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Re: [ontolog-forum] Thing and Class

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Antoinette Arsic <aarsic@xxxxxxxx>
Date: Wed, 10 Sep 2008 17:36:58 -0400
Message-id: <B97D098AB1B4AD4DA8CCF15C8FF2EFD2288FDE6241@xxxxxxxxxxxxxxxxxxxxxxxxxx>
I'm really not getting this mKR language thing.    (01)

SGIS
Antoinette Arsic
Sr. Systems Engineer
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________________________________________
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx 
[ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Richard H. McCullough 
[rhm@xxxxxxxxxxxxx]
Sent: Wednesday, September 10, 2008 5:06 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Thing and Class    (02)

This email group seems to be drifting towards supporting
the genus-differentia definition, which is intensional,
and is one of the foundations of the mKR language.    (03)

Dick McCullough
Ayn Rand do speak od mKR done;
mKE do enhance od Real Intelligence done;
knowledge := man do identify od existent done;
knowledge haspart proposition list;
http://mKRmKE.org/    (04)

----- Original Message -----
From: "Pat Hayes" <phayes@xxxxxxx>
To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Wednesday, September 10, 2008 10:42 AM
Subject: Re: [ontolog-forum] Thing and Class    (05)


> On 9/10/08 12:21 PM, leo@xxxxxx wrote:
>> Colleagues ,
>>> Nice thought, but the problem is that these notions are all defined
>>> purely in extensional terms, i.e. in terms of membership. Every
>>> intensional type has a corresponding extension, which is the set of all
>>> things which are of the type; and Michael's taxonomy, above, only refers
>>> to the extensions.
>> I wrote already ( http://www.ototsky.mgn.ru/it/21abreast.htm - 3.
>> Mid-range objectives.) that from the Classification Theory(CT) point of
>> view there mast be not only the Taxonomy but the dual Meronomy part !
>> And this duality must be taken into account.
>> Only two items from the CT :
>> "  - Any Classification System has two Dual parts - "Taxonomy" and
>> "Meronomy". The first one is   "external" and connected with ordinary set
>> theory relations (unions,  intersections, hierarchy (a subclass of))
>> etc..
>>   - The second one is "internal" and connected  with Properties/Parts
>> structure (archetype)."
>
> That is a different distinction. None of the current discussion
> is about part/whole relationships. The intension/extenstion
> question is rather whether subclass (for example) really is a
> purely set-theoretic relationship. In RDFS for example it is
> treated intensionally, so that subCLASS entails subSET of the
> extensions but not the reverse. In an intensional framework, two
> different classes might have the same extension.
>
> Pat
>
>
>>
>> Best,
>> Leonid - http://ototsky.mgn.ru/it
>>
>>
>>>
>>> tim.glover@xxxxxx wrote:
>>>> Pat, noting John Sowas comments about the difference between
>>>> extensional sets, and intensional types, would the situation  be
>>>> improved by substituting "type" for "set" throughout, eg
>>>>
>>>> X: the universal type
>>>> Y: the type of things that have members
>>>> Z: the type of things that do not have members.
>>>> U: the type of things whose members are all of type Y
>>>> V: the type of things whose members are all of type Z
>>>>
>>> Nice thought, but the problem is that these notions are all defined
>>> purely in extensional terms, i.e. in terms of membership. Every
>>> intensional type has a corresponding extension, which is the set of all
>>> things which are of the type; and Michael's taxonomy, above, only refers
>>> to the extensions.
>>>> U and V might be useful types, even if they are not useful sets?
>>> Maybe I spoke too harshly if I said they were useless. They are
>>> obviously widely used notions. But it is dangerous to assume that they
>>> are the only possibilities.
>>>
>>> Pat
>>>>
>>>> Tim.
>>>>
>>>>
>>>>
>>>> ------------------------------------------------------------------------
>>>> *From:* semantic-web-request@xxxxxx
>>>> [mailto:semantic-web-request@xxxxxx] *On Behalf Of *Pat Hayes
>>>> *Sent:* 09 September 2008 18:16
>>>> *To:* [ontolog-forum]
>>>> *Cc:* [ontolog-forum]; James Leigh; SW-forum; Michael F Uschold
>>>> *Subject:* Re: [ontolog-forum] Thing and Class
>>>>
>>>> At 2:35 PM -0700 9/8/08, Michael F Uschold wrote:
>>>>> Azamat said:
>>>>>
>>>>> Sum up: If Thing goes as the universal class, of which everything is a
>>>>> member, it will equivalent to Class, as the class of all classes.
>>>>> Other
>>>>> interpretations will be inconsistent, asking for many questions.
>>>>>
>>>>> Whatever you choose to call these things, I find the following
>>>>> distinctions helpful:
>>>> I don't find them helpful. They embody and give credence to several
