Leo, Steve, and Doug, (01)
To start with Leo's concluding comment, (02)
LO> So I am not convinced that (ontology = logical theory) only. (03)
The relevant clause of the definition specifies that an ontology
is a theory that (04)
characterizes the entities of some domain, which may be
concrete or abstract, real or virtual. (05)
That distinguishes an ontology from a theory that just states
some arbitrary facts about some entities that may be defined,
specified, or identified elsewhere. (06)
LO> Although mathematical theories are abstract, are they not
> a part of the world? By part of the world, I don't necessarily
> mean empirically determinable (though even this can beg the
> question). (07)
That gets into philosophical issues that can be left to other
discussions. My short answer is that a pure (i.e., unapplied)
mathematical theory defines abstract entities that are outside
any kind of space-time coordinates. Therefore, it would be odd
or unusual to say that they were "part" of anything physical,
but they might be "applied" to something physical. (08)
The next two comments are closely related: (09)
SR> We were trying to come up with a categorization scheme into
> which we could place everything that anyone calls an ontology,
> whether it is computer processable or not, consistent or not,
> correct or not. (010)
DH> So, then what should said about folksonomies, topic maps,
> lots of schema that were devised without a theory in mind, and
> all those others that seem to be used "like" these theories?
> In my view, at least, we were trying to understand and somehow
> characterize the common ground that links all these things. (011)
Several points: (012)
1. I explicitly said "formal ontology", but I agree that a more
general definition should say how the other kinds of things
are related to a formal ontology. (013)
2. My definition of logic includes natural languages as supersets
of any or all of the formal logics that have ever been invented.
Therefore, definitions in natural languages are also acceptable
for an ontology, although a machine might not be able to interpret
them. I would call them informal ontologies. (014)
3. My definition of theory is also very general: Any set of axioms
stated in any version of logic, which would include natural
languages for the informal theories. (015)
4. Re folksonomies: I hate that term because it sounds disparaging.
I have nothing against informal classifications, many of which
are superior to some of the so-called formal ones. (016)
5. Re topic maps: I consider them a form of logic, and some versions
of TMs have been formally specified, but other versions are used
in a way that would put them in the informal category. (017)
6. Re "lots of schema that were devised without a theory in mind":
The fact that a theory has not been formally specified does not
imply that the author has "no theory in mind". On the contrary,
people have lots of theories in their minds, which for better
or worse have major impacts on what they do. As my favorite
philosopher C. S. Peirce said, "Every man of us has a metaphysics,
and has to have one; and it will influence his life greatly.
Far better, then, that that metaphysics should be criticized
and not be allowed to run loose." (018)
7. Re common ground: If we generalize the definition by deleting
the word "formal", we get a definition that includes all of the
other proposals. (019)
Following is my previous definition, but generalized to include
informal as well as formal theories: (020)
An ontology is a theory expressed in some language, natural or
artificial, that defines the types, relations, and functions
that characterize the entities of some domain, which may be
concrete or abstract, real or virtual. (021)
If you add the word "formal", then the language must be some
version of formal logic, which could be stated in a formalized
or controlled natural language. Aristotle's original syllogisms,
for example, are a version of formal logic stated in a controlled
dialect of Greek. (022)
John Sowa (023)
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