Dear John, (01)
could you give an example of what you mentioned: (02)
> In different situations, the same method of classification will
> produce a different set. The class remains the same, but the sets
> have different members or elements (03)
thanks,
Erick (04)
On 4 September 2011 16:06, John F. Sowa <sowa@xxxxxxxxxxx> wrote:
> On 9/4/2011 6:48 AM, Patrick Browne wrote:
>> I am trying to establish whether BFO and DOLCE use the same set
>> theoretic semantics when formalizing the terms universal and category.
>
> Before continuing, I must emphasize a fundamental principle of ontology:
>
> Classes in an ontology are *not* sets!
>
> That principle is true of BFO, Dolce, Cyc, SUMO, and every ontology
> from Aristotle to the present.
>
> Whenever you hear the word 'class' think of the word 'classification'.
> For every class, there is some rule, method, principle, or predicate
> that determines whether something is an instance of that class.
>
> In different situations, the same method of classification will
> produce a different set. The class remains the same, but the sets
> have different members or elements. I prefer to use the word 'type'
> instead of 'class' because it avoids the confusion with 'set'.
> But if you must use the word 'class', don't think 'set'.
>
> The questions below result from 2500 years of debate among philosophers
> writing in different languages about different, but related issues.
>
>> Below are some assumptions, followed by two questions.
>> 1. Categories are classes (sets?) of high level generic entities
>> e.g. Physical Object
>
> No. The word 'category' comes from Aristotle's word 'kategoria',
> which is a synonym for the word 'class' as it is used in ontology.
> In the middle ages, 'kategoria' was translated to the Latin
> 'praedicatum', from which we get the word 'predicate'.
>
> If you are using predicate calculus, every class or category is
> defined by some monadic predicate. If you are using some other
> version of logic, whatever corresponds to a predicate is what
> defines a class.
>
> For any monadic predicate P in any situation S, you can talk about
> the set of all x for which P(x) is true. That may be written
>
> {x | P(x) in the situation S}.
>
> But this set is *not* a class or a category. It is just a set.
>
>> 2. Universals are classes (sets?) of particulars e.g. Country
>
> Every class or category is a universal, but classes are not sets.
> There are some debates about whether there are universals that
> are not classes or categories. But those debates don't belong
> in a textbook that teaches beginning students how to use some
> version of logic to represent some subject matter.
>
> My recommendation is to drop the word 'universal' in any textbook
> (except in historical footnotes) and just use the word 'category'.
>
>> 3. Particulars are individual instantiations of universals e.g. Ireland
>
> Yes. But my recommendation is to drop the word 'particular' and use
> the word 'instance'.
>
>> 4. Categories are organized using subsumption hierarchies (sub-set
>> relation).
>
> The word 'subset' is incorrect. Do not use it except when talking
> about whatever sets exist in some situation. The word 'subsumption'
> is another confusing term that I would avoid. It is much clearer
> and simpler to use the terms 'generalize' and 'specialize'. If the
> category A subsumes category B then A is more general than B, and
> B is more specialized that A. I would relegate the word 'subsumption'
> to historical footnotes.
>
>> 5. Universals are organized using subsumption hierarchies (sub-set
>> relation).
>
> The word 'subset' is incorrect. My recommendation is to replace
> 'universal' with 'category' and 'subsumption' with 'generalization'.
> Then say "Categories are organized in generalization hierarchies."
>
>> 6. Particulars are elements of Universals (element-of or set-membership
>> relation)
>
> The terms 'set membership' and 'element' are incorrect. If you avoid
> using the words 'universal' and 'particular', you can just talk about
> categories (or classes) and instances. That way of talking is much
> easier to teach, learn, and understand.
>
>> Question 1: In DOLCE is the relationship between Categories and
>> Universals also a subsumption relation, with the caveat the categories
>> are higher up the hierarchy than universals?
>
> I recommend that people study philosophy. But I don't recommend
> mixing several millennia of philosophical verbiage with a tutorial
> on how to define the categories of an ontology.
>
> To answer question 1, the Dolce categories are organized in a
> generalization (subsumption) hierarchy. I would drop the word
> 'universal' as more distracting than helpful.
>
>> Question 2: In DOLCE could it be the case a particular could be an
>> element of a universal and an element of a category as follows:
>> ((P isElementOf U) and (U isSubsetOf C) => (P isElementOf C) = true) .
>
> This is the kind of question that wouldn't arise if we dispense
> with the incorrect verbiage and the confusing verbiage.
>
> First, don't ever use the word 'subset' when talking about universals,
> categories, and classes. My preferred term is 'subtype', but if you
> use the word 'class' you can say 'subclass'; if you use the word
> 'category', you can say 'subcategory'.
>
> Every category is a universal. The big question is whether you
> want to introduce metalevel categories that have other categories
> as instances instead of subcategories. But you don't need to
> use the word 'universal' to discuss that issue (except, perhaps,
> in philosophical footnotes).
>
> John
>
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> (05)
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