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The Ontological Level

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Introduction In 1979, Ron Brachman discussed a classification of the various primitives used by KR systems at that time 1 . He argued that they could be grouped in four levels, ranging from the implementational to the linguistic level (Fig. 1). Each level corresponds to an explicit set of primitives offered to the knowledge engineer. At the implementational level, primitives are merely pointers and memory cells, which allow us to construct data structures with no a priori semantics. At the logical level, primitives are propositions, predicates, logical functions and operators, which are given a formal semantics in terms of relations among objects in the real world. No particular assumption is made however as to the nature of such relations: classical predicate logic is a general, uniform, neutral formalism, and the user is free to adapt it to its own representation purposes. At th
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revised version - September 7, 1995
_________________________
Invited paper presented at the 16th Wittgenstein Symposium, Kirchberg, Austria, August 1993. To appear in
R. Casati, B. Smith and G. White (eds.), Philosophy and the Cognitive Sciences, Vienna: Hölder-Pichler-
Tempsky, 1994.
The Ontological Level
Nicola Guarino
1. Introduction
In 1979, Ron Brachman discussed a classification of the various primitives used by KR
systems at that time
1
. He argued that they could be grouped in four levels, ranging from the
implementational to the linguistic level (Fig. 1). Each level corresponds to an explicit set of
primitives offered to the knowledge engineer. At the implementational level, primitives are
merely pointers and memory cells, which allow us to construct data structures with no a
priori semantics. At the logical level, primitives are propositions, predicates, logical
functions and operators, which are given a formal semantics in terms of relations among
objects in the real world. No particular assumption is made however as to the nature of such
relations: classical predicate logic is a general, uniform, neutral formalism, and the user is
free to adapt it to its own representation purposes. At the conceptual level, primitives have a
definite cognitive interpretation, corresponding to language-independent concepts like
elementary actions or thematic roles. Finally, primitives at the linguistic level are associated
directly to nouns and verbs.
Brachman noticed an evident gap in this classification: while primitives at the logical
level are extremely general and content-independent, at the conceptual level they acquire a
specific intended meaning that must be taken as a whole, without any account of its internal
structure. He proposed the introduction of an intermediate epistemological level, where the
primitives allow us to specify “the formal structure of conceptual units and their
interrelationships as conceptual units (independent of any knowledge expressed therein)”
2
.
In other words, while the logical level deals with abstract predicates and the conceptual level
with specific concepts, at the epistemological level the generic notion of a concept is
introduced as a knowledge structuring primitive.
Level Primitives
Implementational Memory cells, pointers
Logical Propositions, predicates, functions, logical operators
Epistemological Concept types, structuring relations
Conceptual Conceptual relations, primitive objects and actions
Linguistic Linguistic terms
Fig. 1. Classification of primitives used in KR formalisms (adapted from Brachman 79).
Epistemological level was “the missing level”.
Brachman’s KL-ONE
3
is an example of a formalism built around these notions. Its main
contribution was to give an epistemological foundation to cognitive structures like frames and
semantic networks, whose formal contradictions had been revealed in the famous “What’s in
a link?” paper by Bill Woods
4
. Brachman’s answer to Woods’ question was that conceptual
links should be accounted for by epistemological links, which represent the structural
connections in our knowledge needed to justify conceptual inferences. KL-ONE focused in
2
particular on the inferences related to the so-called IS-A relationship, offering primitives to
describe the (minimal) formal structure of a concept needed to guarantee “formal inferences
about the relationship (subsumption) between a concept and another”. This formal structure
consists of the sum of the constituents of a concept (primitive concepts and role expressions)
and the constraints among them, independently of any commitment as to: (i) the meaning of
primitive concepts; (ii) the meaning of roles themselves; (iii) the nature of each role’s
contribution to the meaning of the concept. The intended meaning of concepts remains
therefore totally arbitrary: indeed, the semantics of current descendants of KL-ONE is such
that – at the logical level – concepts correspond to arbitrary monadic predicates, while roles
are arbitrary binary relations. In other words, at the epistemological level, emphasis is more
on formal reasoning than on (formal) representation: the very task of representation, i.e. the
structuring of a domain, is left to the user.
