Ed Barkmeyer wrote:
>
>> The set is either
>> defined extensionally or generated as the extension of a predicate in a
>> given context.
>
> For "context", I would have said "domain of discourse".
Assuming a model-theoretic approach (and thus applicable to OWL and
RDF(S) semantics)
changing the domain of discourse is not the only way to get a different
extension of a (OWL or RDF(S)) class.
We can keep the domain of discourse the same and change the interpretation.
An interpretation is made up of two parts:
1. an association of the terms of the language with objects in a
structured domain
2. an association of atomic wff with relations over the domain
(I am quoting here from Essence of Logic by John Kelly)
So we can even keep part 1 the same- this is where URIs get assigned to
resources==objects.
We can simply make some changes in part 2.
That way we can talk about objects, identified by their URIs, being part
of more than one interpretation. (01)
I have a feeling "context" is another one of those over-loaded terms,
but in a broad sense I think it means anything extra that needs to be
added to a "statement" (formal or linguistic) in order to determine its
"value", where "statement" and "value" have to be defined in "context",
making this a circular definition. (02)
I would be delighted if someone could provide one or more precise
definitions of "context".
>
>> Once the set is generated, the extension of the predicate
>> in a different context (which might merely mean a different time) is no
>> longer necessarily the same set.
>>
>
> Agreed. A set _is_ the collection of things in it. A different
> collection of things is a different set.
> But that does get into issues of identity.
And one way to get into those issues is to talk about URIs. (03)
And speaking of identity, I have started a new thread about context -
the discussion doesn't seem to be, at least directly, related to rough
sets anymore. And perhaps the topic of context is of more general interest. (04)
--
Tara Athan (05)
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