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[protege-owl] Define more than Subject-Predicate-Object

Timothy Redmond tredmond at
Mon Apr 30 21:29:32 PDT 2007

>> However I would argue that this is not an entirely natural
>> viewpoint.  Say we look at a statement like
>> 	MyFavoritePizza = Pizza and (hasTopping some SausageTopping) and
>> (hasBase all ThinAndCrispyBase).
>> It is possible to express the semantics  of such a statement in terms
>> of triples.  But I would argue that the more natural semantics is the
>> direct model  theoretic semantics ( 
>> semantics/
>> direct.html).

> But I still don't understand what do you mean with the direct model  
> theoretic semantics.
> I've not read about it, but I'll do later.

Say I have a statement that says

	CheeseyPizza = Pizza and (hasTopping some CheeseTopping).

The simplest way to explain its meaning is to  build up the meaning  
piece by piece.  So we define the meaning of the above statement in  
the following steps:

	(hasTopping some CheeseTopping) is  the set of all things that has  
some topping CheeseTopping

	Pizza and (hasTopping some CheeseTopping) is the set of all things  
that are in Pizza and are also in (hasTopping some CheeseTopping)

	(CheeseyPizza = Pizza and (hasTopping some CheeseTopping)) means  
that anything that is a CheeseyPizza is also in (Pizza and  
(hasTopping some CheeseTopping)) and  vice versa.

This approach of building the meaning of a statement piece by piece  
is the standard approach for defining the semantics of a logic.  This  
is how the direct semantics is done - except the direct semantics is  
much more precise.  I think that this is the natural view of the  
semantics for OWL.

But to reduce the statement

	CheeseyPizza = Pizza and (hasTopping some CheeseTopping)

to triples takes and defining the semantics through those triples  
would take a lot more work.  Some of the triples are (approximately)

   CheeseyPizza owl:equivalentClass anon_1
   anon_1 owl:intersectionOf anon_2
   anon_2 rdf:first Pizza
   anon_2 rdf:next anon_3
   anon_3 rdf:first anon_4
   anon_3 rdf:next rdf:nil
   anon_4 owl:onProperty hasTopping
    ... more ...

The rdf semantics defines a meaning to all of these triples.


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