Folks, (01)
As a general definition that covers all ontologies, formal
and informal, I endorse the suggestion by Michael Gruninger: (02)
> The ecumenical definition of "ontology" that Mike Uschold
> and I have used is:
>
> "An ontology includes a vocabulary of terms together with
> a specification of the intended meaning of the terms." (03)
But I also sympathize with Chris Menzel about having a
purely formal definition, especially for formal ontologies.
Unfortunately, the definition of ontology as the equivalent
of a logical theory does not distinguish the vocabulary
that is being defined by the theory from other terms that
may be used in the theory and defined elsewhere. (04)
But that distinction can be made in a purely formal way
just by adding a metalevel note that distinguishes which
terms in the theory constitute the vocabulary that is
being specified. (05)
Following is my suggested specialization of the Gruninger-
Uschold definition to cover formal ontologies: (06)
A formal ontology consists of a theory T stated in some
version of logic and a nonempty vocabulary V. The vocabulary
V is a subset of the names of types and relations used in T. (07)
For example, the following statements constitute a theory, but
not an ontology, because they do not state which terms are being
defined: (08)
There is a man named Bob who is taller than a man named Joe. (09)
Every individual named Tiny Tim is shorter than any
individual named Big Bad Bob. (010)
No letters in circular envelopes are delivered on Tuesdays. (011)
This theory also has many other features that would make it
bad as the theory part of any ontology, such as the inclusion
of low-level statements about individuals. The question of what
makes a good or bad ontology is very important, but that is a
separate issue from the definition of "ontology". (012)
Following is a better specification of an ontology. (013)
Vocabulary: {loopyLetter} (014)
Theory: (015)
Every loopyLetter is a letter in a circular envelope. (016)
No loopyLetter is delivered on a Tuesday. (017)
This would be a special-case ontology that uses terms that may
be defined in other ontologies: letter, in, circular, envelope,
deliver, Tuesday. (018)
John Sowa (019)
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