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Re: [ontolog-forum] Heterarchy & Hierarchy, oh my my

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Cc: bfo-discuss@xxxxxxxxxxxxxxxx, obo-relations@xxxxxxxxxxxxxxxxxxxxx
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Sun, 04 May 2008 09:53:32 -0400
Message-id: <481DBFDC.7050409@xxxxxxxxxxx>
Alan,    (01)

That is the source of the misunderstanding:    (02)

 > I have to say it makes me suspicious when I see claims about
 > any methodology that "automatically generates a ... system
 > that is *proved* to be consistent", if the methodology is one
 > that is intended for people, rather than machines, to apply.    (03)

The FCA methodology (and I hope any other that is proposed to
support ontology development) uses computers to assist people.    (04)

What people do is to define terms.  What the computer does is
to compute the hierarchy (i.e., the lattice).  People should
not assert supertypes or subtypes.  The computer derives them.    (05)

If all maintenance of the ontology is done with the same tools,
it should not matter how many people add definitions.  Whenever
a new term is added, the computer automatically derives its
place in the lattice.  If an inconsistency arises, the person
who wrote the definition is instantly notified.    (06)

I must add a caveat:  The FCA methodology is limited to
definitions that use only monadic predicates to characterize
the terms.  That is clearly a limitation for the detailed
levels of an ontology, but it is not a problem for the
upper and middle levels.    (07)

As I have said many times, I do not believe that the upper
levels of an ontology should have detailed axioms.  The
microtheories at the lower levels are where most of the
complex reasoning and problem solving is done.  For those
theories, complex axioms can make it difficult or impossible
to do the automatic derivations of FCA.  If so, I would not
use FCA for those microtheories.    (08)

Following is my recommendation:    (09)

  1. The upper and middle levels of an ontology should be
     lightly axiomatized, with monadic predicates used to
     represent the distinctions necessary for deriving the
     lattice.    (010)

  2. The lower levels, where complex reasoning is done, should
     be organized in specialized modules or microtheories,
     which can use whatever axioms or methods of logic are
     appropriate for the subject matter.    (011)

I agree with Pat Hayes and Chris Menzel that the terms
'universal' and 'particular', which are historically
important, have become laden with so many millennia of
incompatible philosophical baggage that they have become
more confusing than enlightening.    (012)

My recommendation is to use neutral terms such as 'predicate'
or 'relation'.  Anyone who wishes to privilege certain
predicates or relations with the honorific term 'universal'
is welcome to do so.  But the philosophical positions that
are associated with the terms 'universal', 'particular', or
'abstract particular' should not be allowed to pollute the
formalism or the computational methods it supports.    (013)

John    (014)

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