Current frame-based or object-oriented formalisms suffer from the same problem. For
example, the advantage of a frame-based language over pure first-order logic is that some
logical relations, such as those corresponding to classes and slots, have a peculiar,
structuring meaning. This meaning is the result of a number of ontological commitments,
which accumulate in layers starting from the very beginning of the process of developing a
knowledge base
5
. For a particular knowledge base, its ontological commitments are however
implicit and strongly dependent on the particular task being considered, since the formalism
itself is in general neutral as concerns ontological choices
6
.
In this paper I argue against this neutrality, claiming that a rigorous ontological
foundation for knowledge representation can improve the quality of the knowledge
engineering process, making it easier to build at least understandable (if not reusable)
knowledge bases. We contrast the notion of formal ontology, intended as a theory of the a
priori forms and natures of objects, to that of (formal) epistemology, intended as a theory of
meaning connections
7
. We show in the following how theories defined at the epistemological
level, based on structured representation languages like KL-ONE, cannot be distinguished
from their "flat" first-order logic equivalents unless we make clear their implicit ontological
assumptions by stating formally what it means to interpret a unary predicate as a concept
(class) and a binary predicate as a "role" (slot). We need therefore to introduce the notion of
ontological level, as an intermediate level between the epistemological and the conceptual one
(Fig. 6)
8
. While the epistemological level is the level of structure, the ontological level is the
level of meaning. At the ontological level, knowledge primitives satisfy formal meaning
postulates, which restrict the interpretation of a logical theory on the basis of formal
ontology, intended as a theory of a priori distinctions:
9
among the entities of the world (physical objects, events, processes...);
among the meta-level categories used to model the world (concepts, properties,
states, roles, attributes, various kinds of part-of relations...).
We focus here on the latter kind of distinctions, showing how the basic dichotomy
existing in KR systems between concepts like apple and assertional properties like red can be
understood in terms of the philosophical distinction between sortal and characterising
universals
10
. In section 2 I present examples which show the necessity of making such a
distinction explicit. In section 3 I introduce the notion of ontological commitment as a
constrained interpretation of a logical theory, and I sketch a basic ontology of meta-level
categories of unary predicates. In section 4 I discuss the role of the ontological level in
current knowledge engineering practice.
3
2. Reds and apples.
Suppose we want to state that a red apple exists. In standard first order logic, it is
straightforward to write down something like x.(Ax Rx). If we want however to impose
some structure on our domain, the simplest formalism we may resort to is many-sorted logic.
Yet we have to decide which predicates correspond to sorts: we may write x:A.Rx as well
as x:R.Ax (or maybe ∃(x:A,y:R).x=y). All these structured formalisations are equivalent to
the previous one-sorted axiom, but each contains an implicit structuring choice. At the epis-
temological level, this choice is up to the user, since the semantics of the primitive “sort” is
the same as its corresponding first-order predicate. At the ontological level, what we want is
a formal, restricted semantic account that reflects the ontological commitment intrinsic in the
use of a given predicate as a sort. This means that the choice of a particular axiomatisation is
still up to the user, but its consequences are formalised in such a way that another user can
understand the meaning of the choice itself, and possibly agree on it on the basis of its se-
mantics.
In our case, a statement like x:R.Ax sounds intuitively odd: what are we quantifying
over? Do we assume the existence of “instances of redness” that can have the property of
being apples? According to Strawson, the difference between the two predicates lies in the
fact that apple “supplies a principle for distinguishing and counting individual particulars
which it collects”, while red “supplies such principle only for particulars already
distinguished, or distinguishable, in accordance with some antecedent principle or
method”
11
. This distinction is known in the philosophical literature as the distinction between
sortal and non-sortal (characterising) universals, and is (roughly) reflected in natural
language by the fact that the former are common nouns, while the latter are adjectives. The
issue is also related to the difference between count and mass terms, and has been a matter of
lively debate among linguists and philosophers
12
. The distinction is implicitly present in the
KR literature, where sortal universals are usually called “concepts”, while characterising
universals are called “properties”. The difference between the two is however the result of
heuristic considerations, and nothing in the semantics of a concept forbids any arbitrary
unary predicate from acquiring this status.
