Hello John, (01)
On 11-12-20 10:38 AM, John F. Sowa wrote:
> Dear Ali,
> I've been going through the Gruninger et al. paper. It specifies more
> theoretical structure than I believe is required for OOR. I cannot see
> any relationship or transformation that would be useful for OOR that I
> cannot define just as formally, but more simply in terms of a single
> Lindenbaum lattice, the AGM operators, and a few more easy-to-define
> distinctions such as conservative vs. nonconservative extensions.
I wait with eager anticipation a single theorem (with proof
of course) that backs up your claim.
> I would like to see a single example of a useful OOR operation that
> 1. Could be specified in terms of that paper, but
> 2. Could not be replaced by the same or an equally useful and
> efficient OOR operation that is specified just as formally,
> but much more simply in terms of the approach I outlined.
Actually, John, the burden here is on you to provide such an example.
> 2. Taken together, they reduce the total number of independent
> assumptions further:
> a) The AGM contraction and expansion operators exactly coincide
> with the generalization and specialization relations of the
> lattice: for every contraction/expansion that deletes/adds
> a proposition to a theory, there is a corresponding
> generalization/specialization and vice versa.
> b) The process of theory revision is *identical* to the process
> of generating new ontologies by merging or modifying other
> They are nothing more nor less than two different
> ways of thinking and talking about the same things -- namely
> theories in a lattice.
> 3. There is a large literature about belief (or theory) revision
> that discusses the kinds of operations on ontologies in your paper.
> That literature presents similar issues from a slightly different
> point of view and in different terminology. They also present
> many important ideas that are not discussed in your paper. See,
> for example, the 110 references in the review article by Peppas.
[Peppas 2008] is a paper on belief revision in general. All of these
are dealing with theories with the same signature.
It does not discuss any operations such as faithful interpretation,
or reducibility. (02)
> I believe that the group made a mistake. I can define equivalent
> notions of modularity, reducibility, translations, and mappings with
> an equal level of formality. Use the term 'hierarchy' for the
> implemented subsets of lattices.
>> the various flavours of interpretation which are nowhere to be found
>> in AGM lit
> The AGM lit was intended for nonmonotonic reasoning. It was not
> written for the problem of designing a repository. But I'm sure
> that any flavors you find useful could be defined with a lot less
> complexity in terms of the AGM operators.
"I'm sure it can be done" is right up there with "Proof left for reader" (03)
- michael (04)
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