[ontoiop-forum] OntoIOp teleconference (n.63): Wed 2014.09.10

[John F Sowa]

Till,

I have been tied up with too many simultaneous tasks to call in for
most of the Ontoiop telecons, but I have been following the summaries
and slides.  Your slides dated 2014-09=09 present a good overview,
but I had some comments:

  1. I believe that the discussion can be clarified by using the terms
     'generalization' and 'specialization'.

  2. Approximation in slide 7 is defined as "model in an expressive
     language, reason fast in a lightweight one."  That's a good way
     to make the point.  But it means that the lightweight version
     is a generalization (is implied by) the more expressive version.

  3. Generalization/specialization are the two most widely used
     metalevel relations among theories.  In Cyc, for example,
     they are the basis for the partial ordering of microtheories.
     As another example, Schema.org is a very general (highly
     underspecified) collection of types (or classes) that many
     developers have specialized for applications that are
     inconsistent in the details not specified by Schema.org.

  4. In slide 3, I agree that diversity and interoperability occur at
     all levels.  But they don't require all systems that interoperate
     to be consistent with each other in all their details.  If you
     introduce the term 'generalization', you can say

     a) If two theories A and B are inconsistent in their details,
        they can interoperate on shared data that is specified by
        a common generalization C.

     b) To use data specified in C, neither A nor B may assume any
        properties of that data not specified in C.  But they can use
        the details in conditionals that begin "If x has property p..."

     c) Points 4a and 4b are implicit in the way interoperable systems
        work, and the developers who use Schema.org and similar systems
        can understand them.

  5. Slide 75:  "What is a suitable abstract meta framework for
     non-monotonic logics and rule languages like RIF and RuleML?"

     There's a lot of research that shows the relationships between
     nonmon logics and belief (or theory) revision.  In general,
     every proof in a non-monotonic logic can be converted to a proof
     in a monotonic logic from a suitably revised theory -- i.e., each
     nonmon step adds, deletes, or replaces some monotonic axiom.
     In terms of generalization/specialization, every nonmon proof
     corresponds to a walk in a lattice of theories.  (The full lattice
     may be infinite, but there is no need to generate all the nodes.)

I have found that the terms 'generalization' and 'specialization' can
be explained to a wide audience of developers whose knowledge of logic
is rudimentary at best.  That's important for the OMG.

John