On Thu, Jan 19, 2006 at 07:08:20PM -0500, John Sowa wrote:
> Some points that are still debatable or clarifiable:
>
> CM>>> I prefer a nice, simple definition:
> >>>
> >>> An ontology is a set of sentences in a formal language.
>
> 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."
>
> 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?
>
> 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. (01)
Correct. A trivial and largely useless one. So what? Lots of useful
notions -- theory, in particular -- have tons of useless/trivial/silly
instances. (02)
> I admit that my suggested clause is too long. Therefore, I'd
> shorten it to just one line:
>
> "that is designed to characterize the entities of some domain."
>
> 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. (03)
Well, you say tomAto, John, I say tomAHto. But you *should* say
tomAHto. ;-) I guess one reason I'm pushing the simple definition is
that there will then be no divide between the theoretical and the
practical notions. When we are working on the formal foundations of
ontology, an ontology can't be anything more than a set of sentences.
Why throw messy intentional stuff into the very definition in applied
contexts? You can still say everything you want without doing that:
ontologies are just sets of sentences, but the ontologies that are
*useful* are those that were designed with some purpose in mind. Why
take the useful but *essentially* informal notion of purpose and force
it into the nice, clean, functional notion of ontology I'm proposing? (04)
> I realize that logicians shrink with horror when somebody mentions
> the word "purpose", but for an engineer, that is the whole point: (05)
Oh, nonsense -- intensional logic (with an "s") is in large measure
exactly the logic of intentionality (with a "t"). That hardly came
about by logicians shrinking from notions of purpose and like. The only
thing logicians shrink from is the idea the idea of using inherently
informal intentional notions in *definitions* -- and that is no less
true for engineers. Tell me one useful engineering TOOL that involves
intenionality. (06)
> "Engineering is an application of science for the purpose
> of solving a problem within the limits of budgets, resources,
> and deadlines." (07)
And that goes for ontological engineering as much as anything. But,
once again, that has nothing to do with the presence of intentional
notions in the mathematical foundations of the discipline. (08)
> The ONTAC group does not want a treatise on ontology. They want
> an engineering product: *an* ontology they can actually use. (09)
But good engineering products rest on sound foundations. All I'm
proposing is that we develop the same sort of clean, clear formal
foundation for ontological engineering that Newtonian mechanics provides
for mechanical engineering. (010)
> 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.
>
> 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. (011)
Indeed, undecidable. (012)
> But for most purposes, two different axiomatizations of the same
> theory should be considered *the same* ontology. (013)
I beg to differ. Your proposal is a recipe for confusion. Sometimes,
according to you, ontologies are identified by their axioms, sometimes
by their consequences. When? How often? Come on, John, this is a
no-brainer; there is a precise answer here: Ontologies are sets of
sentences. Period. Ontologies are *equivalent* if their deductive
closures are identical. Clean, clear, simple. (014)
> 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. (015)
That absolutely should *not* happen (unless you are talking about
structurally distinct dialects), but even if it did, so what? (016)
> 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. (017)
Sure, *now*, when there is still precious little clarity and agreement
about the foundations of ontology -- I mean, you guys can't even get
"type" and "class" figured out! :-) But when ontological engineers
start receive training as rigorous as that of mechanical engineers,
especially in logic, the distinction between identity and equivalence
will be as natural as breathing. (018)
Re lattices: (019)
> But that is a topic for another note. (020)
Right -- I was just sort of thinking out loud. The idea of a lattice of
theories is certainly not confused or pernicious. (021)
-chris (022)
_________________________________________________________________
Message Archives: http://colab.cim3.net/forum/ontac-dev/
To Post: mailto:ontac-dev@xxxxxxxxxxxxxx
Subscribe/Unsubscribe/Config: http://colab.cim3.net/mailman/listinfo/ontac-dev/
Shared Files: http://colab.cim3.net/file/work/SICoP/ontac/
Community Wiki:
http://colab.cim3.net/cgi-bin/wiki.pl?SICoP/OntologyTaxonomyCoordinatingWG (023)
|