|From:||Ali Hashemi <ali.hashemi+ontolog@xxxxxxxxxxx>|
|Date:||Sun, 24 Jan 2010 22:35:40 -0500|
On Sun, Jan 24, 2010 at 9:58 PM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:
But people have criticized model theory because there is more to say
These objections don't imply that model theory is wrong for
Just an observation on weakness #1 as identified by John above. This "weakness" also provides some concrete advantages vis-a-vis ontology alignment and mapping.
Specifically, if one accepts the premise that much of our structured thinking (say in a formal logic) reuses the same patterns or "logical building blocks," then these model structures provide a very nice way to identify agreement / conflict between ontologies in the same domain, and/or to highlight interdisciplinary borrowing of concepts, and/or to help clarify metaphors.
By model structure, i mean the set of permissible models attained for a given theory, but decontextualized from the universe of discourse --- so in the trivial example above, the (logical) synonymity holds for the models allowed by "Every A is A" - i.e. if we strip the models from their referent to specific objects, then the sets of the models for the above theories are isomorphic.
Of course, this captures only logically synonymous formulations, and as it has been pointed out, there's more to meaning than that. But this type of synonymity is a very useful insight that can go a long way in alleviating the problems of multiple, competing ontologies.
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