Our position is that, within a KR formalism, the meaning of structuring primitives as
sorts (or concepts, in KR terminology) should be at least specified with formal, necessary
conditions at the meta-level, which force the user to accept their consequences when he/she
decides to use a given predicate as a sort. According to our previous discussion, a predicate
like red – under its ordinary meaning – will not satisfy such conditions, and should be
excluded therefore from being used as a sort. Notice however that this may be simply a
matter of point of view: at the ontological level, it is still the user who decides which
conditions reflect the intended use of the predicate red: a more rigid choice would be
distinctive of higher levels, like the conceptual or the linguistic level. For example, compare
the statement mentioned above with others where the same unary predicate red appears in
different contexts (Fig. 2):
In case (2), red is still a unary predicate whose argument refers to a particular colour
instead of a particular fruit; in (3) the argument refers to a particular colour gradation
belonging to the set of “reds”, while in (4) the argument refers to a human-being, meaning
for instance that he/she is a communist.
4
Red(x)
this apple is red (1)
the color of this apple is red (2)
crimson is a red (3)
John is a red (4)
Fig. 2. Varieties of predication.
We face here the difference of positions between the stereotype Linguist and Philosopher
discussed by Bill Woods in one of the historical papers on knowledge representation
13
:
while the Linguist “is interested in characterising the fact that the same sentence can
sometimes mean different things”, the Philosopher “is concerned with specifying the
meaning of a formal notation rather than a natural language”. Woods goes on by stating that
philosophers have generally stopped short of trying to actually specify the truth
conditions of the basic atomic propositions, dealing mainly with the specification of
the meaning of complex expressions in terms of the meanings of elementary ones.
Researchers in artificial intelligence are faced with the need to specify the semantics
of elementary propositions as well as complex ones.
In a knowledge representation formalism, we are constantly using natural language
expressions within our formulas, relying on them to make our statements readable and to
convey meanings we have not explicitly stated: however, since words are ambiguous in
natural language, it may be important to “tag” these words with a semantic category,
endowed with a suitable axiomatisation, in order to guarantee a consistent interpretation. This
is unavoidable, in our opinion, if we want to share theories across different domains
14
.
How can we account for the semantic differences in the use of red in the formulas given
above? In our opinion, they are not simply related to the fact that the argument belongs to
different domains: they are mainly due to different ways of predication, i.e. different subject-
predicate relationships. Studying the formal properties of these relationships is a matter of
formal ontology.
3. A basic ontology of unary predicate types
A basic ontology, which – according to Strawson’s intuitions – classifies unary
predicates on the basis of their ability to supply an identification principle for their
arguments, is presented in Fig. 3.
unary predicate
sortal
non-sortal
substantial non-substantial
characterizing
generic
Fig. 3. A basic ontology of predicate types.
5
Following Wiggins
15
, sortal predicates are here divided into substantial (like apple or
human-being) and non-substantial (like food or student), while non-sortal predicates include
generic predicates like thing and characterising predicates like red. A preliminary
formalisation of such distinctions will be presented in the sequel.
But of trying to give a “universal” formal definition of the above categories, we shall
pursue here a more modest account: our definitions will be related to a specific knowledge
base described by a standard first order theory, which we are interested in “adding structure”
to. This means that the basic knowledge-building blocks are taken as having been already
fixed, being the predicates of the theory itself; our work will be to offer a formal instrument
for clarifying their ontological implications for the specific purposes of knowledge bases un-
derstanding and reuse among users belonging to the same culture. We assume therefore that
interpretations of our specific theory, rather than describing a real or hypothetical situation in
a world that has the same laws of nature of ours
16
, are states of affairs having an “idealised
rational acceptability”
17
. This choice excludes unwanted metaphysical implications.
Within this framework, let us concentrate on a minimal problem. Suppose we have a
first order, non-functional language L with signature Σ=<C, R>, where C is a set of constant
symbols, R is a finite set of predicate symbols and PR is a set of monadic predicate
symbols. We are interested in some formal criteria for translating L into an order-sorted
language L
s
with signature Σ
s
=<C, S, Q>, where SP is a set of sort symbols called
sortals, and Q=R \S is a set of ordinary predicates.
