Received: from mail-pd0-f190.google.com ([209.85.192.190]:34667) by stodi.digitalkingdom.org with esmtps (TLSv1.2:AES128-GCM-SHA256:128) (Exim 4.85) (envelope-from ) id 1ZFtm2-0001Ew-LQ for lojban-list-archive@lojban.org; Thu, 16 Jul 2015 17:45:17 -0700 Received: by pdbnk16 with SMTP id nk16sf13032798pdb.1 for ; Thu, 16 Jul 2015 17:45:04 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=googlegroups.com; s=20120806; h=date:from:to:message-id:in-reply-to:references:subject:mime-version :content-type:x-original-sender:reply-to:precedence:mailing-list :list-id:x-spam-checked-in-group:list-post:list-help:list-archive :sender:list-subscribe:list-unsubscribe; bh=3XOxSlepUsCEOt946sAnjbmS73R0rUkA3IOAICfC9Ps=; b=ewRqwGvL8zK6o5RltNIG+HiRiUdN1SXRG9ElDKMh6V028eyws/SluSrMm1wzzzY8v/ dN0+51nlFtmaBSzUvEB6hJCIgTsRLo50PWYwBOWlC2LuPEbsrguefMKOZotRtcSA2PNA OcxAuVKhjPf3MzQDsFB5xz+R/cYqKSlt5cCECfeYIGcGHKpdZe8lR5Eo13Vs+XSfL61m l1jQC3HHlipg4rkQAqNbIZUUPQAt4JFWSD9Xf/WlPfPsmmTJAW3SMipBRhxi/nG2cbFf 4zza+ciFMm/UCGw6g15tnfG1OwLS1oWODa9v1sTAFMPFr8tr03x64H5fwIIKSruzN5x9 f6gA== DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=date:from:to:message-id:in-reply-to:references:subject:mime-version :content-type:x-original-sender:reply-to:precedence:mailing-list :list-id:x-spam-checked-in-group:list-post:list-help:list-archive :sender:list-subscribe:list-unsubscribe; bh=3XOxSlepUsCEOt946sAnjbmS73R0rUkA3IOAICfC9Ps=; b=zuStuprRM0/+oT/9j5LkqTBM19rcJ8PupY5CU+/ZbI1RP+QWH5GlcAO8WHIwFvP5Ys KXOC0YOqjErY6OHWOGI6hYrI4wMBT8mSsykxu6ZugZthWv3ieeI1ae3tkLEihs+SRHpO NtB8gJQBvac7EWgwNsLe8uUuq3cyC+czEbPIozXXauQ92PJSDYGPAvD0kgoyVnvGQuuL 1OP/CzOgTAT23aOZYGqFD4uxr3SJNnWSMI8KNwKfOi160Oh8TB/D9TkfPobSNyGCAauo RQuCCVzFT+uGqzN0DysSjZl5HWbMOd7M1gFRoOzGDKV//pTwXOF+kjnnPU59XnV8qnUg G+Ag== X-Received: by 10.50.23.71 with SMTP id k7mr189402igf.6.1437093904701; Thu, 16 Jul 2015 17:45:04 -0700 (PDT) X-BeenThere: lojban@googlegroups.com Received: by 10.107.164.87 with SMTP id n84ls1113716ioe.42.gmail; Thu, 16 Jul 2015 17:45:04 -0700 (PDT) X-Received: by 10.50.138.70 with SMTP id qo6mr210364igb.13.1437093904403; Thu, 16 Jul 2015 17:45:04 -0700 (PDT) Date: Thu, 16 Jul 2015 17:45:02 -0700 (PDT) From: guskant To: lojban@googlegroups.com Message-Id: In-Reply-To: References: Subject: Re: [lojban] Re: {tu'e...tu'u} in NU MIME-Version: 1.0 Content-Type: multipart/mixed; boundary="----=_Part_1565_1577659010.1437093902838" X-Original-Sender: gusni.kantu@gmail.com Reply-To: lojban@googlegroups.com Precedence: list Mailing-list: list lojban@googlegroups.com; contact lojban+owners@googlegroups.com List-ID: X-Spam-Checked-In-Group: lojban@googlegroups.com X-Google-Group-Id: 1004133512417 List-Post: , List-Help: , List-Archive: , List-Unsubscribe: , X-Spam-Score: -3.1 (---) X-Spam_score: -3.1 X-Spam_score_int: -30 X-Spam_bar: --- ------=_Part_1565_1577659010.1437093902838 Content-Type: multipart/alternative; boundary="----=_Part_1566_884288348.1437093902838" ------=_Part_1566_884288348.1437093902838 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Le jeudi 16 juillet 2015 21:35:46 UTC, xorxes a =C3=A9crit : > > > > On Thu, Jul 16, 2015 at 1:23 AM, guskant wrote: > >> >> For the same reason, I prefer the interpretation of "all true or all=20 >> false" for {go} and "one and only one of them is true" for {gonai} to th= e=20 >> interpretation of grouping of binary connectives. >> > > One problem with that interpretation for "gonai" is that it doesn't go=20 > well with "go ... ginai ... gi ..." and such. The natural Lojbanic=20 > interpretation is for "nai" to negate the following connectand. So "gonai= A=20 > gi B gi C" would be true when A differs in truth value from B and from C. > > "One and only one of them" is more useful, but hard to reconcile with the= =20 > general pattern. > > mu'o mi'e xorxes > =20 In the case that we give those special meaning to n-ary forethought=20 connectives, {go} and {gonai} should be defined as broader meaning than=20 XNOR or XOR, so that they become XNOR and XOR respectively in the case of= =20 n=3D2. If {go} and {gonai} are defined as "all true or all false" and "one and=20 only one of them is true", there must be {gocu'i} for the other cases:=20 {gonai ... gi ... gi ...} is not equal to {nago ... gi ... gi ...} in the= =20 case of n>2. Le jeudi 16 juillet 2015 21:58:31 UTC, xorxes a =C3=A9crit : > > > > On Thu, Jul 16, 2015 at 7:30 AM, Alex Burka > wrote: > >> So, to the question of that {gu} and {go} mean with more than 2=20 >> arguments, we kind of find ourselves with tradeoff between logic and eas= e=20 >> of use. >> >> First I get nervous extending them to >2-ary at all, since it becomes=20 >> harder to reason about the negations ({gonai X gi Y} is XOR, but {gonai = X=20 >> gi Y gi Z} is not, it's something strange instead -- and nobody can do= =20 >> truth tables in their head, even fluent speakers). >> >> The interpretations you list are undoubtedly useful (particularly the=20 >> "which one out of these X alternatives"-connective is often asked for,= =20 >> > > "Which one(s) of the following" would be "ge'i ... gi ... gi ... gi ... "= ,=20 > right? > =20 > >> though there is a workable solution using {moi}). But they do not=20 >> correspond to the mathematical interpretation. For example, n-ary XOR is= =20 >> supposed to be true when an odd number of the arguments are true, which = is=20 >> not obvious (or often useful in speech). Changing this can cause=20 >> difficulties with composition, for example logical transformations like = De=20 >> Morgans' laws will not work.=20 >> > > The negation of "ga ... gi ... gi ..." is still "ge nai ... gi nai ... gi= =20 > nai ..." and viceversa. And "go ... gi ... gi ..." should be equivalent t= o=20 > "go nai ... gi nai ... gi nai ... ", but that means "go nai" can't mean= =20 > "one and only one of the following".=20 > =20 Yes, if {gonai} is defined as above, equivalence between {go ... gi ... gi= =20 ...} and {go nai ... gi nai ... gi nai ...} will be broken. We need to keep= =20 {go ... gi ...} and {go nai ... gi nai ...} be equivalent in the case of=20 n=3D2. Would this change of meaning of {GA nai} hurt usefulness of binary= =20 connective system? If we carefully define {GA (nai)} of n-ary connective=20 system, it might be possible to keep the binary connective system safe. --=20 You received this message because you are subscribed to the Google Groups "= lojban" group. To unsubscribe from this group and stop receiving emails from it, send an e= mail to lojban+unsubscribe@googlegroups.com. To post to this group, send email to lojban@googlegroups.com. Visit this group at http://groups.google.com/group/lojban. For more options, visit https://groups.google.com/d/optout. ------=_Part_1566_884288348.1437093902838 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable

