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Re: [ontolog-forum] Ontology of Rough Sets

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Rich Cooper" <rich@xxxxxxxxxxxxxxxxxxxxxx>
Date: Mon, 17 Jan 2011 18:38:32 -0800
Message-id: <20110118023835.1C937138D5B@xxxxxxxxxxxxxxxxx>

Hi Azamat and Chris,


Shame on those who claim that Thing can be a Class and an Instance at the same time!  Only multiple inheritance modelers would even face that issue in the first place.  I am not a C++ fan.  


The Delphi VCL classes descend from TClass and TObject separately.  TObject is not an instance of TClass, so that every instance of TClass is an actual TClass, and every instance of a TObject is a TObject, and ne’er the twain shall hook up.  


Only refinement processes tease out the actual classes and instances.  A program comprises a graph of refined classes and each class has a suite of instances, varying in time of creation and destruction as to definition of each instance at time t.  


But its messy to use iterations of any kind of instances if you cant discern the difference between a class and an instance.  Those infinities can be pesky, but they sure show up in the real world.  


Restrict your database to entities (dynamic) and properties (static) and you can organize it better.  Expand into philosophically interesting directions and get problems.  The choice is clear to me. 






Rich Cooper


Rich AT EnglishLogicKernel DOT com

9 4 9 \ 5 2 5 - 5 7 1 2

From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Christopher Menzel
Sent: Monday, January 17, 2011 5:19 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Ontology of Rough Sets


On Jan 17, 2011, at 5:00 PM, Rich Cooper wrote:

Hi Azamat,


Only the individuals and instances are real...


You appear simply to be asserting your own personal views as if they were self-evident, eternal truths. The whole issue of what is or isn't "real" is a tremendously vexed issue and it's far from clear that any deep metaphysical commitment to this or that fundamental philosophical ontology has any useful role to play in ontological engineering at all — on which point see the recent, very interesting debate between Gary Merrill and Barry Smith/Werner Ceusters. But regardless of where you come down in that debate, nearly every useful ontology in existence takes things other than individuals as "real" — notably, the classes that populate any OWL ontology.

Perhaps you prefer that I use the term “classes” instead of the term “sets” in that no class can contain itself as an element.  


The class THING (or whatever you call the most general class) contains itself as an element in many ontologies.  And I thought you just said that only individuals and "instances" (whatever those are supposed to be) are real. What are you doing talking about classes?

That constraint leaves us free to use the individuals, instances of data types, as the model of ground truth.  In that representation, classes are groups of individuals, instances, et cetera.  Using that representation, the equivalence function could be composed on any or all of the four class types – rough, fuzzy, probabilistic and crisp.


This is much too vague for anyone (well, me) to know what you are claiming.  (This is not a request for more information.)

In my opinion, it is a mistake to construe sets as containing themselves,


This is like saying it is a mistake to construe numbers as "negative". It is obviously not a "mistake" to allow non-well-founded sets; simply broaden the universe of sets beyond the well-founded sets of ZF set theory and they are (provably) just as respectable, theoretically.  There are, moreover, many useful applications of non-well-founded sets.  Perhaps you prefer not to avail yourself of non-well-founded sets; knock yourself out. Others find them useful.

though mathematicians have invested heavily into that interpretation.  


There are a relative few mathematicians who study them and others who have found useful applications of them. I know of no reasonable sense in which "mathematicians have invested heavily" in them.






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