Def. 1. Let L
m
be the modal extension of a first order language L obtained by adding to L
the usual modal operators and , and D be a set. A rigid model
18
for L
m
based on D is a
structure M=<W, , D,
C
,
P
>, where W is a set of possible worlds sharing the same
interpretation
C
for constant symbols of L
m
, is a binary relation on W, D is a domain
common to all possible worlds, and
P
is a mapping that assigns to each predicate symbol P
of L and world wW a unary relation on D.
For a given rigid model M, is a relation between worlds (i.e., interpretations of L)
that may differ in the interpretation of predicates while sharing the same interpretation for
constants. We want to give the meaning of an ontological compatibility relation: two
worlds are ontologically compatible if they describe plausible alternative states of affairs
involving the same elements of the domain. will be in this case reflexive, transitive and
symmetric (i.e., an equivalence relation), and the corresponding modal theory will be S5.
Def. 2. Let L be a first order language and D a domain. An ontological commitment for L
based on D is a set C of rigid models for L
m
based on D, where the relation is an
equivalence relation. Such commitment can be specified by an S5 modal theory of L
m
, being
in this case the set of all its rigid models based on D. A formula Φ of L
m
is valid under C (C
|= Φ) if it is valid in each model MC.
Within this modal framework, preliminary reflection on the distinction between sortal
and non-sortal predicates reveals that the former cannot be necessarily false for each element
of the domain: they must be natural predicates, in the sense of the following definition
19
:
6
Def. 3. Let L be a first order language, P a monadic predicate of L, and C an ontological
commitment for L. P is called natural under C
iff C
|= x. Px.
A more substantial observation that comes to mind when trying to formalise the nature of
the subject-predicate relationship in the examples above, is that the “force” of this
relationship is much higher in “x is an apple” than in “x is red”. If x has the property of being
an apple, it cannot lose this property without losing its identity, while this does not seem to
be the case in the second example. This observation goes back to Aristotelian essentialism,
and can be easily formalised as follows
20
:
Def. 4 A predicate P is ontologically rigid under C iff it is natural under C and C
|=
x.(Px Px).
Ontological rigidity seems a useful property for characterising sortals: stating that apple
is rigid and red is not will clarify the intended meaning of these two predicates in the
statement (1) of Fig. 2. In this case, if aC, the worlds satisfying (A(a) R(a)) or (A(a)
¬R(a)) will turn out to be mutually compatible, while those satisfying (R(a) A(a)) or (R(a)
∧ ¬A(a)) are not (due to the constraints imposed on by the rigidity of A). Assuming that
rigidity is a necessary property for sortals, we can then exclude both x:R.Ax and
∃(x:A,y:R).x=y from our axiomatisation choices for (1).
Notice that the naturalness condition in the above definition excludes cases where
rigidity would be trivially true due to the impossibility of P. On the other hand, ontological
rigidity will be trivially satisfied by predicates being necessarily true for each element of the
domain, like thing or entity. Yet, according to traditional wisdom they are excluded from
being sortals, since no clear distinction criteria are associated with them.
Rigidity cannot be
therefore be considered as a necessary condition for sortals. We call these “top level”
predicates generic predicates
21
. In the same category other rigid predicates should be
included, that, although being not trivially rigid, are still too general to supply a distinction
criterion: object, individual, event... However, a distinctive characteristic of generic
predicates is that they are rigid but divisive, in the sense that they can hold for parts of their
arguments. Various divisivity criteria have been proposed in the literature in order to account
for the distinction between countable and uncountable predicates
22
; to the purposes of the
present paper, the following definition will be good enough:
Def. 5. Let P be a natural predicate under C, and < be a “proper part” relation assumed as
primitive, satisfying the axioms of classical mereology
23
. P is divisive under C iff C
|=
x.(Px ∧ ∃y. y<x) ∧∀x.(Px (y.(y<x Py))).
