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. (01)
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." (02)
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. (03)
> Below are some assumptions, followed by two questions.
> 1. Categories are classes (sets?) of high level generic entities e.g.
> Physical Object (04)
As John said, classes are not sets. (05)
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). (06)
> 2. Universals are classes (sets?) of particulars e.g. Country (07)
Same answer. (08)
> 3. Particulars are individual instantiations of universals e.g. Ireland (09)
If by "individual", you mean "particular", yes. Note that *non-individual*
instantiations of universals are NOT universals. (010)
> 4. Categories are organized using subsumption hierarchies (sub-set
> relation). (011)
Correct, if the parenthetical term is removed. (012)
John is correct in dismissing the equivalence of "sub-set". (013)
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. (014)
> 5. Universals are organized using subsumption hierarchies (sub-set
> relation). (015)
Same answer. (016)
> 6. Particulars are elements of Universals (element-of or set-membership
> relation) (017)
Remove the "or set-membership" and this is correct. (018)
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. (019)
> Question 1: In DOLCE is the relationship between Categories and
> Universals also a subsumption relation, (020)
Yes. (021)
> with the caveat the categories
> are higher up the hierarchy than universals? (022)
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. (023)
> 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) . (024)
This is false, since (U isSubsetOf C) is false. I suggest you mean: (025)
((P isInstanceOf U) and (U isSubClassOf C) => (P isInstanceOf C) = true) (026)
which is correct. (027)
Azamat is correct in stating (028)
> ... "the
> class membership relationship is not transitive, while the class inclusion
> is transitive." (029)
although by (030)
> In fact, ((P isElementOf U) and (U isSubsetOf C) => (P isElementOf C) =
> false)." (031)
he appeared to mean
((P isElementOf U) and (U isElementOf C) => (P isElementOf C) = false).
which is correct. (032)
-- doug foxvog (033)
> 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
>
>
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doug foxvog doug@xxxxxxxxxx http://ProgressiveAustin.org (035)
"I speak as an American to the leaders of my own nation. The great
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- Dr. Martin Luther King Jr.
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