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Re: Mapping to RDF Graphs and reification

From: Pat Hayes <phayes@ihmc.us>
Date: Wed, 3 Dec 2008 13:27:25 -0600
Cc: Daniel Mahler <dmahler@gmail.com>, Jeff Thompson <jeff@thefirst.org>
Message-Id: <BF731A0C-C8B7-4FE5-A005-6158F1186FCB@ihmc.us>
To: Bijan Parsia <bparsia@cs.man.ac.uk>, public-owl-dev@w3.org

On Dec 3, 2008, at 12:23 PM, Bijan Parsia wrote:

>
> On 3 Dec 2008, at 17:34, Daniel Mahler wrote:
>
>> Bijan,
>>
>> On Wed, Dec 3, 2008 at 6:03 PM, Bijan Parsia <bparsia@cs.man.ac.uk>  
>> wrote:
>>>
>>> On 3 Dec 2008, at 16:49, Jeff Thompson wrote:
> [snip]
>>> Consider:
>>>       s p o
>>>       not(s p o)
>>>
>>> (where the second is a negated triple). We want these to  
>>> contradict. The
>>
>> If you represent negation by reification,
>
> "Encode negated sentences using reification", but ok.
>
>> how do you avoid Tarski's paradox?
>
> Tarski's paradox has nothing to do with this. So we avoid it by,  
> well, not going anywhere near it :)
>
> (Standardly, Tarsk's paradox is about having the languages own truth  
> predicate as a part of the language. We have no truth predicate at  
> all.)

Well, someone could argue that since the negation construction  
involves meta-description, iterating it gives you a kind of truth  
predicate, in a sense. Kinda. But Tarski's paradox doesn't arise for  
other reasons, having to do with how impoverished RDF is as an  
expressive logic. To get Tarski's construction to work, the logic has  
to be able to describe its own grammar and its own notion of  
provability, which takes a certain minimal degree of expressivity  
involving quantifiers that RDF does not come anywhere near. (If you  
move to the more expressive logic being encoded in the RDF syntax -  
the one with negation - then it no longer uses reification in the same  
way: RDF reification doesn't reify that logic's syntax.)

Pat


> For the non-Full part, this is just syntax. It is just ugly syntax  
> for "not(s p o)".
>
> Even if full, in some sense, most of the time, it's just syntax. The  
> story is much more complex because it's also denoting objects in the  
> domain and potentially could reflect on the syntax, yadda yadda, but  
> that's no worse than anything else, really.
>
>> (I asked this question question on a w3 rdf list many years ago
>> and I still do not know)
>
>
> Well, I hope you do now :)
>
> Cheers,
> Bijan.
>
>
>
>

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Received on Wednesday, 3 December 2008 19:28:53 GMT

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