Received: from mail-ve0-f185.google.com ([209.85.128.185]:46102) by stodi.digitalkingdom.org with esmtps (TLSv1:RC4-SHA:128) (Exim 4.80.1) (envelope-from ) id 1WowPZ-00016e-5y for lojban-list-archive@lojban.org; Mon, 26 May 2014 08:02:24 -0700 Received: by mail-ve0-f185.google.com with SMTP id sa20sf2246265veb.2 for ; Mon, 26 May 2014 08:01:49 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=googlegroups.com; s=20120806; h=date:from:to:cc:message-id:in-reply-to:references:subject :mime-version:x-original-sender:reply-to:precedence:mailing-list :list-id:list-post:list-help:list-archive:sender:list-subscribe :list-unsubscribe:content-type; bh=mAItboBO+cJI1/zcFFdHxKRdGpQBvBWIqvAcRBORk/4=; b=hN0GTBWytjTHwaBKwVd2YwVZrArCURy84mrvEILpbuKMIkWchPyPWzJqH89dToOrEj 2k4+LOI11xLL3HzMiWxn98tJk7QeDyUzZ54MjvMH+mZfkQuTwud7pcA2rCtITXt9HAtR ImnWTu4ZO28lTtoJMxxcA6X5l0BYmFv5AF5xjMOWeHQUbbPgvRJomgz87giWDY8hfUrU +d6qHVLw/vMZumunLiwJlTXuBzHk/WjRMID2MJ4EdVyRXPYVeFSfMwEBfJeakzOtNEWL u1z2CORTDYmi+l9ATrdRY38CPRVKeHDR1Nkmu9sKl+W5xDKJujwLVvwfHmian7oRTAfI TDrA== DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=date:from:to:cc:message-id:in-reply-to:references:subject :mime-version:x-original-sender:reply-to:precedence:mailing-list :list-id:list-post:list-help:list-archive:sender:list-subscribe :list-unsubscribe:content-type; bh=mAItboBO+cJI1/zcFFdHxKRdGpQBvBWIqvAcRBORk/4=; b=oXmUhUbj//kQRS79sxX/uMQSdbNZ5msxm5xFQwLkI0ZIP0D4ilvOB+zW7b4fKsHE7V WToG3iMdATiKPF0/HzvBMGqGv485960hzWN3yEZ5NzuDnjVchGX1Ww9sRvNiEOLOgMU+ t/MqvolV36JiUG8DyUiltyhQd9ODakJf8upbX6McEnavzFN397U1ZryKToAqvdGxSBeR zZwe8BEf0JuEZzsVU9ZEq36hvGGfcOmJQOxE1tRbrLp4g/FWGPKzr55LCoxHFN8QI2G7 UXWtTJQEQFWwItdSIIRxjx2asSPF3DQ1vDsMcoCJXReJJ0D2Us+Ryqagvxp3AlDJG2kb taHA== X-Received: by 10.50.29.68 with SMTP id i4mr566359igh.0.1401116509771; Mon, 26 May 2014 08:01:49 -0700 (PDT) X-BeenThere: lojban@googlegroups.com Received: by 10.50.141.195 with SMTP id rq3ls1547361igb.39.canary; Mon, 26 May 2014 08:01:49 -0700 (PDT) X-Received: by 10.50.143.1 with SMTP id sa1mr498145igb.12.1401116508990; Mon, 26 May 2014 08:01:48 -0700 (PDT) Date: Mon, 26 May 2014 08:01:47 -0700 (PDT) From: guskant To: lojban@googlegroups.com Cc: mbays@sdf.org Message-Id: In-Reply-To: <20140525194906.GA885@gonzales> References: <390f1b9f-6edd-42f2-8474-ad1f3610cca3@googlegroups.com> <750f9b01-a747-4b12-80ba-e31b7e7bd20e@googlegroups.com> <570dae9f-cda3-42c4-a861-1c7974fe5bfd@googlegroups.com> <20140525194906.GA885@gonzales> Subject: Re: [lojban] Individuals and xorlo MIME-Version: 1.0 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-Google-Group-Id: 1004133512417 List-Post: , List-Help: , List-Archive: Sender: lojban@googlegroups.com List-Subscribe: , List-Unsubscribe: , Content-Type: multipart/alternative; boundary="----=_Part_769_18382044.1401116507873" X-Spam-Score: -0.1 (/) X-Spam_score: -0.1 X-Spam_score_int: 0 X-Spam_bar: / ------=_Part_769_18382044.1401116507873 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Le lundi 26 mai 2014 04:49:09 UTC+9, Martin Bays a =C3=A9crit : > > * Monday, 2014-05-19 at 06:04 -0700 - guskant >:=20 > > > > Le mardi 8 avril 2014 10:09:19 UTC+9, guskant a =C3=A9crit :=20 > > I have finished English translation of my commentary on gadri from a=20 > > logical point of view:=20 > >=20 > http://www.lojban.org/tiki/gadri%3A+an+unofficial+commentary+from+a+logic= al+point+of+view&no_bl=3Dy=20 > >=20 > > Any comments or questions will be appreciated.=20 > > Not that I really want to drag myself into discussing these things=20 > again, but I happened to see this and thought I should recall=20 > a complication. Apologies if I'm repeating something hidden in this=20 > thread.=20 > > Saying that {zo'e} and {lo broda} introduce "constants" isn't really=20 > enough to explain how they work, because of cases where a description=20 > includes a bound variable, e.g.=20 > {ro da poi verba cu prami lo rirni be da} .