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[216.109.115.134]) by gmr-mx.google.com with ESMTPS id x2si1620797qch.0.2014.05.26.10.51.10 for (version=TLSv1 cipher=RC4-SHA bits=128/128); Mon, 26 May 2014 10:51:10 -0700 (PDT) Received-SPF: pass (google.com: domain of kali9putra@yahoo.com designates 216.109.115.134 as permitted sender) client-ip=216.109.115.134; Received: from [66.196.81.157] by nm21.access.bullet.mail.bf1.yahoo.com with NNFMP; 26 May 2014 17:51:10 -0000 Received: from [66.196.81.126] by tm3.access.bullet.mail.bf1.yahoo.com with NNFMP; 26 May 2014 17:51:10 -0000 Received: from [127.0.0.1] by omp1002.access.mail.bf1.yahoo.com with NNFMP; 26 May 2014 17:51:10 -0000 X-Yahoo-Newman-Property: ymail-3 X-Yahoo-Newman-Id: 292568.96745.bm@omp1002.access.mail.bf1.yahoo.com Received: (qmail 84745 invoked by uid 60001); 26 May 2014 17:51:09 -0000 X-YMail-OSG: xoI7BWsVM1moIOITW01XaYtSOB.2fY1blJ9Y6r236EolAkb cs72T3nFbhXLWRVHRLfbzTz9t5kAIVYCW4KluEgVbGp90eje5YDX6jIki4pV WAtPUW39hVrEUcfmigHCLxGmflnafjedYP_vIgkpzQL_5A4gST1m8JA0LaJ2 KvUb0_fJHmq6Y9Q3V05xdDmHnZbXYP.EtCSInXXzvsFO1IbncdbnVlrANi.O BobdikUiZ6kratjqkaWv51md_xTi543iyLtm7CLoMjf2kZ99fue2oUGQsAzC cRW9AUP8wSfj4evT5DcW4ZUXqmMdEKNwQDitbse4rXQ4lXyiPpOcsyTaLtwT GLo52u8AObTiKH89iaMwXGXXJAOWVCDyTi5Ga356zAevELfHGltzNZXC8TXK JIb4VJDrqJIUcgYONuspvOEo1rcFeRNmqUmDo0KSekXhk6wtzlYuWcrzw3bV sEuKGWmadcBfRaJ3RFDQ3ovG3tAUX.vTPpGfX7fQw47VICn6c1HlG75V4g9q BGp3_rpldPy9iRKOIPkSFQKr1_4uQNrnivK_ECj.1_sShfUuhaKAsMZNQIdA Wi_jhDDqz63j7VrROAcbaCX1TOfY0JAmfiYToAgGG8HiVqR9PKUQfx3MSwuz aBn4ljQZkT4_YzcN6.aVhdiyhvRcrwzYZDyKoft8.KNIuvojnTKOZUmUvivb ldOBXvyLGNr3Mngth7WkvblGT3eHjBkeanlyHB5ScmZjOKhJfwC9fZJioOye J7TMM7qf6QEFSZopQ2_8ul68W0nSvFO.VniJjQQf6LLM- Received: from [99.92.109.82] by web181104.mail.ne1.yahoo.com via HTTP; Mon, 26 May 2014 10:51:09 PDT X-Rocket-MIMEInfo: 002.001,bmljZSEKCgoKCk9uIE1vbmRheSwgTWF5IDI2LCAyMDE0IDEwOjAxIEFNLCBndXNrYW50IDxndXNuaS5rYW50dUBnbWFpbC5jb20.IHdyb3RlOgogCgoKCgpMZSBsdW5kaSAyNiBtYWkgMjAxNCAwNDo0OTowOSBVVEMrOSwgTWFydGluIEJheXMgYSDDqWNyaXTCoDoKKiBNb25kYXksIDIwMTQtMDUtMTkgYXQgMDY6MDQgLTA3MDAgLSBndXNrYW50IDxndXNuaS4uLkBnbWFpbC5jb20.OiAKPgo.PiBMZSBtYXJkaSA4IGF2cmlsIDIwMTQgMTA6MDk6MTkgVVRDKzksIGd1c2thbnQgYSDDqWNyaXQgOiAKPj4gSSBoYXYBMAEBAQE- X-Mailer: YahooMailWebService/0.8.188.663 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> Message-ID: <1401126669.55542.YahooMailNeo@web181104.mail.ne1.yahoo.com> Date: Mon, 26 May 2014 10:51:09 -0700 (PDT) From: "'John E Clifford' via lojban" Reply-To: lojban@googlegroups.com Subject: Re: [lojban] Individuals and xorlo To: "lojban@googlegroups.com" Cc: "mbays@sdf.org" In-Reply-To: MIME-Version: 1.0 X-Original-Sender: kali9putra@yahoo.com X-Original-Authentication-Results: gmr-mx.google.com; spf=pass (google.com: domain of kali9putra@yahoo.com designates 216.109.115.134 as permitted sender) smtp.mail=kali9putra@yahoo.com; dkim=pass header.i=@yahoo.com; dmarc=pass (p=REJECT dis=NONE) header.from=yahoo.