>>>> common errors; they do not conform to established usages that go back
>>>> half a century or more; and they aren't properly defined.
>>>>
>>>>>     1.      X: the set of all things in the universe of discourse
>>>>>
>>>>>     2.      Y: the set of all things that have member individuals
>>>>>
>>>>>     3.      Z: the set of all things that do NOT have member
>>>>> individuals
>>>>>
>>>>>     4.      U: the set of all things whose members do not themselves
>>>>>     have members
>>>>>                           (i.e. the set of all things whose members
>>>>>     are members of the class Z)
>>>>>
>>>>>     5.      V: the set of all things whose members also have member
>>>>>     individuals
>>>>>                   (i.e   the set of all things whose members are all
>>>>>     members of the class, Y)
>>>>>
>>>>> The names I find most useful for these things are (substituting into
>>>>> the text above)
>>>>>
>>>>>     1.      THING: the set of all things in the universe of discourse
>>>>>
>>>> What do you mean here by 'universe of discourse'? That sounds like a
>>>> semantic term. A semantic universe of discourse can be very small,
>>>> e.g. {A} is a possible universe of discourse.
>>>>
>>>>>     2.      CLASS: the set of all things that have member individuals
>>>>>
>>>> Does that exclude the empty set/class? (I hope not.) And do the
>>>> members have to be individuals, or can they also include classes? As
>>>> stated, this seems to exclude METACLASS, whose elements don't have
>>>> individuals as members. I presume you did not intend this, though.
>>>>
>>>>>     3.      INDIVIDUAL: the set of all things that do NOT have member
>>>>>     individuals
>>>>>
>>>> But not including the empty set/class, I presume.
>>>>
>>>>>     4.      ORDINARYCLASS: the set of all things whose members do not
>>>>>     themselves have members
>>>>>                           (i.e. the set of all things whose members
>>>>>     are members of the class INDIVIDUAL)
>>>>>
>>>>>     5.      METACLASS: the set of all things whose members also have
>>>>>     member individuals
>>>>>                   (i.e   the set of all things whose members are all
>>>>>     members of the class, CLASS)
>>>>>
>>>> It might be worth remarking that your 'ORDINARYCLASS' and 'METACLASS'
>>>> classifications are not recognized by set theory, and seem to have no
>>>> purpose that I can determine; that the distinction between them isn't
>>>> exhaustive, since it omits the (common) case of a set containing both
>>>> sets and non-sets; and that it has been shown quite rigorously that if
>>>> set theory is consistent at all, then it is also consistent to assume
>>>> that there are no INDIVIDUALs in the above sense, i.e. that everything
>>>> can be treated as a class.
>>>>
>>>> More importantly, the term "individual" as used in logic does not have
>>>> anything like this meaning: it simply means anything in the universe
>>>> of discourse, i.e. anything that one is quantifying over. This may
>>>> include classes, of course, just as it may include anything else.
>>>> Logical individuals can be any kind of thing: the term does not act
>>>> there as a classifier. It is therefore very misleading and confusing
>>>> to treat it as one, as you do here. Looked at from a logical point of
>>>> view, it seems crazy to single out lack of one particular relation as
>>>> being a defining characteristic for individual-hood. Why choose lack
>>>> of class-membership? Why not say that anything that isn't married is
>>>> an INDIVIDUAL, or anything that doesn't have more than three parts, or
>>>> ...?
>>>>
>>>> The recognized term in set theory for INDIVIDUALs in your sense is
>>>> 'ur-elements', from the German "urelemente". Maybe we could call them
>>>> "irreducible individuals" or some such formulation, to avoid this
>>>> (recurrent and exasperating) confusion? Or simply NON-CLASS ?
>>>>
>>>>> Here is the class hierarchy:
>>>> Um... it's not a hierarchy.
>>>>
>>>>> THING (the most general anything)
>>>>> CLASS (the most general class)
>>>>> ORDINARYCLASS
>>>>> METACLASS
>>>>> INDIVIDUAL (the top of the ordinary class hierarchy)
>>>> This is a horribly misleading mis-use of a widely used, almost
>>>> universal, nomenclature. Why screw up a terminology that has worked
>>>> well for 50 years? Its not even the terminology that is used in set
>>>> theory itself, which (unlike logic) actually deals with these
>>>> distinctions.
>>>>
>>>>> INDIVIDUAL and CLASS form a partition of THING
>>>>> ORDINARYCLASS and METACLASS form a partition of CLASS
>>>> No, they most definitely don't. If A is an individual then {A, {A}}
>>>> isn't either ordinary or meta.
>>>>
>>>> Pat
>>>>
>>>>> THING and CLASS have all of the five things below as members:
>>>>>
