SUO: CG: Re: Logic, Topic Maps, and RDF

["John F. Sowa" <sowa@bestweb.net>]

Jack,

Every declarative notation expresses some subset of
logic, often with some implicit or explicit ontology
built in.  In Chapter 1 of my KR book, I use the
example of conventional music notation, which expresses
the same subset of logic as RDF, but with  a highly
specialized notation and with a built-in ontology
for pitch, sequencing, time durations, loudness, etc.

I give some examples in music notation and show how
they can be translated to both CGs and first-order
predicate calculus.  Neither notation, however, is
one that a trained musician would choose for everday
use.  But the exercise is important for showing
the relationships.  It is also important if you
want to define an ontology for music or to write
programs that analyze or generate music.

  > Sometimes my brain feels like it was bombed back
  > to the stone age (I took neither the blue or
  > the red pill). I am completely unable to imagine
  > how RDF, like topic maps, can be a subset of CG.
  > Could you please elaborate?

Consider the example "George married Laura", which
could be represented as a triple

    George -> married -> Laura

A direct translation to CGs could use the
default type label Entity, which is a supertype
of everything else.  Following is the equivalent
CG:

    [Entity: George]->(Married)->[Entity: Laura].

If more information is available about the types
of George and Laura, it can be used to restrict
the type labels to more specific subtypes.

Some of that information might be specified in
RDF schema or in OWL, which also express subsets
of Common Logic, as I mentioned in my note to Murray.
Following is the short summary of the CL work:

    http://www.jfsowa.com/talks/clprop.htm
    Common Logic Proposal

As a purely declarative notation, Topic Maps are
also a version of logic.  But as I said in an
earlier note, they usually represent relationships
between types rather than instances.  In that
sense, they express a subset of first-order
logic used as a metalanguage.  That is also
supported by CL abstract syntax and concrete
syntaxes, such as CGs, KIF, and predicate
calculus.

John

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