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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: Sat, 28 Jun 2014 07:53:29 -0400
Message-id: <53AEACB9.6050107@xxxxxxxxxxx>
Ed and Mark,    (01)

> The ternary predicate approach that John describes is viable,
> but clumsy.  The ternary predicate approach requires a different
> ternary predicate  if you want to specify location instead of time,
> or a quaternary predicate  to specify both, etc.    (02)

> This is why I claimed that IKL “that” (or Sowa “describes”) is
> necessary.   It is just plain unrealistic to expect every predicate
> to have variants  for time and location – not to mention other
> modifiers that English would  express using adverbs.    (03)

I agree that adding an extra argument to every relation is clumsy.
And I was *not* recommending it.  The points I wanted to emphasize
are theoretical, but with practical implications:    (04)

  1. Quantifying over time can be done in a purely FOL semantics.
     There is no need to introduce the 'that' operator and all
     the semantic issues it entails.  (I cited a book that uses
     a sorted FOL with time as one of the sorts.)    (05)

  2. If you want to factor out those references (to time, location,
     or whatever), you can introduce a purely-syntactic notion of
     context.    (06)

  3. That syntactic notion does not affect the semantics in any way,
     since every use of a context box (or other grouping markers)
     can be eliminated by a syntactic translation that adds an
     extra argument to every relation.    (07)

  4. After the translation in #3, you can use an ordinary Tarski-style
     model theory for the semantics.  There is no need to go to the
     more complex semantics of IKL in the model theory.    (08)

  5. But as a practical KR notation, you don't have to translate
     the context boxes (or other grouping markers) to the form
     with extra relations or arguments.    (09)

For the details of how to represent a kind of context, attach time
and place references to that context, and then eliminate the contexts
by a translation as above, see the following article:    (010)

    Laws, facts, and contexts    (011)

To represent a Tarski-style model, I use *nested graph models* (NGMs),
which have "context boxes" that allow graphs nested within graphs.
For the logic, I use conceptual graph notation, but you could use
just as well use CLIF notation.  (The article was published in 2003
while the CL standard project was in its early days.)    (012)

To see the differences between the three kinds of notations, Figure 9
shows a conceptual graph in its nested form with type labels.  Fig. 10
shows a nested graph model for which the denotation of Fig. 9 is true.    (013)

Then Fig. 11 shows the translation of the NGM in Fig. 10 to a "flat"
form with no nesting.  An 'isin' relation links a node for each relation
to a node that represents the context in which the relation occurs.
This flattened graph could be represented as an ordinary Tarski model.    (014)

Figures 9 to 11 have proposition nodes.  They raise issues that IKL
dealt with in more detail about 3 years later.  If you're not using
verbs like 'believe', you don't need proposition nodes.  Those boxes
could represent situations at particular times and places.    (015)

John    (016)

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