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DTTF: Can 'semantically closed' languages be extended?

From: Jonathan Borden <jonathan@openhealth.org>
Date: Fri, 10 May 2002 14:58:28 -0400
Message-ID: <01a601c1f854$ac9d0f00$0a2e249b@nemc.org>
To: "WebOnt WG" <www-webont-wg@w3.org>
I continue in my attempts to make proper sense of the semantic extensions,
layering issues with respect to OWL and RDF, which have led to the "dark
triples" proposal.

I will be away until 5/17 and wanted to get something out, which hopefully
will generate some discussion and which hopefully will help me to finalize
the summary.

Tarski's "Liar's paradox" led to his stating:

[[
8. THE INCONSISTENCY OF SEMANTICALLY CLOSED LANGUAGES.7

     If we now analyze the assumptions which lead to the antinomy of the
liar, we notice the following:


We have implicitly assumed that the language in which the antinomy is
constructed contains, in addition to its expressions, also the names of
these expressions, as well as semantic terms such as the term "true"
referring to sentences of this language; we have also assumed that all
sentences which determine the adequate usage of this term can be asserted in
the language. A language with these properties will be called "semantically
closed."

We have assumed that in this language the ordinary laws of logic hold.
]]
-- http://www.ditext.com/tarski/tarski.html

It occurs to me that RDF, if all triples are required to be "asserted" i.e.
"true" may be "semantically closed" at least with respect to extensions of
the RDF language.

When Pat H says that it is akin to attempting to "build a perpetual motion
machine" to try to eliminate the inconsistencies in OWL _without_ recourse
to 'unasserted' or 'dark' triples, perhaps he is rephrasing Tarski? If so,
does the Liar's paradox apply to OWL specifically or RDF(S) itself? Perhaps
there is a trivial answer to this, if so, oh well, that's what you get when
you ask a neurosurgeon to try and summarize a whole bunch of arguments
between logicians.

In any case, at the moment, PFPS has produced an example of a paradox which
results from Jeremy's "comprehensive entailments" proposal. Jos has
demonstrated a method by which 'dark triples' aka N3 contexts can resolve
this. Should we assume that the "comprehensive entailments" proposal is
paradoxical?

My current impression is that some method of using RDF triples for purely
syntactic purposes in OWL is needed -- indeed:
http://lists.w3.org/Archives/Public/www-webont-wg/2002May/0087.html, is yet
another example of why syntactic triples are needed.

My current preference would be some way, perhaps a triple, of stating that a
particular predicate is to be used for syntactic purposes, i.e. as a
syntactic . e.g.

<owl:List> <rdf:type> <rdf:syntax> .

or

<owl:List> <rdf:subClassOf> <rdf:Syntax> .

would either jibe with the RDF MT? If so, this would seem to be an easy
change that wouldn't be too intrusive on any syntax (though would require
support from RDF Schema 'inferencing engines'). Dan? Jos?

In any case I wanted this current thinking out for discussion, and hopefully
I will be able to more formally write this up once I get back.

Jonathan
Received on Friday, 10 May 2002 15:02:38 GMT

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