Monday, September 05, 2011 3:18 PM, Doug wrote:
"Azamat is correct in stating
> ... "the
> class membership relationship is not transitive, while the class inclusion
> is transitive."
although by
> In fact, ((P isElementOf U) and (U isSubsetOf C) => (P isElementOf C) =
> false)."
he appeared to mean
((P isElementOf U) and (U isElementOf C) => (P isElementOf C) = false).
which is correct." (01)
Thank you, Doug. That was exactly the meaning of the message. (02)
----- Original Message -----
From: "doug foxvog" <doug@xxxxxxxxxx>
To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Monday, September 05, 2011 3:18 PM
Subject: Re: [ontolog-forum] Universal and categories in BFO & DOLCE (03)
> On Sun, September 4, 2011 6:48, Patrick Browne said:
>> Hi
>> I am trying to establish whether BFO and DOLCE use the same set
>> theoretic semantics when formalizing the terms universal and category.
>> AFAIK DOLCE is an ontology of particulars and universals are not
>> formally part of the representational artifact, but they nonetheless
>> occur in practice.
>
> DOLCE *does* use "category" (often with the modifier "basic") to denote
> its upper level universals (see page 14 of "WonderWeb Deliverable D18"
> http://www.loa-cnr.it/Papers/D18.pdf ). They distinguish "universals"
> from "particulars":
> "The ontological distinction between <i>universals</i> and
> <i>particulars</i> can be characterised by means of the primitive
> relation of <i>instantiation</i>: particulars are entities that
> cannot have instances; universals are entities that can have
> instances."
>
> As John suggests, for ontological purposes, it is probably best not to
> use the terms "universals" and "particulars". But for the rest of this
> comment, i will use those terms to denote DOLCE's use of them, since
> the question appears to be about understanding DOLCE.
>
>> Below are some assumptions, followed by two questions.
>> 1. Categories are classes (sets?) of high level generic entities e.g.
>> Physical Object
>
> As John said, classes are not sets.
>
> So long as you understand that the entities which are instances of a
> category or class may themselves be classes, this is correct for DOLCE
> (with the parenthetical question removed).
>
>> 2. Universals are classes (sets?) of particulars e.g. Country
>
> Same answer.
>
>> 3. Particulars are individual instantiations of universals e.g. Ireland
>
> If by "individual", you mean "particular", yes. Note that
> *non-individual*
> instantiations of universals are NOT universals.
>
>> 4. Categories are organized using subsumption hierarchies (sub-set
>> relation).
>
> Correct, if the parenthetical term is removed.
>
> John is correct in dismissing the equivalence of "sub-set".
>
> Unlike John, i do not mind the use of the term "subsumption".
> His "subtype" or subclass are more specific terms; binary and higher-
> order predicates can also be arranged in subsumption hierarchies although
> not in subtype/subclass hierarchies.
>
>> 5. Universals are organized using subsumption hierarchies (sub-set
>> relation).
>
> Same answer.
>
>> 6. Particulars are elements of Universals (element-of or set-membership
>> relation)
>
> Remove the "or set-membership" and this is correct.
>
> Note that not all elements of Universals are Particulars. Some are
> Universals. As Asmat noted, instances of the (biological) Species
> universal are types of living things, not particular living things.
>
>> Question 1: In DOLCE is the relationship between Categories and
>> Universals also a subsumption relation,
>
> Yes.
>
>> with the caveat the categories
>> are higher up the hierarchy than universals?
>
> Since categories are universals, categories can not be higher
> on the subsumption tree than universals. DOLCE basic categories
> are at the upper level, but intermediate universals are not
> forbidden.
>
>> 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 false, since (U isSubsetOf C) is false. I suggest you mean:
>
> ((P isInstanceOf U) and (U isSubClassOf C) => (P isInstanceOf C) = true)
>
> which is correct.
>
> Azamat is correct in stating
>
>> ... "the
>> class membership relationship is not transitive, while the class
>> inclusion
>> is transitive."
>
> although by
>
>> In fact, ((P isElementOf U) and (U isSubsetOf C) => (P isElementOf C) =
>> false)."
>
> he appeared to mean
> ((P isElementOf U) and (U isElementOf C) => (P isElementOf C) = false).
> which is correct.
>
>
> -- doug foxvog
>
>> I posted a similar query to the BFO mailing list [1]
>>
>>
>> Regards,
>> Pat Browne
>> http://www.comp.dit.ie/pbrowne
>>
>>
>> [1]
>>
>http://groups.google.com/group/bfo-discuss/browse_thread/thread/7ae07db19d62af5e
>>
>>
>> This message has been scanned for content and viruses by the DIT
>> Information Services E-Mail Scanning Service, and is believed to be
>> clean.
>> http://www.dit.ie
>>
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>
>
> =============================================================
> doug foxvog doug@xxxxxxxxxx http://ProgressiveAustin.org
>
> "I speak as an American to the leaders of my own nation. The great
> initiative in this war is ours. The initiative to stop it must be ours."
> - Dr. Martin Luther King Jr.
> =============================================================
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