On 11 Feb, at 1:08 , John F. Sowa wrote:
> ...
> The definition I proposed on January 30 includes everything
> you've requested so far:
>
> 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. (01)
John, I think I might agree with you that something along these lines
is a better definition of "formal ontology" than mine (via., that
"formal ontology = logical theory"). It does seem to capture
something important about proposed ontologies that is missing from
many logical theories. However, it needs a bit of work. First, you
say that T is stated in terms of a nonempty vocabulary V; then you
suggest that V is only a subset of the type and relation names in T.
But you have identified V as T's vocabulary; how could it *fail* to
be anything other than the type and relation names used in T? In
fact, V could well contain vocabulary not used in T (perhaps the
developer intends to extend T or something). So, if anything, it
seems to me that "subset" there should be "superset" (where superset
is taken to be reflexive). (02)
Note however that, even with this revision, there is still the
possibility of "vacuous" ontologies; imagine, e.g., a theory whose
only axiom is "Every loopyletter is a loopyletter". This seems to me
to meet your definition. Hence, you might consider adding that T
must contain at least one axiom that is not a logical truth.
However, because logical truth is only semi-decidable, adding that
qualification now makes it the case that there is no general
procedure for determining whether or not any particular logical
theory is *really* an ontology. (This is one of the reasons I simply
opted for allowing any logical theory to be considered a formal
ontology.) However, in practice it will probably always be the case
that one can demonstrate that at least one of the axioms of a
proposed ontology is not a logical truth. (This is easy to do for,
e.g., PSL.) So maybe the qualification is innocuous; it's
*possible*, but really unlikely, that anyone would attempt to develop
an ontology that turned out to be logically vacuous. At the least,
it seems reasonable that the risk of a subtly vacuous logical theory
being counted as an ontology (and really, *who cares* if that ever
happens?) is greatly outweighed by the benefits of being able to
exclude obviously vacuous logical theories from being considered
genuine ontologies. (03)
Chris Menzel (04)
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