In other words, a predicate P is divisive if its arguments can have proper parts, and,
necessarily, if its instances have proper parts then P holds for one of these. We are now in a
position to give a definition of substantial sortals:
Def. 6. Let P be ontologically rigid under C. It
is a generic predicate in C if it is divisive in
C, and a substantial sortal in C otherwise.
Within our KR framework, the above definition gives a formal characterisation to the
notion of substantial sortals originally introduced by Wiggins, delimiting those rigid
predicates that are sortals. We need now a distinction criterion between non-rigid predicates:
7
some of them (like student) will presumably be non-substantial sortals, while the others (like
red) will be characterising predicates. The intuition behind the distinction between substantial
and non-substantial sortals is that in the first case the identity criterion is given by the
predicate itself, while in the second case it is provided by some superordinate sortal. We
formalise this idea as follows:
Def. 7. Let P be a natural predicate which is not ontologically rigid under C. It is a non-
substantial sortal in C iff there exists a substantial sortal S in C such that C |= x.(Px
Sx), and a characterising predicate otherwise.
Since the set of predicate symbols of L is finite and fixed for all possible ontological
commitments of L, this definition does not imply any “real” second-order quantification in
L
m
, nor does it have any metaphysical implication. For example, suppose that student is a
non-rigid predicate under some commitment C for L. If human-being also belongs to L and
is a superordinate substantial sortal under C, then student will be a non-substantial sortal,
while otherwise it may simply be a characterising predicate. This means that a priori consid-
erations about the real world do not affect our definitions unless they force the user to revise
the original first-order axiomatisation. However, one of the advantages of the ontological
level is that an unwanted formal property for a predicate may trigger a knowledge elicitation
process: in our case, if student sounds strange when used as a characterising predicate, the
reason may be that we have forgotten to include human-being within our axiomatisation.
Adapting some definitions from Cocchiarella
24
, we believe it is important, for
knowledge representation purposes, to make some further assumptions on sortals, which
characterise what we call a well-founded ontological commitment:
Def. 8. An ontological commitment C based on D is well-founded iff:
- each element of D belongs to a substantial sortal;
- if two substantial sortals are not in the subsumption relationship, then they are
mutually disjoint.
From Def. 7 and 8 it follows that:
Theorem 1. Two overlapping non-substantial sortals are subordinate to the same
substantial sortal.
Def. 9. Let C be a well-founded ontological commitment. If a substantial sortal S is
subordinate to another substantial sortal T under C, then S is called a kind of T.
Def. 10. A predicate is called a sortal under a commitment C if it is either a substantial or a
non-substantial sortal under C.
As a final comment concerning the taxonomy of unary predicates we have discussed in
this section, we would like to make the following proposal regarding the relationship
between the terminology currently used in KR formalisms and the philosophical terms we
have defined here (Fig. 4):
8
unary predicate
concept
class
property
(characterizing predicate)
type
(substantial sortal)
non-substantial
sortal
generic
predicate
Fig. 4. A terminology proposal for KR formalisms
4. The Ontological Level
Just as the logical and epistemological levels are characterised by a (standard) formal
semantics, so the ontological level is characterised by a formal ontological account, like the
one introduced in the previous section. Although we have limited ourselves to a few very
basic ontological distinctions, it should be clear that other important distinctions could be
employed within a similar framework, like for instance those between attributes and arbitrary
binary relations. However, the definitions we have given are enough to capture the different
uses of the red predicate shown in Fig. 2, which correspond to distinct ontological
commitments (Fig. 5).
human-being
colour gradation
thing
red
colour
thing
apple
red
thing
red
this apple is red
red
thing
apple
the color of this apple is red
*
* *
crimson is a red
John is a red
*
*
*
(1)
(2)
(3)
(4)
Fig. 5. Different ontological commitments capturing varieties of predication.
Arcs represent subsumption relationships, and asterisks mark substantial sortals.
