, all commonly used slot names containing prepositions (childOf,
connectedTo), verbs (hasPart, ifNeeded) or plurals (parts, instances) cannot be considered as
attributes, and – if possible – they have to be substituted with father, connection, part,
acquisitionProcedure, instance, and so on. We think that this constraint is definitely not a
disadvantage: often what distinguishes a good piece of software from a bad one is the choice of
the right names. Moreover, in the effort for finding right attribute names we often learn more
about the conceptual structure of our domain, and improve the value of our knowledge base. In
our opinion, this value is strictly bound to the easiness of knowledge integration, which in turns
depends on the granularity of the representation and on its cognitive transparency.
Of course, not always is this substitution immediate, natural, or convenient; we argue that
this situation is for us a “signal” that something must (or may be) represented in a totally
different way. To see that, let us consider again Woods’ example. We have seen that it refers to
two different kinds of knowledge; however, within current hybrid systems belonging to
KRYPTON’s mainstream, both pieces of knowledge have to be put into the Abox, without any
possibility of a conceptual distinction. As discussed in greater detail in [10, 12], we propose
instead to consider as terminological knowledge all the knowledge about (the internal structure
of) terms, i.e. about structural relationships between terms. On the other side, relational
knowledge is knowledge about arbitrary relationships between terms. Notice that individuals
are terms, both from the logic and from the linguistic point of view. Therefore, the proposition
“the height of John is 6 feet” is a piece of terminological knowledge about the term john, while
“John hit Mary” is a piece of relational knowledge about a particular relationship existing
between the two terms john and mary. Now, since hit cannot be an attribute of john, the latter
statement has to be expressed as relational knowledge. Our characterization of attributes
enforces in this way an important conceptual distinction.
As an intriguing example of the danger of interpreting KL-ONE roles as arbitrary relations,
consider the KL-ONE role self, whose denotation is the identity relation, introduced by
Levesque and Brachman [14] in order to prove the intractability of subsumption for FL. In the
light of the above discussion, self should not be an attribute, since it is not a concept. By the
way, we feel that it is exactly the nature of attributes as concepts which allows us to use them to
define concepts in terms of something else: how can we think of defining a concept in terms of
the property of being identical to itself?
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4. A basic ontology for attributes
The definition of attributes we have given in the previous section leaves a number of
questions still open. Given that attributes are concepts, which are their ontological properties? Is
there a criterion to decide whether a concept can be an attribute and to define its relational
interpretation? How are attributes related to roles and natural concepts? In this section we try to
answer these questions by proposing a schematic (meta)ontology of concepts, which
distinguishes among natural concepts, roles and attributes (Fig. 1).
Definition 4.1. A domain scheme is a tuple D = <U, C, R, δ>, where U is an arbitrary set
called the universe of discourse, C a set of symbols called concepts, R a set of binary relations
on UxU called relevant relations, and δ a function from U into 2U called denotation function.
Given a domain scheme, we present in the following the conditions for a concept α ∈ C to
be an attribute, removing the assumption made in the previous section, that the relational
interpretation of an attribute is given by the user.
4.1. Relational attributes.
Let us first consider relational nouns such as son or spouse. They have a "natural" relational
interpretation which is directly associated with their name, and therefore they should satisfy
Def. 3.6. We want to introduce an ontological criterion which forces them to be attributes, such
that their relational interpretation is the obvious one. The key idea we explore below is that the
relation we are looking for can be defined in terms of the founding relation.
Definition 4.2. Let D = <U, C, R, δ> be a domain scheme and α ∈ C a concept in D. A
binary relation R ∈ R is called a partial relational interpretation of α in D if there exists a
concept β ∈ C such that α ⇓ β ∧ dom(R) ⊆ δ(β) ∧ range(R) ⊆ δ(α).
Definition 4.3. Let D = <U, C, R, δ> be a domain scheme, α ∈ C a concept in D, and Rα
⊆ R the set of its partial relational interpretations. The concept α is called a relational attribute in
D if Rα is non-empty. Its relational interpretation ρ(α) is given by ρ(α) = ∪
Ri∈RαRi. A
relational attribute is called non-ambiguous in D if the domains of its relational interpretations
are mutually disjoint.
