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Re: [ontac-forum] Theories, Models, Reasoning, Language, and Truth

To: ONTAC-WG General Discussion <ontac-forum@xxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Wed, 14 Dec 2005 21:13:36 -0500
Message-id: <43A0D150.5070501@xxxxxxxxxxx>
Paul,    (01)

The main point of my paper on Theories, etc., was to
summarize some background information about theories,
models, and language.  My goal was to clarify some
fundamental notions in order to support a more informed
discussion of the issues.    (02)

I'd like to comment on the three points on your web site:    (03)

 > that natural language has properties that are not
 > present in, at least, those formal systems that are
 > derived from the Greek traditions.    (04)

The reason why I mentioned Aristotle is to show that
many of the underlying issues have been debated for
over two millennia, and the debate is still open.  I'm
not criticizing the Greeks any more than anybody else.    (05)

One point I wanted to emphasize is that natural languages
are far more complex than many people have assumed.  In
particular, many of the ontologies that have been proposed
can be viewed as implementations of Wittgenstein's first
book, the _Tractatus Logico-Philosophicus_.    (06)

In his later book, the _Philosophical Investigations_,
W. criticized the "grave errors" of his first book.  I am
convinced that Wittgenstein's second book is a much sounder
basis for ontology than his first book.  In effect, W's
first book proposed one giant "language game" represented
by one giant theory -- much like many currently proposed
ontologies.  Many of the AI systems implemented in the
1970s and '80s could be viewed as direct implementations
of W's first book.  As I argued in the knowledge soup
paper (see below), I believe that approach is doomed.    (07)

In W's second book, he argued for an open-ended number of
language games.  What I proposed is to replace the single
theory with an infinite lattice of theories, which could
accommodate an open-ended number of possible language games.    (08)

 > that the interpretant has a great role in localizing
 > experience both via the cognitive as well as the emotive
 > centers.  (but you make no operational suggestion  in
 > this paper - as to how to move forward on core-hub-common
 > ontology plus basic structural data interoperability).    (09)

Yes, I did want to emphasize the importance of purpose and
intended application as a major determinant in the selection
of an appropriate theory to be applied at any level, from
the upper levels to the lowest levels of an ontology.    (010)

 > and that a lattice of theories might be used to support
 > analogous computations (but this is unproved)    (011)

In that paper, I did not go into all the details of how
a lattice of theories could be used.  The main reason is
that there are a great many possible uses:    (012)

  1. The lattice provides a method of organizing and relating
     any collection of theories in a way that shows how they
     are related to one another as ancestors, descendants,
     siblings, or distant cousins.  Since the entire lattice is
     infinite, it will never be completely populated by theories
     that anyone has actually defined.  However, it will always
     provide an explicit location for any and every theory that
     anyone may ever define or propose to define.    (013)

  2. For any given ontology that has been constructed, the lattice
     demonstrates all the ways that ontology can be (a) subdivided
     into simpler modules or (b) be extended in a consistent way
     by adding more modules.  Every consistent theory that anyone
     has ever proposed or ever will propose can be placed somewhere
     in that lattice.  And every inconsistent theory will degenerate
     to the absurd theory at the bottom of the lattice.    (014)

  3. Any large theory -- Cyc, SUMO, Dolce, BFO, etc. -- can be
     situated somewhere in that lattice.  Above it are all the
     generalizations and below it are all the specializations.
     Given any two theories, say SUMO and BFO, their supremum
     would be their lowest common generalization, and their
     infimum would be their highest common specialization.    (015)

  4. If two theories are incompatible -- i.e., inconsistent with
     one another -- their infimum would be the absurd theory at
     the bottom.  That would imply that they could not both be
     used simultaneously for any kind of reasoning.    (016)

  5. On the other hand, two inconsistent theories still have a
     common, consistent generalization -- their supremum.  Even
     though they could not both be used in their entirety, their
     common generalization -- possibly with further extensions --
     could be used as a basis for interoperability.    (017)

  6. The four belief revision operators discussed in that paper
     show how theories can be revised to create a new theory
     that is better suited to some purpose.  Those operators
     enable any theory to be converted to any other theory
     by adding or deleting axioms or by relabeling any of the
     types and relations used in the axioms.    (018)

  7. My proposal for a Unified Framework (UF) with a minimum
     number of axioms is intended to be used in conjunction with
     the lattice.  By having a minimum number of axioms in the UF,
     it simplifies the way axioms from the UF could be added to
     a large ontology without creating inconsistencies.    (019)

There is a lot more that could be said, but this outlines some
of the ways a lattice of theories could be used.  The basic
motivation for the lattice is to address the problems I surveyed
in the following paper:    (020)

    http://www.jfsowa.com/pubs/challenge.pdf
    The Challenge of Knowledge Soup    (021)

In short, it's a proposal to move away from systems based on
Wittgenstein's _Tractatus_ to systems that implement his revised
and corrected second book.    (022)

John Sowa    (023)


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