On Fri, January 21, 2011 13:39, Ed Barkmeyer wrote:
> 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. (01)
> 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. (02)
Fine. (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. (04)
This is fine for representing states. (05)
> The 4D idea that a thing in
> a different state is a different thing, (06)
What is the need to consider a thing in a different state a different
thing? (07)
This is not what the ontological community considers to be a 4D idea.
A 4D object, in this context, is an object that can have different
state at different times. (08)
> and 'objects' are actually
> sequences (or more generally, lattices) of things in states, (09)
This is a different model, that has a far different definition of "thing"
than is generally used in computer ontologies. (010)
> is a means of producing a formal semantics, (011)
One could certainly produce a formal semantics using such definitions. (012)
> but it is totally out of line with the
> intuition of the domain experts. (013)
Then it is probably not worth while to present such a model to them.
If you want to use it "under the covers"/"inside the black box",
because it makes calculations easier, fine. But don't inflict such
a model on domain experts. I would suggest it also be hidden from
the ontology builders and merely be maintained as part of the inference
engine. (014)
> They cannot then "validate" the
> ontology -- they don't understand it. (015)
> I have said in that forum that solving the problem is beyond my
> expertise. It is my conviction that the problem is not really "time",
> but rather "change of state" or "alternative states", and in that sense,
> "time" is a means of labeling "alternative possible worlds". (016)
Time is certainly one way of marking alternative states. (017)
> All we are saying is that the intuitive notion of change is endemic to a
> lot of ontology applications. (018)
Certainly. (019)
> We can usually constrain the immediate application
> to avoid the problem or create a convenient work-around, (020)
If you are only using the data with a single reference time period,
the of work-around need not consider viewing the data in another
temporal context. But if the data is to be dealt with for another
time period, that should affect the work-around method chosen. (021)
> but that usually means that the next application
> the business wants to use the ontology for requires re-writing it. (022)
This suggests that the issue of state needs to be handled in a
different manner. Perhaps the date references need to be kept as dates
and an object representing the current date be included in the
knowledge base for each analysis period. (023)
-- doug f (024)
> -Ed
>
> "Mathematicians are like Frenchmen. Whatever you say to them they
> translate into their own language and at once it becomes something
> entirely different."
> -- Goethe
>
>
>> 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
>>
>>
>
> --
> 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
>
> "The opinions expressed above do not reflect consensus of NIST,
> and have not been reviewed by any Government authority."
>
>
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doug foxvog doug@xxxxxxxxxx http://ProgressiveAustin.org (026)
"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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