Example 4.1. Suppose that the concepts teacher, subject and student are defined in a domain
D (with δ satisfying their obvious meaning), as well as the two relations R1: δ(subject) →
δ(teacher) and R2: δ(student) → δ(teacher). Since teacher is founded both on subject and on
student, R1 and R2 are both partial relational interpretations of teacher, with ρ(teacher)=R1∪R2.
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teacher is therefore a relational attribute. It is non-ambiguous since subject and student are
disjoint.
concept
non-relational
role relational role
natural concept
role attribute
relational
attribute
non-
relational
attribute
quality
part name
pedestrian
by-pass
capacitor
son
spouse
color
position
wheel
engine
person
Figure 1. A basic ontology of attributes, showing their relationships with roles and natural concepts.
Thick arrows represent inclusion relationships,while thin arrows membership relationships.
Let us consider now the left side of Fig. 1. Relational roles represent those concepts which
are founded, non-rigid, and have a relational interpretation: they are therefore the intersection
between roles and attributes. Qualities are relational attributes since they are founded and have a
relational interpretation; they are however disjoint from roles because of their semantic rigidity.
We would like to stress that the distinction between qualities and relational roles is more than a
mere subtlety, since qualities present two important peculiarities with respect to relational roles.
First, their instances are properties, i.e. predicable entities [20]; indeed, red or on may well be
names of predicates, but the same is not true for john as an instance of the relational role son.
Second, their relational interpretation is a function; that is, features are single-valued attributes.
The latter aspect has important computational implications.
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4.2. Non-relational attributes
Coming now to the right side of Fig. 1, let us notice that there is a whole category of
concept-structuring terms which we want to consider as attributes but are not relational nouns.
The most important are those related with part-names. Consider for instance an AL statement
like (wheel car#467 wheel#7279). The term wheel contributes to the characterization of
car#467, but it is not a role, since it does not satisfy Def. 2.3. The reason is that a wheel is
always a wheel, independently of its participation to the structure of a more complex entity.
Notice that it cannot be a relational attribute, since it is not founded. Still, it satisfies Def. 3.6
for attributes, since we could easily conceive a relation named wheel (satisfying the Attribute
Consistency Postulate) mapping cars (or whatever) into particular wheels. However, this
relation would not be part of the nature of a wheel.
Differently from previous cases, the attribute wheel should be therefore linked to its
relational interpretation in an indirect way. It is important to notice that, again, this should not
be an arbitrary relation, since it seems to have a precise ontological nature, imposing a formal
constraint to the relation: it has to be a specialization of a part relation, whose range is restricted
to be a wheel. The Attribute Consistency Postulate is still valid.
But who tells us that we are dealing with a part? If the context was different, say (wheel
john wheel#7279), the preferred interpretation might be, for instance, that wheel#7279 is one of
the wheels John is playing with, or one of the wheels of his car: in both cases, not a part of
John. We can observe then the second difference with respect to other attributes: the ontological
nature of the relation wheel is (indirectly) linked to cannot be predicted a priori on the basis of
its name. That is, it is a property of the link between wheel and the object it refers to. The
conclusion is that while the semantics of relational attributes may be in general easily
understandable from the context (except those cases of ambiguity mentioned in Def. 4.3), this is
not true for non-relational attributes.4 As discussed in [11], we need a granularity finer than that
of current frame-based languages in order to express this kind of knowledge.
A possibility to limit the potential ambiguities of non-relational attributes without resorting to
more expressive languages is to limit their use to (generalized) parts5, as appears in Fig. 1. This
4 The only possible interpretation is a general "belonging" relationship between the attribute and the object it
refers to, but this is too weak for any practical use. This situation has been called by Wilensky the "belonging
fallacy" of frame based languages [23]. Wilensky however does not make our distinction between relational and
non-relational attributes.
5 We acknowledge that the part relationship has not been adequately characterized, since we do not distinguish
among different kinds of parts. A thorough analysis of the problems with parts can be found in [24, 7]. The
intuitive meaning of parts is however sufficient to support the present discussion. A deeper ontology for parts
and features has been explored in [1].
14
means that, for instance, the interpretation of attributes as possessions should be avoided.
Consider for instance the two following statements:
(book padovaPublicLibrary divinaCommedia)
(book john divinaCommedia).
