General Formal Ontology (GFO)
An ontology - understood as a formal knowledge base - is given
by an ``explicit specification of a conceptualization''
(24). This specification - understood as a formal one -
has to be expressed and presented
in a formal language, and there are a variety of formal specification
systems. A point to be clarified is what representation means. In the
analysis of this notion we use the notion of denotation and symbolic structure.
This indicates that in a representation one kind of category cannot be avoided,
the category of symbolic structure.
A main distinction may be drawn between logical languages with model-theoretical
semantics and formalisms using graph-theoretical notations. We sketch
some ideas about both types of formalisms.
A model-theoretic language consists of a structured vocabulary
and a set of axioms
which are formulated in a
. Hence, an ontology (understood as a formal
object) is then a system
; the symbols of denote
categories and relations between categories or between their
instances. can be understood as an operator which associates to a
vocabulary a set of expressions which are usually declarative
formulas. We assume the following conditions:
. An ontology
may be augmented by a derivability relation, denoted by , and
by a semantic consequence relation, denoted by . Then, such
an ontology takes the form of a knowledge system
which includes a class of
interpretations which serves as a semantics for the language .
Graph-based formalisms for ontologies, as they are common for biological
ontologies or at least related to medical terminologies, can be
understood in the following way. Such an ontology is a
. Terms usually cover natural
language aspects and are assigned to concepts and relations . Moreover,
the relations connect concepts, which yields a labelled graph structure
over concepts, such that edges are labelled by
relations. The definitions which are held in such systems, if any,
are usually natural language definitions, sometimes in a semi-structured
Particular systems of this kind can vary in several respects, e.g.
focusing on the distinction between terms and concepts, the
extent to which definitions are provided, the number of relations
available, etc.; a corresponding overview and classification in the
field of medical terminologies can be found in