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>

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

Daniel Mahler writes:
>
> I believe the reification approach to negation leads
> 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,

> since there is no rdf:truth statement
> 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 UTC

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