Some points that are still debatable or clarifiable: (01)
CM>>> I prefer a nice, simple definition:
>>>
>>> An ontology is a set of sentences in a formal language. (02)
JS>> Yes, but. That says what it is, but it doesn't explain why anybody
>> would want one or what they'd do with it. I would therefore add the
>> following clause:
>>
>> "that is designed to characterize the entities of interest in some
>> domain for the purpose of representing, storing, and communicating
>> information about them and performing deductions and computations
>> with that information." (03)
CM> I'm afraid I have to disagree if you want to include this in the
> *definition* of an ontology, as it turns a notion that is clear and
> precise into one that is fuzzy and indeterminate. On my proposed
> definition, there is always a definite answer, at least in principle,
> to the question: Is this an ontology? (04)
The answer may be definite, but it is very far from what people
intend when they talk about ontology. Since arithmetic is formal,
your definition would imply that "2+2=4" would be an ontology. (05)
I admit that my suggested clause is too long. Therefore, I'd
shorten it to just one line: (06)
"that is designed to characterize the entities of some domain." (07)
As soon as we mention "design", we bring in purpose. But that is
precisely what distinguishes an ontology from an arbitrary set of
axioms: somebody has chosen those axioms for that purpose. (08)
I realize that logicians shrink with horror when somebody mentions
the word "purpose", but for an engineer, that is the whole point: (09)
"Engineering is an application of science for the purpose
of solving a problem within the limits of budgets, resources,
and deadlines." (010)
The ONTAC group does not want a treatise on ontology. They want
an engineering product: *an* ontology they can actually use. (011)
CM> ... but theories are deductively closed on this approach,
> and I don't think we should identify ontologies with theories
> in that sense, as, for one thing, you can't distinguish between
> equivalent ontologies that use different axioms. (012)
I agree that what people are asking for is a set of axioms, not
the deductive closure. And I admit that proving equivalence
of two different axiomatizations can be a nontrivial task. But
for most purposes, two different axiomatizations of the same
theory should be considered *the same* ontology. (013)
If you translate an ontology from one CL dialect to another
and then back to the first, you're likely to get a different,
but logically equivalent set of statements. (014)
Furthermore, people will often transform a set of axioms in order
to optimize them for their particular theorem prover, and they want
to claim that they're using "the same" ontology. (015)
CM> Frankly John, I don't see the point of talking about the "lattice
> of theories" for a given language anyway. I think sometimes your
> talk of the lattice suggests that it is itself something might be
> usefully apprehended and studied. In general, however, there are
> uncountably many theories in such a lattice... (016)
There are lots of issues here. But first of all, I'd like to say
that the most interesting lattice is the sublattice of all finitely
specifiable theories (I would allow an infinite number of axioms
specified by a schema -- but the total of schemata plus ordinary
axioms should be finite). That implies tht we're only going to
be dealing with a countable lattice. (017)
CM> Typically, all that's *really* useful to us are the possible
> logical relations that can hold between two *given* theories:
> equivalence, subsumption, compatibility, inconsistency, inconsistent
> but containing equivalent subtheories, etc.... (018)
I agree. I consider the lattice primarily for its heuristic and
pedagogical uses: i.e., I have found it easier to clarify and
explain many operations by treating them as walks and jumps
through the lattice. Among these operations are the AGM axioms
for belief revision, many algorithms for induction and abduction,
and such mundane issues as talking about version numbers of an
ontology as walks through the lattice. (019)
But that is a topic for another note. (020)
John (021)
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