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: , X-Original-From: John E Clifford Content-Type: multipart/alternative; boundary="-482694697-481400451-1401126669=:55542" X-Spam-Score: -0.1 (/) X-Spam_score: -0.1 X-Spam_score_int: 0 X-Spam_bar: / ---482694697-481400451-1401126669=:55542 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable nice! On Monday, May 26, 2014 10:01 AM, guskant wrote: =20 Le lundi 26 mai 2014 04:49:09 UTC+9, Martin Bays a =E9crit=A0: * Monday, 2014-05-19 at 06:04 -0700 - guskant :=20 > >> Le mardi 8 avril 2014 10:09:19 UTC+9, guskant a =E9crit :=20 >> I have finished English translation of my commentary on gadri from a=20 >> logical point of view:=20 >> http://www.lojban.org/tiki/ gadri%3A+an+unofficial+ commentary+from+a+lo= gical+ 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 >=A0 =A0 {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 >=A0 =A0 su'o da zo'u loi re lo'i ro mokca noi sepli py noi mokca ku'o da c= u=20 >=A0=A0=A0=A0=A0=A0=A0=A0relcuktai=20 >=A0 =A0 Two sets of points that are equidistant from a point P is a double= =20 >=A0=A0=A0=A0=A0=A0=A0=A0circle.=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= commentary. Generally, all {zo'e} in a statement that contains one or more bound variab= le(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} sho= uld 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 a= t the same time at the same place, these {zo'e} are not constants but Skole= m 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 universa= l 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=A0 ganai da mlatu gi da jbena dexipa dexire dexici},=A0 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} o= f S4 are replaced by {zo'e}s that are respectively equal to f(x), g(x) and = h(x). If {zo'e} were not Skolem functions, we should have abandoned the int= erpretation "S1 =3D S2" so that the omitted sumti could have been bound var= iables. (It would not be the 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 ano= ther story.) If we want to make explicit that a Skolem function {zo'e} is a Skolem plura= l constant (that is, the referent of {zo'e} does not vary according to {da}= ), we should say the corresponding plural variable earlier than {roda} in t= he prenex of the statement before Skolemization. For example, in order to mean that {zo'e} at x4 of {jbena} refers to the Ea= rth that is common to all cats, the statement before Skolemization should b= e 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 = S5 was said earlier than Ax in the prenex.=A0 Lojban expression of S6.1 might not officially be explained, but I would pr= ofit 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 n= ot distinguish which {zo'e} was on the prenex. Although it might be off-topic, the 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 tagged sumti but also that of terbri s= umti reflects their order. For example, I suggest considering that S6.1 and= S6 are the same as=A0 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 . --=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. ---482694697-481400451-1401126669=:55542 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable
nice!


