=Paper=
{{Paper
|id=Vol-85/paper-10
|storemode=property
|title=The Differentia Principle as a Cornerstone of Ontology
|pdfUrl=https://ceur-ws.org/Vol-85/roche.pdf
|volume=Vol-85
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==The Differentia Principle as a Cornerstone of Ontology==
https://ceur-ws.org/Vol-85/roche.pdf
“Knowledge Management and Philosophy” Workshop in WM 2003 Conference, Luzern, 2-4 april, 2003
The Differentia Principle
as a Cornerstone of Ontology
Prof. Christophe ROCHE
Université de Savoie - Campus Scientifique
73 376 Le Bourget du Lac - cedex - France
tel : +33 (0) 4 79 75 87 79 - fax : +33 (0) 4 79 75 88 88
roche@univ-savoie.fr - http://ontology.univ-savoie.fr
Abstract
The Information Society relies more and more on the co-operation and collaboration of multi-
disciplinary people who need to communicate and share information. Communication and knowledge
sharing are the new economic stakes. But everyone speaks his own language, with his own terms and
meanings. The information society is a Tower of Babel which has to evolve to the knowledge society.
Since the beginning of the nineties, ontologies seemed being as one of the most suitable solutions
faced with this problem and became a very popular research topic in knowledge representation.
Nevertheless several problems remain which claim for clarification. As a matter of fact, there is no
agreement about what an ontology is; and the numerous systems as well as not very clear
epistemological principles are barriers to the real use of ontologies. The ontology problem requires a
multidisciplinary approach based on sound epistemological, logical and linguistic principles.
This article presents the “differentia” principle , as it appears in Aritotle’s works and Porphyry’s
Isagoge, as a cornerstone for building ontology. We shall see that the metaphysical point of view is a
guarantee for ontology commitment, reuse and sharing.
This approach will be illustrated with the OK (for Ontological Knowledge) computational model and
the associated ontology-oriented language LOK.
keywords: ontology, differentia, Porphyry’Isagoge, knowledge representation, terminology,
computational model.
1 Introduction To address this problem, we need a common
(communication) language that actors can read
The Information Society relies more and more and understand. Using a single, normalised
on the co-operation and collaboration of multi- language like KQML (Knowledge Query
disciplinary people who need to communicate, Manipulation Language [3]) can reduce the gap
share and exchange information [1], [2]. of misunderstanding by using a same syntax.
Communication and knowledge sharing are the But, although such languages give some useful
new economic stakes. indications about the pragmatic content of the
The Information Society, virtual enterprise, e- message (by using predefined performatives i.e.
business, etc. rely on communication between commitment actions), the semantic problem has
of interacting and heterogeneous actors : still to be addressed. As a matter of fact, two
people, organisations and even software actors can communicate only if they agree upon
systems. The communication is difficult due to on the meaning of the terms they use.
the fact that each of these actors speaks a Ontology, understood as an agreed vocabulary
different language. The information society is of common terms and meanings wit hin a group
the new Tower of Babel which has to evolve to of people, is a solution to the communication
the knowledge society. and knowledge sharing problem.
C. Roche - “The Differentia Principle as a Cornerstone of Ontology “ - University of Savoie p. 1
“Knowledge Management and Philosophy” Workshop in WM 2003 Conference, Luzern, 2-4 april, 2003
2 Ontology 3 Objectives
Since the beginning of the nineties, ontologies Our main objective is to define the meaning of
have become a very popular research topic in terms (words) which refer to conceptual
computer science including knowledge knowledge (e.g. concepts used in a corporate
representation and infor mation management. knowledge as ‘turning’, ‘milling’, ‘stamping’…
Such a popularity is due to the fact that in a ‘mechanical machining’ ontology). It
ontology provides a means of capturing a implies that we rely on the classical semiotic
shared understanding of terms that can be used triangle 1 [ “term” - - example ]
by humans and programs. where the meaning of a term is the concept to
It is amusing to note that when the main goal of which it refers to.
ontology is to normalise the meaning of terms, Building consensual and coherent ontologies
the term "ontology" itself is not clearly defined: seems a quite unreachable goal without clear
“although ontology is currently a fashionable and sound principles. It is the reason why we
term, no agreement exists on the exact meaning claim that such a problem requires a
of the term” and “seems to generate a lot of multidisciplinary approach:
controversy in discussion about AI (artificial
- Linguistic, as we use words to communicate,
intelligence)” [4], [5]. In fact, ontology finds
- Epistemological, since words refer to
applicability in many domains of application in
knowledge (here concepts) which represents
knowledge and software engineering, and each
of them gives its own definition. their meaning,
Let us see some examples from the general, and - Logical, in order to guarantee some
famous, Gruber’s definition: “An ontology is a coherence.
specification of a conceptualisation” [4] to a
In order to lay stress on the fact that the
more dedicated one: “The main purpose of an
ontology problem is mainly a linguistic (we use
ontology is to enable communication between
words to communicate) and an epistemological
computer systems in a way that is independent
of the individual system technologies, problem (these words have a meaning), we shall
information architectures and application set down our own definition of ontology:
domain.” [6].
