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.
Proof please!
>
> b) The process of theory revision is *identical* to the process
> of generating new ontologies by merging or modifying other
> ontologies.
Proof please!
> 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
approaches
are dealing with theories with the same signature.
It does not discuss any operations such as faithful interpretation,
definable equivalence,
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.
Show me!!!
>
>> 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)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J (05)
|