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. (01)
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/ (02)
----- 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 (03)
> 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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