>>>>>     * THING
>>>>>     * CLASS
>>>>>     * ORDINARYCLASS
>>>>>     * METACLASS
>>>>>     * INDIVIDUAL
>>>>>
>>>>> ORDINARYCLASS has members:
>>>>>
>>>>>     * INDIVIDUAL (any any of its subclasses)
>>>>>    *
>>>>>
>>>>> METACLASS has members:
>>>>>
>>>>>     * CLASS
>>>>>     * METACLASS
>>>>>     * ORDINARYCLASS
>>>>>
>>>>> INDIVIDUAL has members that are inherited from any of its subclasses
>>>>> (e.g. individual persons, or companies, or drugs, depending on the
>>>>> domain).
>>>>> Michael
>>>>> On Thu, Aug 28, 2008 at 12:58 AM, Azamat <abdoul@xxxxxxxxxxxxxx
>>>>> <mailto:abdoul@xxxxxxxxxxxxxx>> wrote:
>>>>>
>>>>>     As a devil's advocate, seemingly unsanctioned with the 3WC,
>>>>>     Richard is doing
>>>>>     a useful work raising sometimes justified objections for SW
>>>>>     candidates
>>>>>     looking for canonization (standardization).
>>>>>     As for James's reading of Thing and Class, it looks more as
>>>>> punning,
>>>>>     possibly intentionally.
>>>>>
>>>>>     The interrelations of classes as well as classes and things are
>>>>>     actually
>>>>>     more subtle and deep, than generally presented in various
>>>>>     specifications.
>>>>>     A member of a class may itself be a class. For example, the class
>>>>>     of humans
>>>>>     is a member of the class of species of animals. An individual
>>>>>     human, even
>>>>>     being a member of its class, is not a member of the latter one,
>>>>>      the class
>>>>>     of species of animals. For a human is not a species of animal.
>>>>>     Whatever the number of human beings, it will not affect the number
>>>>> of
>>>>>     species of animals. This goes as a kind of ontological rule of all
>>>>>     taxonomies: whatever the number of instances, objects,
>>>>>     particulars, it will
>>>>>     not change the number of classes of things. Again, this means that
>>>>>     relationships of class inclusion (subsumption) and class
>>>>>     membership have
>>>>>     some principal differences. Namely, the class inclusion is a
>>>>>     transitive
>>>>>     relation, while the CLASS MEMBERSHIP IS NOT TRANSITIVE. This
>>>>>     fundamental
>>>>>     fact is missing in some large scale, common sense ontologies,
>>>>>     making the
>>>>>     whole hierarchy just as invalid for computing applications.
>>>>>     Sum up: If Thing goes as the universal class, of which everything
>>>>>     is a
>>>>>     member, it will equivalent to Class, as the class of all classes.
>>>>>     Other
>>>>>     interpretations will be inconsistent, asking for many questions.
>>>>>
>>>>>     Hope this will be of use,
>>>>>     Azamat Abdoullaev
>>>>>
>>>>>
>>>>>     ----- Original Message -----
>>>>>     From: "James Leigh" <james-nospam@xxxxxxxxxxx
>>>>>     <mailto:james-nospam@xxxxxxxxxxx>>
>>>>>     To: "Richard H. McCullough" <rhm@xxxxxxxxxxxxx
>>>>>     <mailto:rhm@xxxxxxxxxxxxx>>
>>>>>     Cc: "Semantic Web at W3C" <semantic-web@xxxxxx
>>>>>     <mailto:semantic-web@xxxxxx>>
>>>>>     Sent: Thursday, August 28, 2008 4:30 AM
>>>>>     Subject: Re: Thing and Class
>>>>>
>>>>>
>>>>>     >
>>>>>     > Hi Richard et al.
>>>>>     >
>>>>>     > Here is an informal interpretation of some of the spec written
>>>>>     in plain
>>>>>     > English.
>>>>>     >
>>>>>     > Class stands for classification.
>>>>>     > We use Class to classify things.
>>>>>     > Class is a set of Things.
>>>>>     > "I am a Human" - I just classified myself as Human (I hope I'm
>>>>>     right).
>>>>>     > "I am a Thing" - that is true for everything.
>>>>>     > Human is a classification of all people.
>>>>>     > Thing is a classification of all things.
>>>>>     > Every Human is a Thing. Therefore Thing is a super set of Human.
>>>>>     > Is Human a Thing? No! its a Class!
>>>>>     > Everything Thing is an individual.
>>>>>     > Human is not an individual, it is a classification of
>>>>> individuals.
>>>>>     > Thing is not an individual, it is a classification of
>>>>> individuals.
>>>>>     > Can we classify Classes? Yes we can! Human is a classification
>>>>>     - I just
>>>>>     > classified Human as a classification.
>>>>>     > Human is a Class.
>>>>>     > Thing is a Class.
>>>>>     > Are all Things Classes? No! I am a Thing, but I am not a
>>>>>     classification.
>>>>>     > Is Thing the same as Class? No! Human is not a Thing, but Human
>>>>>     is a
>>>>>     > Class.
>>>>>     >
>>>>>     > Hope this helps,
>>>>>
>>>>>     > James
>>>>>     >
>>>>>     >
>>>>>     >
>>>>>     >
>>>>>
>>>>>
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>>>>
>>>> --
>>>>
>>>> ---------------------------------------------------------------------
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>    (06)



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