Dear Matthew, (01)
The word 'complete' can be applied to different things in different
ways. A theory about some domain can be completely formalized,
even though it does not completely describe that domain. (02)
JFS
>> What I would call an informal ontology would be
>> an incompletely specified theory about some domain -- but such
>> a theory might not look like a typical terminology. (03)
For example, a scientist's first insight towards a new theory
might be expressed in diagrams supplemented with NL statements.
Then little by little, those diagrams and comments could be
refined to mathematical formalisms. (04)
MW
> Could you give a (non-trivial) example of a completely specified
> ontology of some non-mathematical domain? I suggest that in practice, all
> ontologies of more than bits of mathematics, i.e. ontologies of the world,
> are necessarily informal then, since they are inevitably incomplete. (05)
All scientists know that no theory is ever a complete and faithful
description of the world, but many of them are completely formalized.
For example, Newtonian mechanics describes an important aspect of the
world. It has been completely formalized in mathematics, but it is
known to be incomplete in its coverage of the world, and it is only
an approximation even for those aspects it covers. (06)
In computer science, many systems specify programs in a logical
formalism, which is then translated automatically to an executable
form. Pure functional programming, for example, uses only statements
that are one-to-one expressible in FOL. An FP specification would be
a completely formalized theory that completely specifies the program
generated from the theory. (07)
John (08)
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