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Reply-To:     Don Wiggins <dwiggins@BFSEC.BT.CO.UK>
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From:         Don Wiggins <dwiggins@BFSEC.BT.CO.UK>
Subject:      Re: RV: na'e entails na?
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Message-ID: <h0mvLLMr18C.A.yh.110kLB@chain.digitalkingdom.org>

> If the grammar of po`o is robust enough, that looks like it
> could work. (As it stands, it looks to me as if it groups as
>
>   po`o(na (fraso (selgu`e)))
>
> because don't UI bind to the previous word? - But if so you can
> change it to "na fraso po`o selgu`e".)

Yes, as UI it would bind to the previous word.  We could also use "po'onai"

     lo fraso po'onai selgu'e
     lo ((((fraso) po'o) nai) selgu'e)

It is important not to negate the "selgu'e" as well.

> But anyway, if the Engdahl-Wiggins "na ..po`o" proposal works,
> then I shall give up contesting {na`e}.

Trying to be more rigorous, there does appear to be a problem:

    po'o (f (x)) = f (x) ^ !E f': (f' != f) ^ f' (x)

    po'onai (f (x)) = !(f (x) ^ !E f': (f' != f) ^ f' (x)) negating
                    = !f (x) V E f': (f' != f) ^ f' (x)    by DeMorgan's

Notice that first term !f (x).  Going back to our example:

let the universal be { a, b, c, d, e, f }
and fraso (x) = { a, b, c }
and glico (x) = { c, d, e }
but now !fraso (x) = { d, e, f }

po'o (fraso (x)) = { a, b }
!(po'o (fraso (x))) = { c, d, e, f }

And that f appears were it should be (glico (f) is false and there is no other
relation).

In terms of logical manipulation, the simpler definitions of "na'e" and "po'o"
would be more useful, but these definitions do not correspond to English.

ni'oco'omi'e dn.