This is an extension/follow-up to Michael Gruninger's
email formulated by my colleague Till Mossakowski,
who is responsible for the formal underpinnings of
our work at Bremen. He has not been put on the
mailing list as yet (till@xxxxxxxxxxxxxxxxxxxxxxxx);
not sure who takes care
of those details! This extends the points on the
Wiki at:
http://ontolog.cim3.net/cgi-bin/wiki.pl?UpperOntologySummit/UOSdiscussionPage (01)
John B. (02)
C-E LCMC CIO/G6 wrote: (03)
>
>> All,
>>
>> Are we going to discuss the technical feasibility of interrelating
>> multiple upper ontologies? To issue a communique, we'll need a good
>> handle on whether we believe this is technically feasible and will
>> enable semantic interoperability....
>
[MG]
> ...
> - Theory T1 generalizes theory T2 iff T1 is definably interpretable in
> a theory T3 and T2 is a consistent extension of T3.
(corrected version) (04)
I think the question of whether the extension is conservative is
important as well. (An extension of T1 of T2 is conservative if
all consequences of T1 that are expressed in the nonlogical lexicon of
T2 are already consequences of T2. Note that a conservative extension
of a consistent theory is again consistent, but a consistent extension
of a consistent theory need not be conservative.) (05)
> The idea is that we can design a Common Subset Ontology (CSO)
> by solving the following problem for the theories contained in
> the set of existing upper, mid-level, and domain-specific ontologies:
>
> Given two theories T1 and T2, determine whether there exists a theory
> that generalizes both. (06)
> Theories that do not have any generalizations
> are candidates for inclusion in the CSO. (07)
Is it necessary that the generalizing theory is again a theory contained
in some ontology?
Otherwise, the empty theory trivially is the most general theory.
Perhaps it is also useful to have a notion of intersection of theories? (08)
From the Wiki:
> With such a subset, it should be possible to guarantee that an
> ontology developed using the COSMO could be imported into any one of
> the linked ontologies and be logically consistent with that ontology.
Note that this sort of consistency only is guaranteed in case that
the linked ontology is a *conservative* extension of COSMO. (09)
> If the individual linked ontologies have richer detail for specific
> classes, the simpler class representations in the COSMO would serve
> as abstracted "views" of the more detailed concepts. (010)
This notion of view is formalized in CASL, also under the name of
"view". When proving such views, structuring helps a lot: much can
be done using just structural analysis. (011)
Greetings,
Till Mossakowski
--
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