Message-Id: <199709241401.JAA16118@locke.ccil.org>
Reply-To: Don Wiggins <dwiggins@BFSEC.BT.CO.UK>
Date: Wed Sep 24 09:01:49 1997
Sender: Lojban list <LOJBAN@CUVMB.BITNET>
From: Don Wiggins <dwiggins@BFSEC.BT.CO.UK>
Subject:      Re: na'e
X-To:         LOJBAN@CUVMB.CC.COLUMBIA.EDU
To: John Cowan <cowan@LOCKE.CCIL.ORG>
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X-From-Space-Date: Wed Sep 24 09:01:49 1997
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My interpretation of na'e from the refgram, put into symbolic logic is:

Let f and f' be selbri
and x and x' be sumti

then na'e (f (x)) = E f': (f' != f ) ^ f' (x) ^ !f (x)

Now, it is that last term that f (x) is false is the "na'e entails na"
contention in a nutshell.  The alternative definition would have only two
terms.

> 1)      li vo na'e sumji li re li re

From my definition this would be false as sumji (4, 2, 2) is true.  Removing
the extra term makes it true as stated.

Similiarly, f (na'ebo (x)) = E x': (x' != x) ^ f (x') ^ !f (x)

> 2)      na'ebo li vo sumji li re li re

Here, both definitions agree because no other sumti can be found that fulfills
the first two terms.

Consider,

    .i na'ebo li vo zmadu li re

Again there is a conflict because 4 > 2 is true.  According to my definition
this is false.

I believe that both definitions would be self-consistent (but it needs a
logic whizz to come up with a proof).  Therefore, it is simply a matter of
>defining< which form of "na'e" we want.  In my opinion, the refgram states
that "na'e" entails "na".

ni'oco'omi'e dn.