We argue that book should not be used as an attribute of John in the second case, since its
ontological role may be ambiguous: for instance, the interpretation of Divina Commedia as a
part of John should be excluded, but there is no possibility to formally force that. However,
the restriction of attributes to either relational nouns or parts may lead us to a better way to
express the same information. For instance, we can use the relational role possession to state
(possession john divinaCommedia).
In conclusion, we can complete our ontological formalization of attributes as follows:
Definition 4.4. Let D=<U, C, R, δ> be a domain scheme. A concept α ∈ C is called a non-
relational attribute in D if: (i) α is a natural concept; (ii) there exists a relation < ∈ R to which it
has been given the meaning of a proper part relation; (iii) the relational interpretation ρ(α) =
{<x, y> | y < x ∧ y ∈ δ(α)} is not empty.
Definition 4.5. Let D=<U, C, R, δ> be a domain scheme. A concept α ∈ C is called an
attribute in D if it is either a relational or a non-relational attribute in D.
5. Discussion and conclusions
First of all, we would like to stress that the conceptual distinction between "right" and "non
right" attribute names does not depend on the formal semantics we have presented, nor on the
choice to give the same name to attributes-as-relationships and attributes-as-concepts: the first
result of our analysis is an ontological characterization of attributes as the main components of a
concept, which can immediately be applied as a criterion to discriminate between attributes,
other concepts and arbitrary relations. A possible methodology to decide whether A can be an
attribute for an object X could be the following:
1. Check whether A and X satisfy Woods' linguistic test: "something is the/an A of
(some) X". This test ensures that A is a concept, and that it may be actually related
with X.
2. If the linguistic test succeeds then
if A is founded on X then
return true (A is a relational attribute).
else if A is the name of a part of X then
15
return true (A is a non-relational attribute)
else return false.
Let us briefly compare our methodology with the one recently proposed by Brachman and
colleagues for the CLASSIC language [5]. These authors propose a general principle for
distinguishing concepts from roles (in the KL-ONE sense) which is very simple and works well
in many cases. The principle is that objects which depend on other objects for their existence
must be roles. In our terminology, this means that foundation is the only criterion used to
decide about attributes. The excessive simplicity of this criterion forces the authors to admit
exceptions to their rule: for instance, although they acknowledge that grape may have an
independent existence (and therefore is not founded), they use it as a role for wine because it is
natural to refer to a "wine's grape". In this way Brachman and colleagues implicitly admit the
importance of Woods' linguistic test, but they do not include it among their principles.
Now, according to our discussion, grape is not a good attribute for wine since, although it
fits Woods' linguistic test, it is not founded, nor is it the name of a part of a wine. A better
attribute may be constituent, with value restriction grape. Our methodology gives a criterion to
check whether an attribute is the right one for a given object, and, in case of failure, forces us to
reformulate knowledge in terms of more basic relations. Moreover, it can be easily specialized
to discriminate between relational roles, features and parts.
However, the real limitation of CLASSIC's methodology is that the principles they
introduce are only used to suggest possible roles, but not to exclude some relations from being
roles. This means that roles standing for arbitrary relations like hit or likes are explicitly
admitted: "roles are relationships between individuals".
Coming now to the semantics we have presented, it may be observed that it actually assigns
more than one interpretation to those concepts which are also attributes. We have already
observed that, technically, the denotation of any symbol of the alphabet is still unique. We
would like to add however that this kind of situation is frequent in natural language: it is the
way of reference to a symbol (i.e., in many cases, the syntax) which characterizes its actual
semantics. In the case of KL-ONE roles, Trost and Steinacker [22] distinguish between
definitional and functional references (e.g. a hammer as an artifact and a hammer as instrument
of an action), but reach a conclusion which is the opposite of ours: they do not admit any
necessary common meaning between the two interpretations, while we have presented some
ontological motivations for their mutual dependence.
16
Acknowledgements
This research has been made in the framework of a special National project on Hybrid
Systems, supported by the "Progetto Finalizzato Informatica e Calcolo Parallelo" of the Italian
National Research Council. I would like to thank Luca Boldrin, Daniele Giaretta and Dario
Maguolo for their comments on earlier versions of this paper.
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