In case (1), red is not rigid, and it has no superordinate substantial sortal: it is a
characterising predicate, having as argument a physical object. In case (2), red is still not
rigid, but it is subordinate to colour, which is assumed to be rigid and not divisive (a colour
has no parts): it is a non-substantial sortal, having as argument the colour of a physical
object. In case (3), red is rigid, since its argument is a colour gradation (crimson has to be a
red): it is a substantial sortal, and also a kind of colour gradation. Finally, in case (4), red is
9
used as a contingent property of human-beings and hence is not rigid, but it is not a
characterising predicate since it is assumed that being a red implies being a human-being: red
is therefore a non-substantial sortal like in (2), under a different ontological commitment.
It is important to stress that, although the notion of ontological commitment we have
defined is bound to a quantified modal logic, the computational (bad) properties of such a
theory have nothing to do with those of the first order language we started with. Even with a
language of very limited expressiveness like a description logic
25
, we can embed it in a full
quantified modal logic, and use this to define the ontological commitment of the original
language. This means that we give up the task of performing any automatic deduction on the
modal theory, since we are only interested in its semantic properties. However, given a KR
formalism at the epistemological level, we may be interested in somehow expressing its
ontological commitment within the formalism itself. In other words, this is a matter of
ontological adequacy of a KR language. We can get this ontological adequacy by suitably
restricting the semantics of the epistemological level primitives (assuming for instance that
“concepts” used in description logics have the semantics of sortals), or otherwise by having a
syntactic way to “tag” a predicate symbol with an ontological category (stating for instance
that human-being is a 'substantial sortal', where the latter is a primitive symbol). Some meta-
level capability is necessary in the second case. In conclusion, while the ontological level is
neutral with respect to the underlying epistemological level, not any epistemological level
formalism may be considered as ontologically adequate.
Level Primitive concepts... Main feature Interpretation
Logical are predicates Formalisation Arbitrary
Epistemological are structuring primitives Structure Arbitrary
Ontological satisfy meaning postulates Meaning Constrained
Conceptual are cognitive primitives Conceptualisation Subjective
Linguistic are linguistic primitives Language Subjective
Fig. 6. Main features of the ontological level.
The main features of the ontological level are compared in Fig. 6 to that of other levels.
The ontological level is the only level where the intended meaning of a KR language is
constrained in a formal way. Lower levels have an arbitrary interpretation, since a logical
theory admits a number of models much higher than the intended ones; higher levels (which
can still be “implemented” at the ontological level) have a subjective interpretation, which can
however be the refinement of a formal interpretation already constrained at the ontological
level.
5. Conclusions
In Brachman, Fikes et al. 1983, the authors discussed the example reported in Fig. 7
below. They argued that a question like “How many kinds of rocks are there?” cannot be
answered by simply looking at the nodes subsumed by ‘rock’ in the network, since the
language allows them to proliferate easily. Hence they give up answering such dangerous
questions within a KR formalism, by specifying a functional interface designed to answer
“safe” queries about analytical relationships between terms independently of the structure of
the knowledge base, like “a large grey igneous rock is a grey rock”. On the other hand, the
10
same authors, in an earlier paper
26
, stressed the importance of terminological competence in
knowledge representation, stating for instance that an “enhancement mode transistor” (which
is “a kind of transistor”) should be understood as different from a “pass transistor” (which is
“a role a transistor plays in a larger circuit”).
rock
igneous rock
sedimentary rock
metamorphic rock
large rock grey rock
large grey igneous rock
grey
sedimentary
rock
pet metamorphic rock
Fig. 7. Kinds of rocks (From Brachman, Fikes et al. 1983)
We hope to have shown in this paper that – in the spirit of Woods’ statement cited in
section 3 – terminological competence can be gained by formally expressing the ontological
commitment of a knowledge base. If, in the example above, predicates corresponding to
rock, igneous-rock, sedimentary-rock and metamorphic-rock are marked as substantial
sortals (as they should be according to their ordinary meaning), while all the others are
marked as non-substantial sorts (since they are not rigid), then a safe answer to the query
“how many kinds of rocks are there?” would be “at least 3”.
It is important to make clear however that the complete formal characterisation of the
taxonomy described in section 3 – and the taxonomy itself – are still a matter of discussion.
