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Re: [ontolog-forum] Ontology modules and namespaces

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Tue, 27 Oct 2009 22:31:05 -0500
Message-id: <35837241-82EB-4B58-9697-C3B6FE72E0F0@xxxxxxxx>
On Oct 27, 2009, at 4:56 PM, Matthew West wrote:
> Dear Ian,
>> PS - IDEAS is higher order,
> MW: Actually it probably isn't. You would need to get someone like  
> Chris
> Menzel to explain, but having classes with members that are classes  
> that
> have members that are individuals is apparently not enough to make it
> higher order. If I understood correctly this is because you can do a
> transformation into a first order form,...    (01)

That is correct.  To be genuinely higher-order requires an additional  
semantic constraint on the number of classes there are in the domains  
of the higher-order quantifiers.  Absent that constraint, "higher- 
order" interpretations can be transformed into first-order.  But it's  
hard to know exactly because IDEAS appears to be a box and arrow  
language with lots of evocative labels ("Thing", "Individual", "Type",  
"PowerType", ...) but no semantics.  That they have powertypes in  
particular is suggestive of full higher-order logic, but again it's  
just a label without a semantics, so there is no way to know.    (02)

>> and extensional. It's founding categories are individual (something  
>> with spatio-temporal extent), type and tuple. I can see how CL  
>> handles type and tuple (albeit through some arcane notion,
> MW: CL is an abstract syntax.    (03)

With a rigorous semantics.    (04)

> The concrete syntaxes actually include a graphical notation -  
> conceptual graphs.    (05)

Exactly correct.    (06)

> If you chose, you could probably map the ideas notation to the CL  
> abstract syntax, or a subset of it.    (07)

So long as the syntax of the notation is well-defined and it has a  
clear semantics, you surely could.    (08)

>> probably starting with "for all..."), but it doesn't seem to have a  
>> fundamental category of something with spatio-temporal extent.
> MW: It does not have to. It just has not made that commitment, and  
> should not either, CL is a language not an ontology.  It does not  
> prevent you from declaring that there are individuals that are  
> spatio-temporal extents.    (09)

Again, exactly correct.    (010)

>> As that's the criterion on which the entire ontology is founded, I  
>> think I'd rather use a notation that is also founded on this  
>> principle.
> MW: Well the advantage of that for you is that you will be able to  
> make convenient diagrams. The disadvantage is that no-one who is not  
> a 4 dimensionalist will want to use your notation.    (011)

Indeed.    (012)

>> Maybe we just built the right wheel for what we're doing, instead  
>> of re-inventing one.
> MW: Well if it's a graphical notation, chances are it's just boxes  
> and lines again.    (013)

That's all I've found, but perhaps there is a rigorous semantics for  
it lurking somewhere.    (014)

Chris Menzel    (015)

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