> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
> Sent: 04 September 2011 16:57
> To: [ontolog-forum] ; John F. Sowa
> Cc: Nicola Guarino
> Subject: Re: [ontolog-forum] Universal and categories in BFO & DOLCE
>
>
> On Sep 4, 2011, at 9:06 AM, John F. Sowa 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.
>
> Well, not quite all. What you say is also true for most ontologes
expressed in
> RDFS, ISO Common Logic and OWL Full, but OWL DL - which is now widely used
for
> ontology development on the Web - does impose an extensionality condition
on
> classes, so there classes are indeed sets. I personally regret this
decision
> and argued against it, but did not prevail in the WG debates on this
matter. (01)
MW: Also 4D ontologies that use possible worlds can define classes as sets,
as has been discussed on this list in the past. (02)
A problem with defining classes as sets for ontologies with other
foundations is that you cannot talk about imaginary things like unicorns,
because they all equate to the null set, and other definitions might
accidentally give identical sets, even though they are not necessarily
identical. (03)
Regards (04)
Matthew West
Information Junction
Tel: +44 1489 880185
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Skype: dr.matthew.west
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http://www.matthew-west.org.uk/ (05)
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>
> > 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.
>
> Actually, that particular circumstance (same class, different sets) cannot
> occur in RDF-based notations or ISO-CL, although they do allow the inverse
> (same set, different classifications; examples being humans vs hairless
> bipeds, or fairies vs angels (both empty).) But see below.
>
> > 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.
>
> Yes. FWIW, the currently active RDF working group, tasked with updating
and
> revising the RDF specs, is in the process of wrestling with this issue.
RDF
> has always allowed two different classes to have the same set extension,
but
> now it also needs to allow for the possibility of a single RDF 'graph'
> retaining its identity while its underlying set changes; in other words to
> have a 'state' which changes with time. Set language (used in the current
RDF
> specs) is sharply inconsistent with this notion, as sets do not change:
they
> are completely specified by their membership, and have no other identity
> criteria.
>
> I mention this only to emphasise that these issues, while having roots (as
> John points out) in 2500 years of philosophy, are still very much at the
> forefront of current ontology engineering practice.
>
> Pat Hayes
>
> >
> >> 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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