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Re: AW: {Disarmed} Re: blank nodes (once again)

From: Pat Hayes <phayes@ihmc.us>
Date: Fri, 25 Mar 2011 08:47:19 -0500
Cc: Michael Schneider <schneid@fzi.de>, semantic-web@w3.org
Message-Id: <C7D15F87-6152-4908-949E-29263190C6CB@ihmc.us>
To: Michael Brunnbauer <brunni@netestate.de>

On Mar 25, 2011, at 5:00 AM, Michael Brunnbauer wrote:

> 
> re
> 
> On Fri, Mar 25, 2011 at 12:00:52AM +0000, Michael Schneider wrote:
>> since skolemization retains equisatisfiability. But skolemization does /not/
>> lead to logically equivalent graphs.
> 
> I don't think this is of practical relevance. In logic skolemized statements
> are not logically equivalent to the original ones because you have introduced
> new symbols *in the whole system* and the truth of the original statement is
> independend of these symbols. If you look at statements and their skolemized
> versions as *different axiom systems* it should be possible to construct a
> model for the skolemized versions out of a model of the original versions
> and vice versa. the systems are somehow equivalent. I cannot substantiate that
> because I am not a logician.

You do OK :-) 

The technical relationship is exactly preserving satisfiability, as you say here. If you skolemize S to get sk(S), then S does not entail sk(S) because they have different vocabulaires, but sk(S) is satisfiable if and only if S is: you can take any model of S and extend it to a model of sk(S), over the same universe and with all the old names still denoting what they did in the first model.

Pat


> 
> Regards,
> 
> Michael Brunnbauer
> 
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Received on Friday, 25 March 2011 13:48:04 UTC

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