Definitions of Ontology - First Part: from Christian Wolff to Edmund Husserl
SUMMARY
INTRODUCTORY REMARKS
a) One of the best available dictionaries gives the following definition of Ontology:
"1. A science or study of being: specifically, a branch of metaphysics relating to the nature and relations of being; a particular system according to which problems of the nature of being are investigated; first philosophy.
2. a theory concerning the kinds of entities and specifically the kinds of abstract entities that are to be admitted to a language system." (1)
b) The first sense is commonly used in the philosophical tradition:
"In contemporary philosophy, formal ontology has been developed in two principal ways. The first approach has been to study formal ontology as a part of ontology, and to analyse it using the tools and approach of formal logic: from this point of view formal ontology examines the logical features of predication and of the various theories of universals. The use of the specific paradigm of the set theory applied to predication, moreover, conditions its interpretation.
The second line of development returns to its Husserlian origins and analyses the fundamental categories of object, state of affairs, part, whole, and so forth, as well as the relations between parts and the whole and their laws of dependence - once all material concepts have been replaced by their correlative form concepts relative to the pure 'something'. This kind of analysis does not deal with the problem of the relationship between formal ontology and material ontology." (2)
c) The second sense is used in research on Artificial Intelligence and Knowledge Representation; one of the best known definitions is Tom Gruber's:
"An ontology is an explicit specification of a conceptualization.
The term is borrowed from philosophy, where an ontology is a systematic account of Existence. For knowledge-based systems, what “exists” is exactly that which can be represented. When the knowledge of a domain is represented in a declarative formalism, the set of objects that can be represented is called the universe of discourse. This set of objects, and the describable relationships among them, are reflected in the representational vocabulary with which a knowledge-based program represents knowledge. Thus, we can describe the ontology of a program by defining a set of representational terms. In such an ontology, definitions associate the names of entities in the universe of discourse (e.g., classes, relations, functions, or other objects) with human-readable text describing what the names are meant to denote, and formal axioms that constrain the interpretation and well-formed use of these terms." (3)
This definition has been criticized by Nicola Guarino that, after examining seven possible interpretations of ontology, (4) writes:
"A starting point in this clarification effort will be the careful analysis of the interpretation adopted by Gruber. The main problem with such an interpretation is that it is based on a notion of conceptualization (introduced in: Genesereth, Michael R. and Nilsson, L. "Logical Foundation of Artificial Intelligence" Morgan Kaufmann, Los Altos, California, 1987) which doesn't fit our intuitions, (...): according to Genesereth and Nilsson, a conceptualization is a set of extensional relations describing a particular state of affairs, while the notion we have in mind is an intensional one, namely something like a conceptual grid which we superimpose to various possible state of affairs. We propose in this paper a revised definition of a conceptualization which captures this intensional aspect, while allowing us to give a satisfactory interpretation to Gruber's definition." (5) Guarino gives this definition: "Since this paper is deliberately addressed to an interdisciplinary audience, it is advisable to pay attention to some preliminary terminological clarifications, especially because some crucial terms appear to be used with different senses in different communities'. Let us first consider the distinction between "Ontology" (with the capital "o"), as in the statement "Ontology is a fascinating discipline" and "ontology" (with the lowercase "o"), as in the expressions "Aristotle's ontology" or "CYC's ontology". The same term has an uncountable reading in the former case, and a countable reading in the latter. While the former reading seems to be reasonably clear (as referring to a particular philosophical discipline), two different senses are assumed by the philosophical community and the Artificial Intelligence community (and, in general, the whole computer science community) for the latter term.
In the philosophical sense, we may refer to an ontology as a particular system of categories accounting for a certain vision of the world. As such, this system does not depend on a particular language: Aristotle's ontology is always the same, independently of the language used to describe it. On the other hand, in its most prevalent use in AI, an ontology refers to an engineering artifact, constituted by a specific vocabulary used to describe a certain reality, plus a set of explicit assumptions regarding the intended meaning of the vocabulary words. This set of assumptions has usually the form of a first-order logical theory, where vocabulary words appear as unary or binary predicate names, respectively called concepts and relations. In the simplest case, an ontology describes a hierarchy of concepts related by subsumption relationships; in more sophisticated cases, suitable axioms are added in order to express other relationships between concepts and to constrain their intended interpretation.
The two readings of ontology described above are indeed related each other, but in order to solve the terminological impasse we need to choose one of them, inventing a new name for the other: we shall adopt the AI reading, using the word conceptualization to refer to the philosophical reading. So two ontologies can be different in the vocabulary used (using English or Italian words, for instance) while sharing the same conceptualization." (6)
(1) Webster's Third New International Dictionary
(2) Liliana Albertazzi - "Formal and material ontology" in: Roberto Poli & Peter Simons (ed.) - "Formal Ontology" - Kluwer 1996 p. 199
(3) Tom Gruber "A translation approach to portable ontology specifications". In: Knowledge Acquisition 5, (1993) pp. 199-220
(4) Nicola Guarino - "Ontologies and Knowledge Bases. Towards a terminological clarification" (1995) p. 1
(5) ibid. p. 2
(6) Nicola Guarino "Formal ontology and information systems". In: N. Guarino (ed.), Formal Ontology in Information Systems. Proceedings of the First International Conference, Trento, Italy, 6-8 June 1998. IOS Press, 1998 p. 4
DESCRIPTIVE, FORMAL AND FORMALIZED ONTOLOGY
"I shall distinguish descriptive, formal and formalized ontology. Each of these ontologies comes in two guises: domain-dependent and domain-independent. Domain-dependent ontologies concern categorically closed regions of being; on the other hand, a domain independent ontology may be properly called general ontology. (...)Descriptive ontology concerns the collection of such prima facie information either in some specific domain of analysis or in general.
Formal ontology distills, filters, codifies and organizes the results of descriptive ontology (in either its local or global setting). According to this interpretation, formal ontology is formal in the sense used by Husserl in his Logical Investigations. Being 'formal' in such a sense therefore means dealing with categories like thing, process, matter, whole, part, and number. These are pure categories that characterize aspects or types of reality and still have nothing to do with the use of any specific formalism.
Formal codification in the strict sense is undertaken at the third level of theory construction: namely that of formalized ontology. The task here is to find the proper formal codification for the constructs descriptively acquired and formally purified in the way just indicated. The level of formalized constructions also relates to evaluation of the adequacy (expressive, computational, cognitive) of the various formalisms, and to the problem of their reciprocal translations.
The close similarity between the terms 'formal' and 'formalized' is somewhat unfortunate. One way to avoid the clash is to use 'categorical' instead of 'formal'.
Most contemporary theory recognizes only two levels of work and often merges the level of the formal categories either with that of descriptive or with that of formalized analysis. As a consequence, the specific relevance of categorical analyses is too often neglected.
The three levels of ontology are different but not separate. In many respects they affect each other. Descriptive findings may bear on formal categories; formalized outcomes may bear on their twin levels, etc. To set out the differences and the connections between the various ontological facets precisely is a most delicate task."
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