« A n ontology is a conceptualisation to which
Nevertheless, although an ontology may take a
one or several vocabularies can be associated
variety of forms, it will include a vocabulary of and which participates to the meaning of terms.
terms and some specification of their meaning Defined for a given objective, an ontology
[6], [7], [8], [9]. expresses a point of view shared by a community.
The result is ontology has gained considerable An ontology is represented in a language whose
popularity and several ontologies were defined, theory (semantics) guarantees the properties of
whether general or specific: Cyc, Mikrokosmos, the ontology in terms of consensus, coherence,
Enterprise Ontology, TOVE, Sowa’s, etc. as sharing and reuse. »
well as ontology-oriented languages and
software environments were realised: OIL, Well, but what about the theory ?
DAML, Protégé, KAON, Ontolingua…
But, several problems remain which claim for 4 Porphyry’s Isagoge
clarification. As a matter of fact, it is very
difficult to reuse and share ontologies. For Words have a weight. Unlike some computer
example, how can we combine the definitions scientists 2 , we think that we have to keep in
coming from the two enterprise ontologies mind that ontology belongs to metaphysics. Let
TOVE [10] and Enterprise Ontology [11] ?
The differences between the semantics of the 1
from a linguistic point of view, one speaks of a
systems, as well as not very clear combination of a “signifier” and a “signified”
epistemological principles, are barriers to the (Saussure’s structuralism).
2
real use and re-usability of ontologies. And how “The use of the term ontology is somewhat
can we trust in, and then use, an ontology which unfortunate since it has a definite meaning in the
does not offer “any kind of guarantees” [12] ? philosophical literature which has little to do with
describing the content of information repositories”.
KACTUS - Esprit Project 8145.
C. Roche - “The Differentia Principle as a Cornerstone of Ontology “ - University of Savoie p. 2
“Knowledge Management and Philosophy” Workshop in WM 2003 Conference, Luzern, 2-4 april, 2003
us begin from an etymological point of view. linguistic. It focuses on the essence of objects
Ontology come from the Greek ‘ontos’, whose rather than on what could opposite words 5 .
meaning is being, and from the Greek ‘logos’,
whose meaning is both language and reason. 5.1 Concept
So, when some people say that “Ontology is the
branch of metaphysics that deals with the nature If the concept is the meaning of term, its own
of being” and others “an Ontology is a meaning is clearly defined:
systematic account of Existence3 ” it is not the
same definition : Being and Existence are “a concept is defined by specific differentiation.
different. It means that a concept is defined from a
previously existing concept adding a new
Building ontologies is a difficult tasks, in differentia which is then called the ‘specific
particular if we want some guarantees like differentia’ of the newly created concept”.
consensual definitions. It is necessary to follow
clear guidelines based on sound epistemological Such a recursive definition tightly links
principles. Let us give some of them : concepts and introduces an important new
notion: the differentia. The “specific
- set and concept are two different notions. A differentia” relationship between two concepts
set is not a concept, even if a concept can be is more than the classical “is-a” relationship
understood as a set of individuals subsumed since it introduces constraints between the
by the concept, sibling and subsumed concepts. Let us notice
- valued attributes describe the state of things that the meaning of a concept can also be
but do not define them, defined by the set of its differentiae.
- a concept is not a well formed formula:
“Being is. Being is not true or false”. 5.2 Differentia & Accident
It is the reason why the Porphyry’s Isagoge Differentiae are the elementary units from
always remains a novel work for knowledge which the meaning of a concept is built. This
representation. The quinque voces (the five means that the differentiae have no meaning in
predicables): genus, differentia, species, themselves. Unlike an attribute a differentia
proprium and accident can be considered as cannot be removed from the definition of an
backbone principles for building ontology. object without changing its nature; nor be
valued. For example, for the ‘Turning’ concept,
The fundamental idea is that concepts are ‘piece rotation’ is a differentia whereas
organised according to the essence of things and ‘rotation speed’ is an attribute.
not according to their state.