=20 > > If I recall correctly, there was the other year some agreement that {lo= =20 > rirni be da} there should be taken to introduce a contextually specified= =20 > function from children to parents (like a Skolem function), which in=20 > some sense salvages the idea of constancy (it's constantly=20 > a non-constant function!). But anyway, I think it's something that needs= =20 > to be explained in any theory of gadri.=20 > > I note that the "double circle" example in the text=20 > su'o da zo'u loi re lo'i ro mokca noi sepli py noi mokca ku'o da cu= =20 > relcuktai=20 > Two sets of points that are equidistant from a point P is a double=20 > circle.=20 > is of this form, but doesn't give the intended meaning under the above=20 > interpretation (or any other that I can think of).=20 > > Martin=20 > Thank you for the question. Here is my answer. I will add this topic to the= =20 commentary. Generally, all {zo'e} in a statement that contains one or more bound=20 variable(s), no matter if they are explicit or not, must be Skolem=20 functions. If they were not, the official interpretation (CLL 7.7) of=20 implicit {zo'e} should have been modified. For example, we may freely say: S1- {ro mlatu cu jbena}. According to CLL 7.7, it has the same meaning as S2- {ro mlatu cu jbena zo'e zo'e zo'e}. (I omit x2 of {mlatu} for simplicity.) Unless all cats in this universe of discourse were born to common parents= =20 at the same time at the same place, these {zo'e} are not constants but=20 Skolem functions f(x) g(x) h(x) respectively: S3- {roda zo'u ganai da mlatu gi da jbena zo'e zo'e zo'e}, that is Ax ~M(x) v J(x,f(x),g(x),h(x)), where x corresponds to {da}, and is a singular variable bound by a=20 universal quantifier A, ~ is negation, v is OR, M and J are predicates. S3 is a Skolemized form of a statement S4- {roda su'oidexipa su'oidexire su'oidexici zo'u=20 ganai da mlatu gi da jbena dexipa dexire dexici},=20 that is Ax EY1 EY2 EY3 ~M(x) v J(x,Y1,Y2,Y3), where Y1 Y2 Y3 are plural variables bound by existential quantifiers E. In Skolemizing S4 into S3, {su'oidexipa}, {su'oidexire} and {su'oidexici}= =20 of S4 are replaced by {zo'e}s that are respectively equal to f(x), g(x) and= =20 h(x). If {zo'e} were not Skolem functions, we should have abandoned the=20 interpretation "S1 =3D S2" so that the omitted sumti could have been bound= =20 variables. (It would not be the case if we accepted the idea in "Section=20 4.3.1. If zo'e could be a bound plural variable" of my commentary, but it= =20 is another story.) If we want to make explicit that a Skolem function {zo'e} is a Skolem=20 plural constant (that is, the referent of {zo'e} does not vary according to= =20 {da}), we should say the corresponding plural variable earlier than {roda}= =20 in the prenex of the statement before Skolemization. For example, in order to mean that {zo'e} at x4 of {jbena} refers to the=20 Earth that is common to all cats, the statement before Skolemization should= =20 be S5- {su'oidexici roda su'oidexipa su'oidexire zo'u ganai da mlatu gi da jbena dexipa dexire dexici}, that is EY3 Ax EY1 EY2 ~M(x) v J(x,Y1,Y2,Y3). By skolemizing S5, we obtain a statement that is S6.1- Ax ~M(x) v J(x,f(x),g(x),h), where h is a Skolem plural constant: h does not depend on x because EY3 of= =20 S5 was said earlier than Ax in the prenex.=20 Lojban expression of S6.1 might not officially be explained, but I would=20 profit the property that Lojban prenex can include constants: S6- {cy zo'u ro mlatu cu jbena fo cy}, which is the same as {cy roda poi mlatu zo'u da jbena fo cy} and {cy roda zo'u ganai da mlatu gi da jbena fo cy}. In S6, I used {cy} instead of {zo'e} for the constant, otherwise we could= =20 not distinguish which {zo'e} was on the prenex. Although it might be off-topic, the following thread on the order of tagged= =20 sumti and its scope suggests me of an idea: https://groups.google.com/d/topic/lojban/PhZD1fO64jc/discussion I suggest that not only the scope of tagged sumti but also that of terbri= =20 sumti reflects their order. For example, I suggest considering that S6.1=20 and S6 are the same as=20 S7- {fo cy fa ro mlatu cu jbena}. --=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_769_18382044.1401116507873 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable


