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Re: [ontolog-forum] Levels

To: Christopher Menzel <cmenzel@xxxxxxxx>
Cc: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Pat Hayes <phayes@xxxxxxx>
Date: Mon, 12 Feb 2007 14:46:59 -0600
Message-id: <p06230908c1f67c972b47@[]>
>On Feb 12, 2007, at 12:12 PM, Pat Hayes wrote:
>>>  You're right that import statements should not be considered part of
>>>  an ontology.  I agree it's the imported axioms that are part of the
>>>  ontology.
>>  Wait. Of course the imports statements are part
>>  of the ontology. What are you guys talking about?
>*If* ontologies are logical theories    (01)

Well, if "theory" has to mean deductively closed, 
then I would say no, they are not. That is, an 
ontology to me means a set of sentences (usually 
finite, usually not deductively closed) in an 
ontology language. Which is, roughly, a formalism 
with a model theory.    (02)

>, then it seems to me that this 
>confuses a mechanism for saying what (some of) the axioms of an 
>ontology are with the ontology.    (03)

Why do you call this "confuses"? The assertion of 
what some of the axioms are can be part of the 
theory. You seem to be insisting on a 'levels' 
distinction here which I fail to see the reason 
for (and plenty of reasons to reject.) BTW, Cyc 
has been doing this for years.    (04)

>  Suppose I'm writing my ontology for 
>TAMU faculty and admin again, and you've got a nice higher-level 
>ontology for universities over there at IHMC.  My statement "import 
>(reiterate, endorse, whatever) Pat's university ontology" is not part
>of my ontology    (05)

YES IT IS. Check out the specs. In both OWL and 
CL , the imports is a *sentence*, and the 
truth-recursions apply to it like any other 
sentence. True, they involve paying attention to 
some rather unusual non-traditional matters, like 
network identifiers denoting theories; but they 
are sentences, and they are part of the ontology. 
They are not in some other meta-level, they are 
not written in a different language, and they are 
not a mechanism. Their meaning is specified 
semantically, not operationally. (Tamel even 
suggested allowing imports sentences to partake 
in the usual sentence recursion, so one could 
have conditional or quantified import sentences. 
In IKL we could make the identifier denote the 
proposition expressed by the ontology, but CL 
wasn't ready for that, so we didn't bite that 
particular bullet.)    (06)

>; it's a mechanism for saying what my axioms are that 
>makes efficient use of an open network.
>I'm not dogmatically wedded to the idea that formal ontologies are 
>logical theories of some ilk, but if you're right, and my import 
>statement is literally part of my ontology, then formal ontologies 
>are not (in general) logical theories,    (07)

Well, it depends on what you count as a logic, I 
guess. Is CL a logic? Because CL has importing 
with a full model theory, cf. section 6.3 in the 
ISO final draft    (08)

http://cl.tamu.edu/docs/cl/24707-31-Dec-2006.pdf    (09)

See also lines E17 and E20 in the semantics table 
in 6.2.  As I put quite a lot of work into 
getting this (I hope) right, I guess I am rather 
unwilling to admit that it is broken or 
irrelevant.    (010)

>and we'd better get clear 
>about the connection between the former and the latter.  You seem to 
>be favoring the idea that ontologies are rather more concrete than 
>I'd been thinking.  Do you think it would be better to say that a 
>logical theory is only one of several components of an ontology?    (011)

See above. Whatever we decide should be the 
definition of "ontology" (God alone knows why we 
need a definition, but...), it had better be the 
case that the 10,000 or so existing OWL 
ontologies turn out to be ontologies by our 
definition. Now, *they* are collections of 
assertions in OWL (or maybe the XML documents 
which encode those assertions, or the RDF graphs 
which encode..., etc.; choose your favorite 
encoding level). These are finite entities and 
their sentences satisfy semantic constraints 
which fully determine their meanings. And the 
'imports' sentences that they contain are part of 
them, just as much as any other sentences. I'm 
happy to say that they are sets of logical 
sentences, myself.    (012)

Pat    (013)

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