A differentia is an unit from which meanings
Differentia and accident allow to clearly are built and which divides concepts into two
identify essential knowledge when genus and no connected sets. In fact, adding a differentia
species allow to identify and organize concepts. to an existing concept creates two new ones, the
first one to which the differentia belongs to and
the second one which will never be able to own
5 The Differentia Approach that differentia . That differentia is called the
“specific differentia” of the former new
The approach by differentia 4 fulfils the criteria concept. The fact that a differentia cannot
previously defined. In fact this approach is belong to a concept is itself a specific
more epistemological and logical than differentia which can also be named. This is the
reason why differentiae are defined by couples
of opposite differentiae, like ‘metal
3 5
For AI systems, what "exists" is what can be unlike Saussure’s Structuralism which opposes
represented. rather than to define. Nevertheless combining
4
we prefer to use “differentia” (differentiae in structuralism and differentia is fruitful: arbitrary
plural) rather than “difference” which is too vague in nature of signs, meaning structure, finite number of
English when differentia is a very specific thing. differentiae as elementary units of meaning.
C. Roche - “The Differentia Principle as a Cornerstone of Ontology “ - University of Savoie p. 3
“Knowledge Management and Philosophy” Workshop in WM 2003 Conference, Luzern, 2-4 april, 2003
preservation’ and ‘no metal preservation’ or 5.3 Properties
‘material removal’ and ‘material deposit’. Thus,
owning a differentia for a concept implies it The definition of concepts by specific
will never contain the opposite differentia, nor differentiation could appear quite restricting,
the concepts it could subsume. Such a property but in fact it offers several good properties
will be very useful for building and using which explain such a choice:
ontologies. It is a guarantee of the coherence of
the ontology and forbid multiple inheritance. - everybody can agree with this definition: an
‘Electro-plating’ is an ‘electro chemical’
The meaning of concepts is then structured into ‘Machining’;
binary trees based on couples of opposite - the differentiae are the elementary units of
differentiae. The specific differentia of a meanings. This implies that the agreement
concept is the opposite specific differentia of its problem is reduced to the sole problem of
sibling, and vice versa. In fact, the concept tree agreement on the differentia names and not
is less important than the sets of differentiae on the concept names ;
which define the concepts. As a matter of fact, - no multiple hierarchy and therefore no
the differentia is the elementary unit of meaning problem of inheritance of different values;
and the concept names are arbitrary. - sound logical properties which are exploited
Furthermore, the same sets of differentiae can during the building of ontology and which are
be represented by different binary trees as the also exploited in applications.
order of differentiae in a set does not matter ( a
‘Human Being’ is a ‘Being’ which is mortal 6 The OK Model
and reasonable or a ‘Human Being’ is a ‘Being’
which is reasonable and mortal). So, we can A computational model based on differentia
conclude that: “the meaning of a term is defined theory, called OK for Ontological Knowledge,
by a set of differentiae”. was defined as well as a dedicated language,
Such a definition and the fact that differentiae called LOK, and a software environment, the
are defined by couples of opposite differentiae OK Station©.
imply a logical semantics of term meaning. This
logical semantics is a guarantee of coherent 6.1 The LOK language
ontologies and it is very useful for applications:
information retrieval, acquisition... The LOK language (Language for Ontological
Last but not least, the agreement problem is Knowledge) is an ontology-oriented language
reduced to the sole problem of agreement on the composed of more than 150 instructio ns, with a
terms that denotes differentiae. It is all the ‘à la Lisp’ syntax. Those instructions are
simpler since the application domain is structured into two sets. The first set contains
technical and the differentiae are ‘visual’ and all the necessary instructions for definition and
‘concrete’ like ‘tool rotation’, ‘no metal modification of ‘term-meaning’ couples that
preservation’, etc. and since few couples of constitute the ontology. Let us take an example
opposite differentiae (let us say n couples) can extracted from the following simple ontology
define a lot of concept names (until to 2n about machining (see figure 1).
names).
C. Roche - “The Differentia Principle as a Cornerstone of Ontology “ - University of Savoie p. 4
“Knowledge Management and Philosophy” Workshop in WM 2003 Conference, Luzern, 2-4 april, 2003
figure 1. a simple example of ontology
The building of this ontology begins by the Machining’ plus the specific differentia ‘metal
definition of the differentiae using the preservation’.
‘defineDifference’ LOK function: This simple mechanical machining ontology is
( defineDifference defined by the following LOK file (figure 2):
‘metal preservation’),
(defineDifference
‘piece rotation’ ‘tool rotation’ ),
The last instruction creates two opposite
differentiae whereas the ‘(defineDifference
‘metal preservation’)’ instruction creates only
one differentia. In this latter case, the opposite
differentia is automatically created with the
same name and the prefix ‘a-‘ (‘a-metal
preservation’).
