Received: from mail-vb0-f61.google.com ([209.85.212.61]:42951) by stodi.digitalkingdom.org with esmtps (TLSv1:RC4-SHA:128) (Exim 4.76) (envelope-from ) id 1Sxede-0001C1-7o; Sat, 04 Aug 2012 06:43:38 -0700 Received: by vbzb23 with SMTP id b23sf2065701vbz.16 for ; Sat, 04 Aug 2012 06:43:23 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=googlegroups.com; s=beta; h=x-beenthere:date:from:to:cc:message-id:in-reply-to:references :subject:mime-version:x-original-sender :x-original-authentication-results:reply-to:precedence:mailing-list :list-id:x-google-group-id:list-post:list-help:list-archive:sender :list-subscribe:list-unsubscribe:content-type; bh=nkKBb52gKwu2Lw+C4C4SMqLeXQ2dL0idIyZUVTU9yy8=; b=17znL2n2KlqXpBa9g2efaHwX67vrtR/ojp2MDpXqwVFIbIE6zf38q5ghzefs+fCCVK qBeTgcI2hZvF3Wl+Ikgue0hhDBZ6/Wzxr8eLYH+7pkTocGlpTP4LyRJCh60DAWuOPV/q SPlSzZUodAXsurfmlLXVXIpZU+Y/CK+Ez1fjY= Received: by 10.52.95.238 with SMTP id dn14mr608351vdb.1.1344087803127; Sat, 04 Aug 2012 06:43:23 -0700 (PDT) X-BeenThere: lojban@googlegroups.com Received: by 10.52.66.242 with SMTP id i18ls3890601vdt.5.gmail; Sat, 04 Aug 2012 06:43:22 -0700 (PDT) Received: by 10.52.20.196 with SMTP id p4mr589592vde.13.1344087802552; Sat, 04 Aug 2012 06:43:22 -0700 (PDT) Date: Sat, 4 Aug 2012 06:43:21 -0700 (PDT) From: Gleki Arxokuna To: lojban@googlegroups.com Cc: lojban@egroups.com, jjllambias@hotmail.com Message-Id: In-Reply-To: <20000625000846.27040.qmail@hotmail.com> References: <20000625000846.27040.qmail@hotmail.com> Subject: Re: [lojban] RE:Trivalent Logics MIME-Version: 1.0 X-Original-Sender: gleki.is.my.name@gmail.com X-Original-Authentication-Results: ls.google.com; spf=pass (google.com: domain of gleki.is.my.name@gmail.com designates internal as permitted sender) smtp.mail=gleki.is.my.name@gmail.com; dkim=pass header.i=@gmail.com Reply-To: lojban@googlegroups.com Precedence: list Mailing-list: list lojban@googlegroups.com; contact lojban+owners@googlegroups.com List-ID: X-Google-Group-Id: 1004133512417 List-Post: , List-Help: , List-Archive: Sender: lojban@googlegroups.com List-Subscribe: , List-Unsubscribe: , Content-Type: multipart/alternative; boundary="----=_Part_1173_14123366.1344087802039" X-Spam-Score: -0.7 (/) X-Spam_score: -0.7 X-Spam_score_int: -6 X-Spam_bar: / ------=_Part_1173_14123366.1344087802039 Content-Type: text/plain; charset=ISO-8859-1 doi xorxes xu do pu troci lo nu pilno lo cimei logji xusycmuma'o ca'o lo nu tavla? On Sunday, June 25, 2000 4:08:46 AM UTC+4, Jorge Llambias wrote: > > > la pycyn cusku di'e > > >Ooops! For functional completeness the system needs min(x,y), too and > that > >seems harder to get. Once it is gotten, however, it alone generates all > of > >the connectives (binary, unary, more-ary), or rather the Sheffer function, > >min(x,y)+1, does. > > Is there a simple :) way to see that this is true? > > It seems to me that max(x,y) is the most useful "or", and > min(x,y) is the most useful "and", so it is nice that they > are relatively straightforward to generate. > > >I think (disclaimer) that min can be defined with f1=f2 :-1 for -1, 0 > >otherwise and f3 as 1for 1, 0 otherwise. But my head is not functioning > >well > >in -1,0,1 arithmetic at the moment. > > It does indeed give the minimum. So this is really the same > situation we have in Lojban with respect to 3-way connectives, > right? They can all be generated but not without repeating > some of the arguments in some cases. > > Now the question is, do we have anything like a complete > three-value unary system in Lojban? Obviously not a logic > system (we only have na and ja'a there) but maybe with some > set of attitudinals? > > {ju'a} or {je'u} (1,0,-1) > {ju'o} (1,-1,-1) > {la'a} (1,0,0) > {ca'e} or {se'o} or {ai} (1,1,1) > {pe'i} (0,0,0) ?? > > Could we produce some coherent system out of what we have? > > co'o mi'e xorxes > > ________________________________________________________________________ > Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com > > > ------------------------------------------------------------------------ > High long distance bills are HISTORY! Join beMANY! > http://click.egroups.com/1/4164/4/_/17627/_/961891727/ > ------------------------------------------------------------------------ > > To unsubscribe, send mail to lojban-unsubscribe@onelist.com > > -- You received this message because you are subscribed to the Google Groups "lojban" group. To view this discussion on the web visit https://groups.google.com/d/msg/lojban/-/gdl11c11ECAJ. To post to this group, send email to lojban@googlegroups.com. To unsubscribe from this group, send email to lojban+unsubscribe@googlegroups.com. For more options, visit this group at http://groups.google.com/group/lojban?hl=en. ------=_Part_1173_14123366.1344087802039 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable doi xorxes xu do pu troci lo nu pilno lo cimei logji xusycmuma'o ca'o = lo nu tavla?

