Moreover, one need not agree on a unique set of primitives. There might be 7-8
different sets with mappings between them, but no real "join" or
generalization of the primitives - i.e. 7-8 different FO's that all efforts
have been unable to merge.
I.e. instead of a single hub-spoke, you have 7-8 hubs and ensuing spokes, with
the hubs connected to one another.
[[PC]] How would the hubs be connected to
each other? If the mappings are not 1 to 1, what kinds of relations would
have to be defined? Would you introduce new more basic elements to create
the translations among the 7-8 hubs? Would accurate translations be
possible? (If they are 1 to 1, the ontologies are essentially identical,
a case I have never seen).
MW: Ideally you would have biconditional
assertions of equivalence, i.e. that some pattern of instances of ontology A
was equivalent to some pattern of instances in ontology B. There would not need
to be any additional terms.
MW: Now you might want to abstract from both
ontologies the underspecified terms John has been talking about, but that is
just an aid to simplifying the mapping process.
Here’s a dichotomy: (1) two
candidates for an FO are logically contradictory. Attempted mappings
without stringent effort to isolate and avoid the inconsistency may cause
disastrous errors in translation among them.
MW: I don’t think so. Take 3D and 4D,
it is not so difficult. Anything in 3D can be mapped into 4D using the approach
above. Not everything a 4D ontology can be mapped into 3D, but these would be
things a 3D ontology would claim do not exist anyway, so you would not care
about the loss.
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