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Re: [ontolog-forum] Requesting Opinions on the Benefits of Predicates as

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Fri, 13 Jun 2014 13:51:44 -0400
Message-id: <539B3A30.4010201@xxxxxxxxxxx>
On 6/13/2014 11:42 AM, Barkmeyer, Edward J wrote:
> you [Frank] are also correct about named graphs being used as buckets
> of triples.  Used in that way, a named graph is a “knowledge management
> object” – a “set of knowledge” (only maybe a “theory”) that is
> manipulated as a body. And in particular, that is a way in which
> metadata can be attached to parts of a knowledge base.  For example,
> this set of triples together represents a state of the world at a
> given time.    (01)

I agree.  For anybody who would like to estimate the rate of progress
in our understanding of these issues, I'd like to point out that the
version of logic by C. S. Peirce in 1906 is very similar to the IKL
logic developed by an impressive group of AI researchers in 2006.    (02)

Both of them support "named graphs being used as buckets of triples"
or "a knowledge management object".  Unfortunately, both of them were
largely ignored.  For a collection of papers about IKL that I saved
from being deleted, see http://www.jfsowa.com/ikl/    (03)

To illustrate the similarities, I'll refer to examples from the
following paper:  http://www.jfsowa.com/pubs/eg2cg.pdf    (04)

The goal of the IKL project was to support interoperability among
a very wide range of AI systems, and it included developers from
some of the largest, including Cyc.  The study group concluded that
they could be supported by adding one new feature to Common Logic:
a "that" operator for supporting metalanguage.    (05)

For the extensions to Common Logic, see Section 5, pages 16 to 20,
of eg2cg.pdf.  As an example, see Figure 20 on p. 16, which shows
Peirce's existential graph for the sentence "That you are a good girl
is much to be wished."  (Note the word 'that'.)    (06)

A linear approximation to Peirce's EG would be    (07)

    (You are a good girl)————is much to be wished    (08)

Peirce allowed blanks in his identifiers, each of which represents the
name of some relation.  In Common Logic, any name that contains blanks
must be enclosed in double quotes:    (09)

  1. "You are a good girl" is the name of a relation with zero
     arguments.  For EGs and for Common Logic, a 0-adic relation is
     a proposition.    (010)

  2. The parentheses represent EG ovals, which correspond to "buckets"
     that enclose whatever graph or subgraph is being considered.    (011)

  3. "is much to be wished" is the name of a monadic relation, whose
     argument is represented by the line attached to the name.    (012)

  4. That line is what Peirce called "a line of identity".  It represents
     an existential quantifier (or a blank node in RDF).    (013)

  5. By the EG conventions, an oval with no attached line represents
     negation.  But the attached line says "there exists something p"
     and the graph nested in the oval states the proposition p.    (014)

With this interpretation, Figure 20 can be translated to the following
sentence in the extended CLIF notation for IKL:    (015)

   (exists (p)
     (and (= p (that "You are a good girl")) ("is much to be wished" p)))    (016)

This IKL sentence may be read "There exists a p, p is the proposition
that you are a good girl, and p is much to be wished."    (017)

In the extended CGIF notation for IKL, the equivalent is    (018)

    [Proposition *p ("You are a good girl")] ("is much to be wished" ?p)    (019)

This example shows that EG, CG, and CLIF notations can be used to
express IKL.  But there is much more to IKL than just notation.
For more detail and examples, see the remainder of eg2cg.pdf and
the documents listed in http://www.jfsowa.com/ikl/ .    (020)

The IKL User Guide shows the mappings to IKL from OWL and other logics.    (021)

John    (022)

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