RE: some basic questions, thanks

>I think you should distinguish the "subclass" 
>and the "equivalent class", they are different.
>
>-----Original Message-----
>From: Li Qin [mailto:bethqin@hotmail.com]
>Sent: 2003îN9åé20ì™ 0:37
>To: yzqu@seu.edu.cn; www-rdf-logic-request@w3.org; zhubin@cai.pku.edu.cn
>Subject: Re: some basic questions, thanks
>
>2. If fruit is the union of sweetfruit and 
>nonsweetfruit, grape is the subclass of fruit, 
>does it mean that grape is the union of 
>sweetfruit and nonsweetfruit?

No. It is a subclass of that union, however.

>Being the union of other classes is not a 
>property which can be inherited by its 
>subclasses, I think.

Indeed it is not, you are correct. I suggest that 
you do not think of union and intersection as 
*properties* of classes at all: they are 
operations on classes which produce new classes. 
The new classes stand on their own, and are 
determined by the instances they have, 
independently of how they were defined.

>4. I mean, e.g. graduate student is a subclass 
>of student. When do you annotate someone as the 
>instance of student instead of its subclasses?

It is always correct to use the superclass, but 
if you know a subclass, then using that can give 
you more information. But being an instance of a 
subclass implies also being an instance of any 
superclass: these classes are not like types or 
categories in an OO language, they are just 
mathematical sets. Think of a Venn diagram, for 
example.

>Let's say college student consists of 
>undergraduate student and graduate student, both 
>undergraduate student and graduate student can 
>have their own instances which are also 
>instances of college student, does college 
>student have its own instances other than that?

If it is defined as the union of undergrad and 
grad, no. If it is only defined as some 
superclass then it might have other instances: 
there is no way to tell without having more 
information. For example, there might be 
part-time students who are not considered to be 
either undergraduate or graduate.


>  >From: "Yuzhong Qu"
>  >To: "Zhu Bin" ,"Li Qin"
>  >Subject: Re: some basic questions, thanks
>  >Date: Fri, 19 Sep 2003 14:11:13 +0800
>  >
>  >Li Qin wrote:
>  >
>  >1. Intersection, as a set operation to get the common part of two sets,
>  >does not introduce any hierarchy at all.

Right.

>Here, if A is the intersection
>  >of B and C means that A is the subclass of B and C, this intersection
>  >introduces hierarchy.

Well, maybe not. That is a potentially dangerous 
way to think about it. There are uses of the 
terms 'class' and 'subclass' which imply a strict 
hierarchy, eg in JAVA and other structured 
programming languages. The OWL-style subclass 
hierarchy is not like that at all, however, and 
the analogy can be misleading. For example, it is 
quite possible to have subClasses which overlap, 
or to be a subClass of several other different 
classes: the subClass hierarchy is entirely 
described in terms of instance membership, and is 
not tree-structured or like a classification 
hierarchy. It is a lattice of sets, not a tree of 
classifications or a hierarchy of types.

>  >
>  >* The intersection of B and C can be 
>understood as the greatest lower bound of B and 
>C.
>  >
>  >2. "If A is the subclass of union of B and C" does not mean that A is
>  >the union of B and C. My question concerns the case that A is the union
>  >of B and C.
>  >If A is the union of B and C, the instances of B and C are instances of
>  >A.
>  >If A is the superclass of B and C, the instances of B and C are
>  >instances of A.
>  >What is the difference?
>  >
>  >* The properties of a superclass are 
>applicable to the instances of the subclasses.

That is not quite correct. The properties which 
apply to the elements of a superclass are 
applicable to the instances of the subclasses: 
but that is because those instances are the very 
same things as the instances of the superclass.

>  >
>  >3. If A is the complement to B, A is the difference between an unkown
>  >class and B.

No, it is the difference between the universe and 
B. In OWL, it is the difference between owl:Thing 
and B.

>Does this unkown class the union of A and B or the
>  >superclass of A and B?

It is the union, which is a superclass of both. 
(The phrase "the superclass" has no meaning here 
as there are usually more than one of them)

>  >
>  >* Just guess, use the union structure.
>  >
>  >4. When do you use a class instead of its subclasses for their
>  >instances, if they all have their own instances?

Well, you may not be interested in which subclass 
they are in. For example, if you want to say 
something about all the employees of a company, 
you may not care to distinguish the full-time 
from the part-time employees.  Or think of an 
ontology of animals which has some facts about 
all mammals, some about all bears, and some about 
brown bears.

>  >
>  >* Sorry, I can't understand your question.
>  >
>  >5. If A is the union of B and C. What is the relationship between the
>  >instances of A, B and C?

All the instances of B and of C are instances of 
the union A, and every instance of A is an 
instance of one of B, C (maybe of both).

>  >
>  >* Agree with Zhu Bin's point.
>  >
>  >
>  >
>  >Yuzhong Qu
>  >Dept.Computer Science and Engineering
>  >Southest University, Nanjing, China
>  >http://cse.seu.edu.cn/People/yzqu/en
>  >
>  >

Pat Hayes
-- 
---------------------------------------------------------------------
IHMC	(850)434 8903 or (650)494 3973   home
40 South Alcaniz St.	(850)202 4416   office
Pensacola			(850)202 4440   fax
FL 32501			(850)291 0667    cell
phayes@ihmc.us       http://www.ihmc.us/users/phayes