Re: Despair! The exact meaning of Complement??

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:
>> Suppose I have a class Person with 9 individuals:
>> 
>> 3 with property male = TRUE, could be put in a subclass Man
>> 3 with property male = FALSE
>> 3 without a male property

To me this does not make sense as stated. Do you really mean 'property' in the OWL sense? If so, what are the domain and range of this property? And what exactly do you mean by "without a property" ? 

But the rest of your question really only turns on the class Man, which contains the first three elements of Person. 

>> 
>> Then WHAT is the outcome of "NOT Man" (i.e.: NOT (male value TRUE)):

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. RIght now one has to guess what exactly it is you mean. I will presume that you are asking about the owl:complementOf the OWL class Man, which is a subclass of Person.

>> 
>> a. the REST of the class Person, i.e. 3 with male = TRUE plus 3 without male property.
>> b. ONLY the 3 individuals with the property male = FALSE, since FALSE is the opposite Of TRUE and can be interpreted as the complement of "NOT (male value TRUE)".
>> c. NO answer at all, since it is not absolutely sure whether the 3 individuals without a male property mentioned here, still might have it mentioned somewhere (according to OWA), but is at this moment not known to the reasoner. Ergo: it can't give an answer.
>> 
>> The above reasoners give different answers or none at all! (at least all different from what I myself expect: answer a.)

As far as I can see, the correct answer is none of the above. The complement of the class Man is the class of every thing in the universe (every element of owl:Thing) that is not in the class Man. Notice I do not mention the class Person in this answer. The owl complement is not taken with respect to some superclass, but to the entire OWL universe. So it includes the other six persons but also, for example, any non-human creatures, non-living things, numbers, dates, strings, lists and indeed anything else at all that is not in the class Man. Not surprisingly, it can be extremely hard to actually list all the elements of a complement class. 

FWIW, your answer (a) is the intersection of the complement of Man with Person, ie owl:Intersection(Person owl:ComplementOf( Man) )

>> 
>> 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 another: Is it allowed to make the most upper class "Thing" equivalent to a defined class?

No. 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. 

Pat Hayes

>> 
>> Thank you very much in advance,
>> 
>> DJ
>> 
> 

------------------------------------------------------------
IHMC                                     (850)434 8903 or (650)494 3973   
40 South Alcaniz St.           (850)202 4416   office
Pensacola                            (850)202 4440   fax
FL 32502                              (850)291 0667   mobile
phayesAT-SIGNihmc.us       http://www.ihmc.us/users/phayes