-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Ed Barkmeyer
Sent: Friday, January 21, 2011 1:39 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Ontology of Rough Sets (01)
Christopher Menzel wrote:
> On Jan 21, 2011, at 9:46 AM, doug foxvog wrote:
>
>> ...
>> A standard distinction between a set and a class, is that membership in
>> a [set] cannot change, while membership in a class can.
>>
>
> I think it's useful to distinguish two claims when it comes to the identity
>conditions of classes:
>
> (1) Classes are not extensional (i.e., distinct classes can have the same
>members/instances)
>
> (2) Classes can change their membership.
>
> In the formal semantics of a number of KR languages, (1) is true but,
>strictly speaking at least, (2) is not. Notably, classes in OWL are
>explicitly non-extensional: since a class is stipulated only to *have* an
>extension in OWL's formal semantics, nothing prevents distinct classes from
>having the same extension. The same is true of RDF. However, simply because
>there is no formal notion of change built into OWL's semantics, there is no
>possibility, within a given interpretation, that a class change its
>membership. As noted in an earlier message in this thread, without augmenting
>the notion of an OWL interpretation somehow, change can only be represented
>formally in terms of something like a series of interpretations that are
>thought of as temporally ordered. That said, (2) does seem to be a strong
>*intuitive* idea in the KR, AI, and database communities.
> (02)
The particular problem I have recently got involved in is the intrusion
of temporal concepts into would-be ontologies in business applications.
In the supply-chain area, for example, it is important to be able to
talk about schedules and shipments being "late". Getting past the
indexical issues, which are fixed by translating the intuitive "now"
into specific time relationships, the particular problem is that
shipments and orders do change state, and actions are taken on the basis
of reclassification. (03)
A major problem for us is that the industry folk throw these concepts
into what was an ontology for the "snapshot" model of decision-making --
the state of the world at the time the decision is to be made. This
gives rise to formalizing ideas like "proposition X is false at time A
and true at time B." And that problem arises from the idea that states
of things are characterized by propositions, which seems to be
fundamental to applications of ontologies. The 4D idea that a thing in
a different state is a different thing, and 'objects' are actually
sequences (or more generally, lattices) of things in states, is a means
of producing a formal semantics, but it is totally out of line with the
intuition of the domain experts. They cannot then "validate" the
ontology -- they don't understand it. (04)
[LEO:] One alternative is to use a hybrid logic, where propositions are true at
a given state or time, i.e., using nominals, and which extends propositional
modal logic. This originated many years ago (Prior), but Gabbay's "labelled
deduction" thread (where it was still multiple logics correlated at a
meta-level) and "dynamic logic" brought it forward again in recent years (at
least to my knowledge). Then Blackburn et al "pushed it down" into the object
logic. Or another possible alternative is to use a "context" logic such as IKL.
Perhaps microtheories ala Cyc. I agree that most non-ontologists have
difficulties with 4-D. I do think an indexed ontology language would be useful,
and suggested multiple indexing of ontological expressions in a short paper in
2005. I am not an expert in these topics, more of an interested observer,
having come on these topics from natural language semantics. Probably Chris
Menzel or Pat Hayes or John Sowa could tell you more. (05)
... (06)
-Ed (07)
"Mathematicians are like Frenchmen. Whatever you say to them they
translate into their own language and at once it becomes something
entirely different."
-- Goethe (08)
> Finally, the idea that sets are extensional and classes are not is definitely
>not standard among logicians and mathematicians, who typically associate the
>notion of class with theories like VNBG, wherein both classes and sets are
>extensional.
>
> -chris
>
> (09)
--
Edward J. Barkmeyer Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263 Cel: +1 240-672-5800 (010)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (011)
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