Wacek, (01)
I'm happy that you were making a point that anybody who
knew anything about logic would consider obvious: (02)
> I was repeatedly complaining on the OBO- and BFO-related
> lists about the insistence, within that framework, on
> single inheritance. (03)
Those people were probably confusing some of the practical
problems in programming languages (where few, if any,
programs are formally defined) with issues in logic,
where everything is formally defined. (04)
> I mention this because the answer to my complaints, if any,
> was invariably that single inheritance a) increases efficiency
> of reasoning, b) is more natural and easier to use, and c) is
> good for interoperability. (05)
When it comes to logic, those three statements are hopelessly
false, confused, and misleading: (06)
a) There are *always* multiple ways to derive a proof of
any theorem. Failing to permit them in a hierarchy does
*nothing* to speed up theorem proving, and it can in many
cases block important short cuts. (07)
b) Every animal, vegetable, and mineral on planet earth
can be classified in an open-ended number of ways.
Arbitrarily picking one and prohibiting the others is
unnatural, confusing, and horribly difficult to use. (08)
c) It does *nothing* to promote interoperability. On the
contrary, it can *block* interoperability when one
system arbitrarily blocks paths that another uses. (09)
d) You can add the problems created by single inheritance
in trying to merge ontologies. The result invariably
has a superset of the inheritance paths of both. If
multiple inheritance is prohibited, merging becomes
impossible. (010)
In previous notes, I mentioned the large group of people who
use Formal Concept Analysis to derive lattices, which support
multiple inheritance in very clear, efficient, and easily
visualizable ways. (011)
For a very brief summary, see Section 7 on lattices in
my tutorial on math and logic: (012)
http://www.jfsowa.com/logic/math.htm (013)
For more detail, including lots of software, see the FCA home page: (014)
http://www.upriss.org.uk/fca/fca.html
Formal Concept Analysis Homepage (015)
For some pretty pictures of lattices generated by FCA, see (016)
http://www.upriss.org.uk/fca/examples.html
Formal Concept Analysis Examples (017)
John (018)
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