Le jeudi 16 juillet 2015 21:35:46 UTC, xorxes a =C3=A9crit=C2=A0:


On Thu, Jul 16, 2015 at 1:23 AM, guskant=C2=A0&l= t;gusni...@gmail.com>=C2=A0wrote:

For the same reason, I prefer the interpretation of= "all true or all false" for {go} and "one and only one of t= hem is true" for {gonai} to the interpretation of grouping of binary c= onnectives.

One problem with that int= erpretation for "gonai" is that it doesn't go well with "= ;go ... ginai ... gi ..." and such. The natural Lojbanic interpretatio= n is for "nai" to negate the following connectand. So "gonai= A gi B gi C" would be true when A differs in truth value from B and f= rom C.

"One and only one of them" is mor= e useful, but hard to reconcile with the general pattern.

mu'o mi'e xorxes
<= br>
=C2=A0

In the case that we give= those special meaning to n-ary forethought connectives, {go} and {gonai} s= hould be defined as broader meaning than XNOR or XOR, so that they become X= NOR and XOR respectively in the case of n=3D2.

If = {go} and {gonai} are defined as "all true or all false" and "= ;one and only one of them is true", there must be {gocu'i} for the= other cases: {gonai ... gi ... gi ...} is not equal to {nago ... gi ... gi= ...} in the case of n>2.


Le jeudi 16 juil= let 2015 21:58:31 UTC, xorxes a =C3=A9crit=C2=A0:


On Thu, Jul 16, 2015 at 7:30 AM, Alex Burka <dur...@gmail.com> wrote:
So, to the question of that {gu} and {go} mean with more th= an 2 arguments, we kind of find ourselves with tradeoff between logic and e= ase of use.

First I get nervous extending them to >2-ary at all, s= ince 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 "wh= ich one out of these X alternatives"-connective is often asked for,

"Which one(s) of the follow= ing" would be "ge'i ... gi ... gi ... gi ... ", right?
=C2=A0
though there is a workable so= lution using {moi}). But they do not correspond to the mathematical interpr= etation. For example, n-ary XOR is supposed to be true when an odd number o= f 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 ... g= i nai ... gi nai ... ", but that means "go nai" can't me= an "one and only one of the following".=C2=A0

=C2=A0

Y= es, if {gonai} is defined as above, equivalence between {go ... gi ... gi .= ..} and {go nai ... gi nai ... gi nai ...} will be broken. We need to keep = {go ... gi ...} and {go nai ... gi nai ...} be equivalent in the case of n= =3D2. Would this change of meaning of {GA nai} hurt usefulness of binary co= nnective system? If we carefully define {GA (nai)} of n-ary connective syst= em, it might be possible to keep the binary connective system safe.

--
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