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

From: thomas lörtsch <tl@rat.io>
Date: Tue, 26 Jan 2021 13:44:13 +0100

To: "Peter F. Patel-Schneider" <pfpschneider@gmail.com>
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> On 25. Jan 2021, at 20:43, Peter F. Patel-Schneider <pfpschneider@gmail.com> wrote:
>
> 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
>
> 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

Arg… yes, I should have said: <> a :lie {| a :lie |}

> then there would be a contradiction, as <>
> a :lie would be a triple in the graph.  But still no paradox.

Okay.

> 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.

Good. I might try to come up with something that has no model but as of now I understand your response as saying that this attempt is probably futile. Which is a good :)

Thanks everybody for the remarks and/or the patience!

Thomas

> peter
>
> 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
>>
>>
>>
>
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Received on Tuesday, 26 January 2021 12:44:36 UTC

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