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Re: Can RDF* introduce paradoxes? And what if?

From: Peter F. Patel-Schneider <pfpschneider@gmail.com>
Date: Mon, 25 Jan 2021 14:43:42 -0500
To: public-rdf-star@w3.org
Message-ID: <4cc602ff-f3f5-2f40-2ac9-f8ce2953730a@gmail.com>
Given that :lie is just an RDF node (and an RDFS class) there is nothing here
that dictates any truth value for any node in the graph.  So no paradox and
not even a contradiction.

Even if :lie had its intended meaning (that its instances are false
propositions) there is no contradiction.  All that is being stated is that <>
a :lie is not a true proposition and thus cannot be in the graph.  There is
nothing here requiring <> a :lie to be a triple in the graph (which would make
it a true proposition), so no contradiction.

If this was what used to be PG mode then there would be a contradiction, as <>
a :lie would be a triple in the graph.  But still no paradox.

A paradox in a semantic extension of RDF is something that demonstrates that
there can be no models for any RDF graph that is allowable in that extension. 
(For example, if "A"^^xsd:int _:b1 _:b2 were a triple in all RDF graphs then
the extension of RDF that recognizes the datatype xsd:int would be
paradoxical.)  In early versions of set theory there were lots and lots of
sets that always existed, including a set X which is defined as the set of
things that are not in X.  X cannot be in X and X cannot not be in X.   As
these are the only two options, a paradox results, but only because this set
always exists.


On 1/25/21 10:38 AM, thomas lörtsch wrote:
> [This question definitely shows a troublesome lack of understanding and research. Feel free to ignore.]
> One of the dangers of reification is that it introduces the possibility of paradoxes. The proposed literal-like semantics of RDF* doesn’t seem to give any protection from that. IIUC the following constitutes a paradox:
>     << <> a :lie >>  a :lie .
> Or is it only a contradiction? Maybe the monotonic nature of RDF and its lack of all-quantification does make paradoxes impossible? Or at least not harmful? Maybe it would be sufficient to disallow the self-referential <> ?
> Is there anything that should be done? That can be done? What are the dangers?
> Thanks,
> Thomas
Received on Monday, 25 January 2021 19:43:57 UTC

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