New version (was: Re: [SCL] functions and functional relations:proposal to change the SCL semantics)

[Jay Halcomb]

Pat, I haven't finished checking details yet (and reserve my own right to
complain :), but I do like this new idea so far.

Jay

----- Original Message ----- 
From: "Pat Hayes" <phayes at ihmc.us>
To: "Chris Menzel" <cmenzel at tamu.edu>
Cc: <scl at philebus.tamu.edu>
Sent: Monday, February 09, 2004 22:59
Subject: New version (was: Re: [SCL] functions and functional
relations:proposal to change the SCL semantics)


> OK, I wrote up the new version before reading your email, but I didnt
> actually overwrite the old version, so you can see the new one (which
> IMO is a lot better and will be better still in another working
> half-day) at
>
> http://www.ihmc.us/users/phayes/SCL_current_2004_rf.html
>
> (rf for 'relation+function').
>
> There are quite a lot of other rewrites as well. In particular Ive
> put the conventional binary = back into the syntax and MT, and
> renamed the variadic one 'scl:same' (cf. owl:sameAs), and have
> further simplified the 'fitting' idea (now named 'folding' and
> presented as an extra structure defined recursively rather than a
> condition to be satisfied. This will simplify some proofs, I think.)
>
> There is a new (or newly sharpened) intuitive idea now behind the
> design of the whole language, a kind of overall story that makes a
> certain global sense, where the entire design is motivated by the
> idea of reconciling two different conventional structures which
> disagree about the signature to use for a notation. See the
> introductory discussion and the later figures and the surrounding
> discussion for this.
>
> I'm quite excited by this idea, it seems to make sense of a lot of
> stuff that was kind of arbitrary, if elegant, before. For example, it
> 'explains' why SCL needs to allow variadicity. And it provides a
> potentially quite convincing argument for the *utility* of SCL,  not
> just its semantic elegance. It makes for a much neater story of how
> SCL relates to GOFOL (ie one motivated by something more important
> than just keeping Ian Horrocks satisfied.)  And it handles the full
> WW syntax !
>