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

Timothy Redmond tredmond at stanford.edu
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 (http://www.w3.org/TR/owl-
>> semantics/
>> direct.html).

> But I still don't understand what do you mean with the direct model
> theoretic semantics.

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.

-TImothy

```