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reification, negation & paradox in daml (corrections)

From: Daniel Mahler <mahler@cyc.com>
Date: Tue, 16 Jan 2001 17:27:07 -0600
Message-ID: <14948.55499.816422.512740@mcallister.cyc.com>
To: www-rdf-logic@w3.org

I should read what I write more carefully.
type corrections below.

Daniel Mahler writes:
 > 
 > I believe the reification approach to negation leads
 > directly to Tarski's paradox.
 > In hindsight this is not be a surprise since
 > <http://www.w3.org/DesignIssues/Toolbox#truth>
 > is a truth predicate.
 > Normally, one would require more logical machinery
 > then graond atoms and conjuction to do real dammage.
 > However, the peculiarities of the graph model
 > seem to make it very easy to construct a Goedel sentence,
 > since we can explicitly construct cycles in the representations of
 > reified statements, thus creating representations
 > of fixed points of parametrized statements.
 > 
 > <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-schema-ns#"
 >           xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
 >           xmlns:daml="http://www.daml.org/2000/12/daml+oil#"
 > 	  xmlns:toolbox="http://www.w3.org/DesignIssues/Toolbox#"
 >           >
 > 
 > <rdf:Description rdf:ID="goedel">
 > 		 <rdf:type resource="rdf:Statement"/>
 >                  <rdf:subject resource="goedel">
 >                  <rdf:predicate resource="toolbox:truth"/>
 >                  <rdf:subject rdf:value="0"/>

I meant <rdf:object rdf:value="0"/> above

 > <rdf:Description>
 > 
 > <rdf:RDF>
 > 
 > If we then wanted to query the model
 > about the rdf:truth of "goedel",
 > it can be neither 1 nor 0.
 > We could just say it is 0,

read toolbox:truth for rdf:truth throughout

 > since there is no rdf:truth statement
 > actually asserted about "goedel".
 > However, that would be a very strong form
 > of the closed world assumption
 > and it would render reificataion devoid
 > of any logical content.
 > 
 > Since we are using the truth predicate to define
 > negation, rather then attempting to describe
 > an existing operator like Tarski,
 > it seems we are forced to abandon classical
 > logic to avoid the paradox.
 > 
 > This problem is not limited to negation,
 > but will also apply to using reification to simulate
 > second order predicates and modalities.
 > The general scope of this problem
 > was discussed by Montague.
 > There is also a very detailed discusion of the issues in
 > Raymond Turner's "Truth and Modality for Knowledge Representation"
 > book. The upshot is that only fairly weak operators
 > can be handled consistently using predicates over reified sentences.
 > 
 > Daniel Mahler
 > Cycorp Inc
 > 
 > 
 > 
 > 
Received on Tuesday, 16 January 2001 18:32:39 GMT

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