On Sunday, June 25, 2000 4:08:46 AM UTC+4, Jorge Llambi= as wrote:

la pycyn cusku di= 'e
>Ooops! For functional completeness the system needs min(x,y)= , too and that
>seems harder to get. Once it is gotten, however= , it alone generates all of
>the connectives (binary, unary, more-ary= ), or rather the Sheffer function,
>min(x,y)+1, does.
Is there = a simple :) way to see that this is true?
It seems to me that max(x,y= ) is the most useful "or", and
min(x,y) is the most useful "and", so it = is nice that they
are relatively straightforward to generate.
>= I think (disclaimer) that min can be defined with f1=3Df2 :-1 for -1, 0
= >otherwise and f3 as 1for 1, 0 otherwise. But my head is not funct= ioning
>well
>in -1,0,1 arithmetic at the moment.
It doe= s indeed give the minimum. So this is really the same
situation we have = in Lojban with respect to 3-way connectives,
right? They can all be gene= rated but not without repeating
some of the arguments in some cases.
=
Now the question is, do we have anything like a complete
three-value = unary system in Lojban? Obviously not a logic
system (we only have na an= d ja'a there) but maybe with some
set of attitudinals?
{ju'a} or {= je'u} (1,0,-1)
{ju'o} (1,-1,-1)
{la'a} (1,0,0)
{ca'e} or {se'o} or= {ai} (1,1,1)
{pe'i} (0,0,0) ??
Could we produce some coherent sys= tem out of what we have?
co'o mi'e xorxes
______________= __________________________________________________________
Get= Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com

-------------= -----------------------------------------------------------
Hi= gh long distance bills are HISTORY! Join beMANY!
http://click.= egroups.com/1/4164/4/_/17627/_/961891727/
---------------------= ---------------------------------------------------
To unsu= bscribe, send mail to lojban-unsubscribe@onelist.com
<= p>

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You received this message because you are subscribed to the Google Groups "= lojban" group.
To view this discussion on the web visit https://groups.google.com/d/msg/lojban/-/gd= l11c11ECAJ.
=20 To post to this group, send email to lojban@googlegroups.com.
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