As a concept is defined from a previously
existing one, the first thing to do is to create a
root concept. This is done with the
‘defineRootConcept’ instruction. For example
the following LOK instruction :
( defineRootConcept
‘Mechanical Machining’ )
creates a new term, the string ‘Mechanical
Machining’, without meaning because it is the
root.
After that, new concepts can be defined. This
consists in giving a new term and its meaning figure 2. a LOK file
built from the meaning of an existing concept
along with a specific differentia: The second set of instructions are exploiting
( defineConceptFrom 'Mechanical Machining' instructions mainly for queries. For examples:
( rightConcept 'Stamping' (allConceptsWithDifference
( specificDifference 'a-metal preservation')
'metal preservation' ))) returns the two terms ‘Milling’ and ‘Turning’
creates the new term ‘Stamping’, whose whereas : (listOfLeafConcepts)
meaning is the meaning of ‘Mechanical
C. Roche - “The Differentia Principle as a Cornerstone of Ontology “ - University of Savoie p. 5
“Knowledge Management and Philosophy” Workshop in WM 2003 Conference, Luzern, 2-4 april, 2003
returns the terms ‘Turning’, ‘Milling’ and References
‘Stamping’ as they are the only concepts from
which new ones can be defined (leaf concepts). [1] G.R. Olsen, M. Cutkosky, J.M. Tenenbaum, T.R.
All these instructions are used by the different Gruber. “Collaborative Engineering based on
modules of the OK Station. Knowledge Sharing Agreements”, ASME Database
Symposium, Minneapolis, 1994
[2] T.R. Gruber, J.M. Tenenbaum, J.C. Weber. “Toward
7 Conclusion a Knowledge Medium for Collaborative Product
Development”, Artificial Intelligence in Design
If ontologies have gained a large popularity in Conference, Pittsburgh, USA 1992
many domains of application as one of the most [3] Y. Labrou, T. Finin “A proposal for a new KQML
suitable solutions faced with the communication Specification”, Internal Report TR CS-97-03,
and knowledge sharing problems, several Computer Science and Electrical Engineering
problems remain. As a matter of fact, an Department (CSEE), University of Maryland
Baltimore County (UMBC), February 1997.
ontology will really be used only if everybody
agrees on it and if some consistency is ensured. [4] T.R. Gruber, http://www-ksl.stanford.edu/kst/ what-
Using a same language is not sufficient, clear is-an-ontology.html
linguistic and epistemological principles are [5] Nicola Guarino “Ontologies and Knowledge Bases.
needed in order to reach a real ontology Towards a Terminological Clarification” Towards
Very Large Knowledge Bases, IOS Press,
commitment. Ontology problem requires a Amsterdam, 1995
multi-disciplinary approach.
[6] http://www.ontology.org
We claim that the metaphysical approach of [7] http://www.ontoknowledge.org/oil/
ontology must be kept in mind and that the [8] M. Uschold, M. Gruninger. “Ontologies: Principles,
Porphyry’s Isagoge always remains a novel Methods and Applications” Knowledge Engineering
work for knowledge representation. The Review, vol ; 11, n°2, June 1996
quinque voces (the five predicables): genus, [9] Mike Uschold and Martin King “Towards a
differentia, species, proprium and accident can Methodology for Building Ontologies” internal
be considered as backbone principles for report AIAI-TR-183, July 1995
building ontology. The fundamental idea is that [10] M.S. Fox, The TOVE Project: Towards a Common
concepts are organised according to the essence Sense Model of the Enterprise, in Enterprise
of things and not according to their state. Integration, C. Petrie (Ed.), Cambridge MA: MIT
Press, 1992
At last, we presented a model for ontological [11] M. Uschold, M. King, S. Moralee, Y. Zorgios, “The
knowledge called OK (Ontological Knowledge) Enterprise Ontology” AIAI, The University of
Edinburgh, 1997
dedicated to conceptual knowledge, i.e. to the
meaning of terms denoting abstract knowledge [12] K. Mahesh “Mikrokosmos” http:// crl.nmsu.edu
/Research/Projects/mikro/htmls/ontology -htmls
(concept). This model is based on the “specific
/onto.index
differentia” theory which relies on sound
principles taken into account linguistic and
epistemological notions which may appear quite
restricting. But such an approach where a
concept is defined by specific differentiation
provides many advantages: consensual
definitions and logical properties which ensure
consistency which are guarantees of ontology
commitment, reuse and sharing.
The OK model has been imple mented. The
result is the OK Station© , a software
environment dedicated to building, defining and
exploiting ontologies. It is currently used to
define ontologies in various areas.
C. Roche - “The Differentia Principle as a Cornerstone of Ontology “ - University of Savoie p. 6