- From: Richard Waldinger <waldinger@AI.SRI.COM>
- Date: Fri, 11 Jun 2004 12:31:54 -0700
- 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 UTC