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Re: Negation (reprise?)

From: Richard Waldinger <waldinger@AI.SRI.COM>
Date: Fri, 11 Jun 2004 12:31:54 -0700
Message-ID: <40CA08AA.508@ai.sri.com>
To: Graham Klyne <gk@ninebynine.org>
Cc: www-rdf-logic@w3.org

Dusko Pavlovic wrote:

>>
>>
>> problems, I wondered if there was anything here that might inform 
>> handling of negation in Semantic Web systems...
>>
> unlikely. the message talks about semantics of *continuations*. the 
> connection with the logical operation negation is that continuations 
> are based on a contravariant operator (functor)
>
>       A ---> B
> -----------------------
> B=>R ----> A=>R
>
> along the curry-howard isomorphism ("propositions-as-types") this can 
> be thought of as a negation, provided that the type R of results is 
> thought of as the proposition "false". this leads to nice models of 
> constructivist logic, with programs as proofs, which people worked on 
> a lot in the 80es...
>
> -- dusko
>
>
>
>




Graham Klyne wrote:

>
> The excerpt below comes from a Haskell language mailing list.  I have 
> no idea (yet) what it precisely means, but seeing the term "type 
> negation", and having noticed that Haskell (Hindley-Milner) type 
> inherence problems seem to have similarities with more general 
> inference Semantic Web problems, I wondered if there was anything here 
> that might inform handling of negation in Semantic Web systems...
>
> [[
> Yes, I think this is the right way to go. If you look at work by 
> Power, Thielecke and Streicher on continuations [*], you will find 
> that they model type negation as a self-adjoint functor on a closed 
> premonoidal category, and IIRC a closed premonoidal category is 
> equivalent to a thing called a closed kappa-category with a 
> computational monad on it. The self-adjointness corresponds to the 
> involutivity of negation.
> ]]
>
> The full message, with some references, is here:
>   http://www.haskell.org//pipermail/haskell-cafe/2004-June/006225.html
>
> #g
>
>
> ------------
> Graham Klyne
> For email:
> http://www.ninebynine.org/#Contact
>
Received on Friday, 11 June 2004 18:53:47 GMT

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