On Jan 22, 2011, at 8:58 PM, Christopher Menzel wrote: On Jan 22, 2011, at 6:47 PM, Pat Hayes wrote: On Jan 22, 2011, at 4:50 PM, Christopher Menzel wrote: ...A class can change its membership from one interpretation to another merely with the addition or removal of statements.
Sure.
i'm not sure I agree, and I wonder if Chris really does.
I don't. I hastily read Doug's claim to be the rather trivial claim that a class can change its membership from one interpretation to another by the addition or removal of elements from its extension. What does this even mean, "a class can change its membership from one interpretation to another" ? A given class NAME may be interpreted differently in different interpretations, of course: but the classes themselves - the entities, whatever they are, which are denoted by the class names and which are, therefore, classes - cannot "change ... membership from one interpretation to another" since they ARE entities in a given interpretation. It does not make sense to speak of 'moving' a class (or anything else) 'from' one interpretation 'to' another.
I'm not following. Suppose I have a class name c in my language and let M be an OWL interpretation in which c denotes OWL class C. Now create a new interpretation M' that differs from M only in that we alter the extension that is assigned to c's denotation C. Doesn't that make credible sense of the idea that C's members have changed?
I guess that does make a kind of sense, provided we are all agreed that we are talking within the Common Logic model theory. But it would not make sense if we were using classical Tarskian semantics or, for example, the OWL normative semantics. And I think it is a misleading way of speaking, since it is easily misunderstood as saying that one can take a set and change its members (and it still be the same set....) And even if it did, how would this be achieved by addition or removal of STATEMENTS? Classes do not (usually) contain statements.
Agreed.
That said, (2) does seem to be a strong *intuitive* idea in the KR, AI, and database communities.
This is the meaning i was referring to.
Never meant to suggest otherwise! :-)
Then allow me to suggest otherwise. As someone somewhat familiar with at least the KR and AI communities, I do not recall that the idea that class membership can change is, in fact, a strong intuitive idea there. If it were, the AI/KR field would have been happily using class language rather than, say, speaking of situations, ever since 1969. Temporal reasoners use many formal devices to represent time and change, but this simplistic notion of classes changing their membership is not one of them. If one were to try to use it in a realistic example, one would rapidly discover why.
I'll defer to you vis-á-vis the AI community; perhaps I've overgeneralized there. But in my own experience building "real world" database models and ontology models, I often heard folks talking about classes changing membership. Notably, in an implementation of a database model, intuitively, the instances of the classes identified in the model change with every update.
And I guess I have to defer to you when it comes to databases. But then I wonder why there has ever been a notion of, for example, a temporal database? After all, if database classes can change with time, why do we need to do anything special to make them 'temporal' ?
Pat
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