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
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
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
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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