In some discussion related to the workshop, I sent the following
message, which clarifies a comment about my talk and elaborates
on some related issues. (01)
John Sowa
_________________________________________________________________ (02)
I just wanted to correct one point in the report on my talk: (03)
> To map between different ontologies, the Vivomind Analogy Engine
> throws axioms out, and searches instead for analogies in their
> structures. (04)
Although it is true that VAE does not require axioms in order to
find patterns in whatever information it processes, it doesn't
"throw axioms out". In fact, one of my examples showed how VAE
can derive a formal alignment of two different ontologies. Such
mappings found by VAE could be automatically translated to *axioms*
or other formalizations that relate those ontologies. (05)
I said something along those lines in my reply to the comment by
Nicola: (06)
> Guarino comments that people can communicate without need of axioms
> as they share a common context, but in order to teach computers how
> to operate, the requirements are different: he would not trust an
> airport control system working by analogy. (07)
I am definitely in favor of using axioms when they are available,
but most of the time, suitable axioms are not available. When axioms
used for one application are available for other uses, it is extremely
unlikely that they could be used in another application without major
modifications and revisions. (08)
As for airport control systems or other mission-critical applications,
I would not trust any system -- axiomatized or not -- that had not
undergone extensive testing. I most definitely would *not* trust
one that was based on some "off the shelf" axioms that had been
developed for a different application. (09)
I would like to cite some papers by Alan Bundy, who has been working
on automated theorem proving methods for the past 30 years. He is
most definitely *not* against using axioms, but he and I strongly
agree that there is no such thing as a single, best universal
axiomatization that can be applied to all problems. Even for two
different problems within the same very narrow field, it may be
necessary to use very different axiomatizations. See, for example, (010)
http://www.inf.ed.ac.uk/publications/report/0837.html (011)
And even for a single problem, it may be useful to use multiple
different methods and axiomatizations: (012)
http://www.inf.ed.ac.uk/publications/report/0954.html (013)
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