O= n Monday, May 26, 2014 10:01 AM, guskant <gusni.kantu@gmail.com> wrot= e:




L= e lundi 26 mai 2014 04:49:09 UTC+9, Martin Bays a =E9crit :* Monday, 2014-05-19 at 06:04 -0700 - guskant <= ;gusni...@gmail.com>:

> Le mardi 8 avril 2014 10:09:19 UTC+9, guskant a =E9= crit :
> I have finished English translation of my commentar= y on gadri from a=20
> logical point of view:
> http://www.lojban.org/tiki/ gadri%3= A+an+unofficial+ commentary+from+a+logical+ point+of+view&no_bl=3Dy
>=20
> Any comments or questions will be appreciated.

Not that I really want to drag myself into discussing th= ese things
again, but I happened to see this and thought I should r= ecall
a complication. Apologies if I'm repeating something hid= den in this
thread.

Saying that {zo'e} and {lo broda} introduce "constants" = isn't really
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 agr= eement that {lo
rirni be da} there should be taken to introduce a contex= tually specified
function from children to parents (like a Skolem functio= n), which in
some sense salvages the idea of constancy (it's constant= ly
a non-constant function!). But anyway, I think it's some= thing that needs
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 sepl= i py noi mokca ku'o da cu
        relcukta= i=20
    Two sets of points that are equidistant fr= om a point P is a double
        circle.
is of this form, but doesn't give the intended meaning u= nder the above
interpretation (or any other that I can think of).

Martin

Thank yo= u for the question. Here is my answer. I will add this topic to the comment= ary.

Generally, all {zo'e} in = a statement that contains one or more bound variable(s), no matter if they = are explicit or not, must be Skolem functions. If they were not, the offici= al interpretation (CLL 7.7) of 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<= /div>

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 bor= n to common parents at the same time at the same place, these {zo'e} are no= t 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},<= /div>
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 qua= ntifier A,
~ is negation,
v is OR,
M and J ar= e predicates.

S3 is a Skolemized fo= rm of a statement

S4- {roda su'oide= xipa su'oidexire su'oidexici zo'u 
ganai da mlatu gi da jben= a dexipa dexire dexici}, 
that is
Ax EY1 EY2 EY3 ~= M(x) v J(x,Y1,Y2,Y3),
where Y1 Y2 Y3 are plural variables bound b= y existential quantifiers E.

In Sko= lemizing S4 into S3, {su'oidexipa}, {su'oidexire} and {su'oidexici} of S4 a= re replaced by {zo'e}s that are respectively equal to f(x), g(x) and h(x). If {zo'e} were not Skolem functions, we should have abandoned the interpre= tation "S1 =3D S2" so that the omitted sumti could have been bound variable= s. (It would not be the 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 Skolem plural constant (that is, the re= ferent of {zo'e} does not vary according to {da}), we should say the corres= ponding plural variable earlier than {roda} in the prenex of the statement = before Skolemization.
For example, in order to mean that {zo'e} a= t x4 of {jbena} refers to the Earth that is common to all cats, the stateme= nt before Skolemization should be

S= 5- {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 skol= emizing 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 depen= d on x because EY3 of S5 was said earlier than Ax in the prenex. 

Lojban expression of S6.1 might not off= icially be explained, but I would profit the property that Lojban prenex ca= n include constants:

S6- {cy zo'u r= o 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 ga= nai 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, the following thread on the order of tagged sumti and its sco= pe suggests me of an idea:
https://groups.google.com/d/topic/lojb= an/PhZD1fO64jc/discussion

I suggest= that not only the scope of tagged sumti but also that of terbri sumti refl= ects their order. For example, I suggest considering that S6.1 and S6 are t= he same as 

S7- {fo cy fa ro m= latu cu jbena}.




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