Le lundi 26 mai 2014 04:49:09 UTC+9, Martin Bays a= =C3=A9crit :
* Monday, 20= 14-05-19 at 06:04 -0700 - guskant <= gusni...@gmail.com>:

> Le mardi 8 avril 2014 10:09:19 UTC+9, guskant a =C3=A9crit :
> I have finished English translation of my commentary on gadri from= a=20
> logical point of view:
> enough to explain how they work, because of cases where a description
includes a bound variable, e.g.
    {ro da poi verba cu prami lo rirni be da} .

If I recall correctly, there was the other year some agreement that {lo
rirni be da} there should be taken to introduce a contextually specifie= d
function from children to parents (like a Skolem function), which in
some sense salvages the idea of constancy (it's constantly
a non-constant function!). But anyway, I think it's something that need= s
to be explained in any theory of gadri.

I note that the "double circle" example in the text
    su'o da zo'u loi re lo'i ro mokca noi sepli py noi mokca = ku'o da cu
        relcuktai=20
    Two sets of points that are equidistant from a point P is= a double
        circle.
is of this form, but doesn't give the intended meaning under the above
interpretation (or any other that I can think of).

Martin


=
Generally, all {zo'e} in a statement that contains one or more bound v= ariable(s), no matter if they are explicit or not, must be Skolem functions= . If they were not, the official interpretation (CLL 7.7) of implicit {zo'e= } should have been modified.

For example, we may f= reely say:

S1- {ro mlatu cu jbena}.

=
According to CLL 7.7, it has the same meaning as

<= /div>
S2- {ro mlatu cu jbena zo'e zo'e zo'e}.
(I omit x2 of {= mlatu} for simplicity.)

Unless all cats in this un= iverse of discourse were born to common parents at the same time at the sam= e place, these {zo'e} are not constants but Skolem functions f(x) g(x) h(x)= respectively:

S3- {roda zo'u ganai da mlatu gi da= jbena zo'e zo'e zo'e},
that is
Ax ~M(x) v J(x,f(x),g(x= ),h(x)),
where x corresponds to {da}, and is a singular variable = bound by a universal quantifier A,
~ is negation,
v is = OR,
M and J are predicates.

S3 is a Skol= emized form of a statement

S4- {roda su'oidexipa s= u'oidexire su'oidexici zo'u 
ganai da mlatu gi da jbena dexi= pa dexire dexici}, 
that is
Ax EY1 EY2 EY3 ~M(x) v= J(x,Y1,Y2,Y3),
where Y1 Y2 Y3 are plural variables bound by exis= tential quantifiers E.

In Skolemizing S4 into S3, = {su'oidexipa}, {su'oidexire} and {su'oidexici} of S4 are replaced by {zo'e}= s that are respectively equal to f(x), g(x) and h(x). If {zo'e} were not Sk= olem functions, we should have abandoned the interpretation "S1 =3D S2" so = that the omitted sumti could have been bound variables. (It would not be th= e case if we accepted the idea in "Section 4.3.1. If zo'e could be a bound = plural variable" of my commentary, but it is another story.)

=
If we want to make explicit that a Skolem function {zo'e} is a S= kolem plural constant (that is, the referent of {zo'e} does not vary accord= ing to {da}), we should say the corresponding plural variable earlier than = {roda} in the prenex of the statement before Skolemization.
For e= xample, in order to mean that {zo'e} at x4 of {jbena} refers to the Earth t= hat is common to all cats, the statement before Skolemization should be

S5- {su'oidexici roda su'oidexipa su'oidexire zo'u
ganai da mlatu gi da jbena dexipa dexire dexici},
that is=
EY3 Ax EY1 EY2 ~M(x) v J(x,Y1,Y2,Y3).

B= y skolemizing S5, we obtain a statement that is
S6.1- Ax ~M(x) v = J(x,f(x),g(x),h),
where h is a Skolem plural constant: h does not= depend on x because EY3 of S5 was said earlier than Ax in the prenex. = ;

Lojban expression of S6.1 might not officially b= e explained, but I would profit the property that Lojban prenex can include= constants:

S6- {cy zo'u ro mlatu cu jbena fo cy},=
which is the same as
{cy roda poi mlatu zo'u da jbena = fo cy}
and
{cy roda zo'u ganai da mlatu gi da jbena fo = cy}.

In S6, I used {cy} instead of {zo'e} for the = constant, otherwise we could not distinguish which {zo'e} was on the prenex= .


Although it might be off-topic, t= he following thread on the order of tagged sumti and its scope suggests me = of an idea:
https://groups.google.com/d/topic/lojban/PhZD1fO64jc/= discussion

I suggest that not only the scope of ta= gged sumti but also that of terbri sumti reflects their order. For example,= I suggest considering that S6.1 and S6 are the same as 
S7- {fo cy fa ro mlatu cu jbena}.




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