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Date: Thu, 16 Jul 2015 18:58:29 -0300
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Subject: Re: [lojban] Re: {tu'e...tu'u} in NU
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On Thu, Jul 16, 2015 at 7:30 AM, Alex Burka <durka42@gmail.com> wrote:

> So, to the question of that {gu} and {go} mean with more than 2 arguments,
> we kind of find ourselves with tradeoff between logic and ease of use.
>
> First I get nervous extending them to >2-ary at all, since it becomes
> harder to reason about the negations ({gonai X gi Y} is XOR, but {gonai X
> gi Y gi Z} is not, it's something strange instead -- and nobody can do
> truth tables in their head, even fluent speakers).
>
> The interpretations you list are undoubtedly useful (particularly the
> "which one out of these X alternatives"-connective is often asked for,
>

"Which one(s) of the following" would be "ge'i ... gi ... gi ... gi ... ",
right?


> though there is a workable solution using {moi}). But they do not
> correspond to the mathematical interpretation. For example, n-ary XOR is
> supposed to be true when an odd number of the arguments are true, which is
> not obvious (or often useful in speech). Changing this can cause
> difficulties with composition, for example logical transformations like De
> Morgans' laws will not work.
>

The negation of "ga ... gi ... gi ..." is still "ge nai ... gi nai ... gi
nai ..." and viceversa. And "go ... gi ... gi ..." should be equivalent to
"go nai ... gi nai ... gi nai ... ", but that means "go nai" can't mean
"one and only one of the following".

"Exactly one of", "all but exactly one of", "at least two of", etc should
be based on numerals (so that "ro" corresponds with "ge" and "su'o" with
"ga").

mu'o mi'e xorxes

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<div dir=3D"ltr"><br><div class=3D"gmail_extra"><br><div class=3D"gmail_quo=
te">On Thu, Jul 16, 2015 at 7:30 AM, Alex Burka <span dir=3D"ltr">&lt;<a hr=
ef=3D"mailto:durka42@gmail.com" target=3D"_blank">durka42@gmail.com</a>&gt;=
</span> wrote:<br><blockquote class=3D"gmail_quote" style=3D"margin:0 0 0 .=
8ex;border-left:1px #ccc solid;padding-left:1ex"><div style=3D"word-wrap:br=
eak-word"><div style=3D"font-family:Helvetica,Arial;font-size:13px;color:rg=
ba(0,0,0,1.0);margin:0px;line-height:auto">So, to the question of that {gu}=
 and {go} mean with more than 2 arguments, we kind of find ourselves with t=
radeoff between logic and ease of use.</div><div style=3D"font-family:Helve=
tica,Arial;font-size:13px;color:rgba(0,0,0,1.0);margin:0px;line-height:auto=
"><br></div><div style=3D"font-family:Helvetica,Arial;font-size:13px;color:=
rgba(0,0,0,1.0);margin:0px;line-height:auto">First I get nervous extending =
them to &gt;2-ary at all, since it becomes harder to reason about the negat=
ions ({gonai X gi Y} is XOR, but {gonai X gi Y gi Z} is not, it&#39;s somet=
hing strange instead -- and nobody can do truth tables in their head, even =
fluent speakers).</div><div style=3D"font-family:Helvetica,Arial;font-size:=
13px;color:rgba(0,0,0,1.0);margin:0px;line-height:auto"><br></div><div styl=
e=3D"font-family:Helvetica,Arial;font-size:13px;color:rgba(0,0,0,1.0);margi=
n:0px;line-height:auto">The interpretations you list are undoubtedly useful=
 (particularly the &quot;which one out of these X alternatives&quot;-connec=
tive is often asked for, </div></div></blockquote><div><br></div><div>&quot=
;Which one(s) of the following&quot; would be &quot;ge&#39;i ... gi ... gi =
... gi ... &quot;, right?</div><div>=C2=A0</div><blockquote class=3D"gmail_=
quote" style=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1=
ex"><div style=3D"word-wrap:break-word"><div style=3D"font-family:Helvetica=
,Arial;font-size:13px;color:rgba(0,0,0,1.0);margin:0px;line-height:auto">th=
ough there is a workable solution using {moi}). But they do not correspond =
to the mathematical interpretation. For example, n-ary XOR is supposed to b=
e true when an odd number of the arguments are true, which is not obvious (=
or often useful in speech). Changing this can cause difficulties with compo=
sition, for example logical transformations like De Morgans&#39; laws will =
not work. </div></div></blockquote><div><br></div><div>The negation of &quo=
t;ga ... gi ... gi ...&quot; is still &quot;ge nai ... gi nai ... gi nai ..=
.&quot; and viceversa. And &quot;go ... gi ... gi ...&quot; should be equiv=
alent to &quot;go nai ... gi nai ... gi nai ... &quot;, but that means &quo=
t;go nai&quot; can&#39;t mean &quot;one and only one of the following&quot;=
.=C2=A0</div><div><br></div><div>&quot;Exactly one of&quot;, &quot;all but =
exactly one of&quot;, &quot;at least two of&quot;, etc should be based on n=
umerals (so that &quot;ro&quot; corresponds with &quot;ge&quot; and &quot;s=
u&#39;o&quot; with &quot;ga&quot;).</div><div><br></div><div>mu&#39;o mi=
9;e xorxes</div></div></div></div>

<p></p>

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