In particular, the notion of divisiveness is still problematic
27
, since we may assume for
instance that there are parts of an igneous rock which are still rocks, invalidating the example
above (but not its spirit). Our answer to this objection is that in the notion of a rock, and of a
physical object in general, there is implicit a notion of external boundary
28
, such that an
undetached part of a rock is not a rock, but just a part of it: this is why we can answer a
question like “how many rocks are there?”, while it is difficult to answer “how many parts of
rock are there?”. A more thoroughly account of the basic ontology sketched in section 3 will
be the subject of a forthcoming paper; the preliminary distinction criteria introduced here have
in our opinion the advantage of simplicity, avoiding the need to make use of subtle notions
like ontological foundation, discussed in previous works
29
.
The title chosen for this paper should however suggest to the reader that the particular
ontology of unary predicates we have proposed is not the main issue here. Rather, we
believe that the main contribution of section 3 is the notion of ontological commitment
expressed in terms of a modal framework: the use of a modal logic, as a tool to constrain the
intended semantics of the underlying non-modal theory, seems to be unavoidable if we wish
to express ontological constraints unambiguously. In the perspective of formal ontology
mentioned in the introduction, these constraints should also be related to a priori distinctions
among the entities of the world, while we have limited ourselves to meta-level categories. Far
from claiming to have said the last word on the latter issue, we tried to show here that (i)
some formal properties which account for distinctions among predicate types can indeed be
11
worked out, although complete, unproblematic definitions may not be given; (ii) when the
semantics of structuring primitives used in KR languages is restricted in order to take into
account such formal distinctions at the ontological level, the potential misunderstandings and
inconsistencies due to conflicting intended models are reduced; (iii) further research in this
area is needed, and it should be encouraged within the KR community, in co-operation with
the philosophical and linguistic communities.
Acknowledgements
I am especially indebted to Massimiliano Carrara and Pierdaniele Giaretta for having
introduced me to the philosophical distinctions concerning universals. I also thank Luca
Boldrin, Matteo Cristani, Barry Smith and Claudio Sossai for their valuable comments on
earlier versions of this paper.
Notes
1 Brachman 1979.
2 Brachman 1979, p. 30.
3 Brachman 1979, Brachman and Schmolze 1985.
4 Woods 1975.
5 See for instance Davis, Shrobe et al. 1993.
6 See Genesereth and Nilsson 1987.
7 The use of the term “epistemology” sounds somehow reductive here, but I believe this reflects its
common understanding in the KR literature.
8 A preliminary ontological analysis of the primitives used in KL-ONE-like formalisms appeared in
Guarino 1992, while the notion of ontological level has been first introduced in Guarino and Boldrin
1993a and Guarino and Boldrin 1993b.
9 Formal ontology has been recently defined as "the systematic, formal, axiomatic development of the
logic of all forms and modes of being" Cocchiarella 1991.
10 See Strawson 1959, Wiggins 1980.
11 Strawson 1959 p. 168.
12 See Pelletier and Schubert 1989 for an overview.
13
Woods 1975. For a philosophical position different from the one criticized by Woods, see Mulligan et al.
1984.
14 Gruber 1993.
15 Wiggins 1980; Carrara 1992.
16 Cocchiarella 1993.
17 Putnam 1981, cited in Aune 1991, p. 543.
18 We use here the terminology introduced in Fitting 1993.
19 Cocchiarella 1993.
20 Barcan Marcus 1968.
21 In Pelletier and Schubert 1989 they are called “super sortals”.
22
Regarding the criticisms made for instance in Pelletier and Schubert 1989, see the comments in the
conclusions. See also Guarino et al. 1993 for a finer account of this and other ontological distinctions.
23 See for instance Simons 1987. We assume here that L
m
and C are suitably extended to nclude <.
24 Cocchiarella 1993, Cocchiarella 1977.
25 See a brief review in Woods and Schmolze 1992.
26 Brachman and Levesque 1982.
27 Pelletier and Schubert 1989.
27 Smith 1992.
27 Guarino and Boldrin 1993a.
12
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Author address:
Nicola Guarino, LADSEB-CNR, National Research Council, I-35020 Padova, Italy
tel. +39 49 8295751, fax +39 49 8295763, email guarino@ladseb.pd.cnr.it
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