Folks (01)
Having followed this forum for some time, I have a feeling that I may have
missed something so obvious that noone has thought to mention it  that is,
is there a formal definition of an ontology? An ontology cannot be just be a
bowl of axiom soup, so how does one tell that a particular collection of
axioms is an ontology  the question is posed on the analogy that
mathematicians differentiate between a group, a ring and a field by the
axioms they include. My naive guess for this would be based on set theory,
and look something like: (02)
1) A set S can be defined as S = {x s.t. x satisfies some combination of
predicates};
2) Given a set of predicicates P = {p1, p2,...,pn} and a set of logical
operaters L = {l1, l2,...,ln} (perhaps just AND, OR and NOT), then denote
Spl as a set defined from some combination of predicates in P and operators
in L, and Spl* is the set of all possible sets Spl (perhaps regularised to
remove contraditions);
3) An ontology is constructed by taking a collection of sets from Spl* and
identifying a partial ordering of those sets using the usual subset
relationship. (03)
This would split the study of ontology into three area:
1) the formal problem of ontology as being concerned with the types of
mappings (homomorphisms, homeomorphisms, etc) between different ontologies
based on the choices from some Spl*
2)the practical problem as finding an ontology that supports the decision
procedures in a particular process (I include classifying something as a
decision procedure).
3) the computational problem of defining of terminating and efficient
procedures for comparing ontologies and mapping between them.
(Thanks to Pat Hayes for this suggestion  even his more acerbic comments
can be quite enlightening.) (04)
I would then expect there to have been a number of competing definitions,
and any number of arguements discussing the relative merits of these
definitions. And possibly some argument demostrating that this whole
approach is flawed. (05)
My question is, where are these definitions and the ensuing arguments? and
is there a good summary of these? (06)
Sean Barker
Bristol, UK (07)
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