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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: Wacek Kusnierczyk <Waclaw.Marcin.Kusnierczyk@xxxxxxxxxxx>
Date: Sun, 04 May 2008 19:53:41 +0200
Message-id: <481DF825.8010407@xxxxxxxxxxx>
John, thank you for the comment.  I am familiar with lattices from, 
among others, your KR book, which was one of the sources of inspiration 
for my previously mentioned complaints.    (01)

I hope for some more, *serious* discussion from the side of the OBO 
community.    (02)

vQ    (03)

John F. Sowa wrote:
> Wacek,
> I'm happy that you were making a point that anybody who
> knew anything about logic would consider obvious:
>  > I was repeatedly complaining on the OBO- and BFO-related
>  > lists about the insistence, within that framework, on
>  > single inheritance.
> 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.
>  > 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.
> When it comes to logic, those three statements are hopelessly
> false, confused, and misleading:
>   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.
>   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.
>   c) It does *nothing* to promote interoperability.  On the
>      contrary, it can *block* interoperability when one
>      system arbitrarily blocks paths that another uses.
>   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.
> 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.
> For a very brief summary, see Section 7 on lattices in
> my tutorial on math and logic:
>     http://www.jfsowa.com/logic/math.htm
> For more detail, including lots of software, see the FCA home page:
>     http://www.upriss.org.uk/fca/fca.html
>     Formal Concept Analysis Homepage
> For some pretty pictures of lattices generated by FCA, see
>     http://www.upriss.org.uk/fca/examples.html
>     Formal Concept Analysis Examples
> John
>       (04)

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