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Re: [ontolog-forum] The notion of a "classification criterion" as a clas

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sun, 25 Apr 2010 08:02:20 -0400
Message-id: <4BD42F4C.10909@xxxxxxxxxxx>
Pat, Bene, and Alan,    (01)

This thread shows why trees are inadequate for representing hierarchies
of ontological categories.  Aristotle's syllogisms support lattices.
Leibniz's Universal Characteristic, based on his Ars Combinatoria,
supports lattices.  The method of Formal Concept Analysis (FCA),
which is widely used to verify that OWL definitions are consistent,
supports lattices.    (02)

If you use lattices and the FCA software (or other related techniques),
you automatically solve the problems that normalization was designed
to address.  That includes the issues discussed in the cited paper:    (03)

http://www.cs.man.ac.uk/~rector/papers/Modularisation-normalisation-rector.pdf    (04)

PH> ... the semantic model underlying OWL-DL is very straightforward.
 > So, ask how your vision can be re-stated in terms of classes
 > considered as simple sets.    (05)

If you do that, you run into the same issues:  For any set, the
set of all subsets forms a lattice.  If you have a formalism that
can only support trees, you can't represent all possible relations
among sets.  The normalization methods that have been proposed are
techniques for dealing with such issues.    (06)

My recommendation is to use a system that supports full lattices
instead of just trees.  For further info, check Google for
the terms "FCA OWL" -- but you might add the word 'concept'
to the search list to avoid extraneous hits.    (07)

John    (08)

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