|From:||William Frank <williamf.frank@xxxxxxxxx>|
|Date:||Sat, 20 Sep 2014 11:02:36 -0400|
2. How is abstraction, which often includes a change in terminology, most usefully defined and related to generalization?
I found this very interesting,raising additional mathematical questions that could be useful in the systematization of relationships between ontologies, beyond those of interoperability, and perhaps reapplied to interoperability in a more fruitful manner.1. How is 'generalization' and 'specialization' as a relation between classes realated to the relation defined here between theories? I believe that in fact, the relation between classes is actually derived from the relations between theories about the classes.
For example, it seems to me that abstraction, as in the way that a tree structure is an abstraction of organization charts, single cell reproduction, asymmetric keypair protection, ... is also a generalization, so that the REST of the theories of single cell reproduction and asymmetric keypair protection will be incompatable, but the abstraction **and** generalization to the theory of tree structures is a point of shared generalization. (or, as in the way a group is an abstraction of addition with identity zero as well as of multiplication with identity one).
And, in the tree example, the REST of the theories of single cell reproduction and asymmetric keypair protection are not, as in your definitions, 'inconsistent', because they do not even share the same vocabularies or meanings for the terms they use. Only the abstraction that maps several different meanings, say 'protected by', 'parent organization of' 'parent cell of', to an abstract relation,named say 'predicessor' or 'parent' is shared, and is a 'generalization' of all of them.
So, mappings of vocabularies may help resolve some of the problems being suggested in this thread.
On Fri, Sep 19, 2014 at 10:15 AM, John F Sowa <sowa@xxxxxxxxxxx> wrote:
In another forum, I sent a note about using the terms 'generalization'
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