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Re: Despair! The exact meaning of Complement??

From: Bijan Parsia <bparsia@cs.man.ac.uk>
Date: Mon, 28 Feb 2011 09:22:48 +0000
Cc: dja222@hotmail.com
Message-Id: <C3A235E7-3E8C-461C-A2F5-E6627071D111@cs.man.ac.uk>
To: Owl Dev <public-owl-dev@w3.org>
On 28 Feb 2011, at 00:30, Pat Hayes wrote:

> 
> On Feb 27, 2011, at 7:46 AM, Ian Horrocks wrote:
> 
>> Begin forwarded message:
>> 
>>> Resent-From: public-owl-comments@w3.org
>>> From: Dave Andersen <dja222@hotmail.com>
>>> Date: 25 February 2011 15:56:21 GMT
>>> To: <public-owl-comments@w3.org>
>>> Subject: Despair! The exact meaning of Complement??
>>> 
>>> Dear Working Group,
>>> 
>>> After fiddling a day or so away with Pellet, Hermit and Fact++ to get things right (NOT!), I finally turn to you for the ultimate answer for the exactdefinition of Complement:

The "ultimate" answer for the *exact* definition may be found in the semantics spec:	
	http://www.w3.org/TR/2009/REC-owl2-direct-semantics-20091027/#Class_Expressions

Trasliterated it reads:
The interpretation of ObjectComplementOf(AClassExperessoin)  is the whole domain (i.e., the interpretation of owl:Thing) set minus the interpretation of AClassExpression.

So, ObjectComplementOf(Person) is the set of all things that are not persons.

[snip]
> What do you mean by "outcome"? BTW, it would help enormously if you could pose your question using actual OWL terminology and even OWL syntax, if possible.

This. If you've been testing in reasoners then you have some files. Please send!
[snip]
>>> Another question: is W3C Monotonicity defined as strictly decreasing/increasing (staying equal NOT allowed) or nonincreasing/decreasing (staying equal allowed)?
> 
> THis question does not make sense as stated. Monotonicity in this context refers to provability. It means that if you add some axioms (assertions) to an OWL ontology, then anything you could derive before is still derivable after the addition. 

And thus "Staying equal" is allowed.

>>> And another: Is it allowed to make the most upper class "Thing" equivalent to a defined class?
> 
> No

Actually, Pat, it is allowed:

owl:Thing = Person.
Person = ....

Is perfectly legal OWL DL even.

> . Even if it is strictly legal, it would be a very bad idea, as an ontology that did this would be immediately inconsistent with almost every other ontology. 

I think you had a thinko. Synonymy with Top is often odd, but it doesn't force inconsistency (or vacuity) anymore than a class being synonymous with bottom (i.e., unsatisfiable) forces inconsistency. It's not always bad modelling practice (e.g., when you want to constrain the whole domain). Domain and range axioms come to mind.

Indeed, there are normal forms which consist of axioms of the form Thing SubClassOf ...

Cheers,
Bijan.
Received on Monday, 28 February 2011 09:23:18 GMT

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