Received: from mail-qc0-f192.google.com ([209.85.216.192]:53426) by stodi.digitalkingdom.org with esmtps (TLSv1:RC4-SHA:128) (Exim 4.80.1) (envelope-from ) id 1WpAct-0006P6-19 for lojban-list-archive@lojban.org; Mon, 26 May 2014 23:12:56 -0700 Received: by mail-qc0-f192.google.com with SMTP id l6sf2509390qcy.9 for ; Mon, 26 May 2014 23:12:36 -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=/Ue+Yi5BSuWHL73As4IgNa1h3wnsUcXSPGJd4miskBA=; b=eVHIcegkMQihTyxeii5RRts9c8wuUrXy858pdxlqqhxlzOUsS9COOOUwNA1M4KEWwu W8C+81ozQbe8bTDpiuOXmJisqFnrGLlSitmjxIvsQ84dKMFuivVdBpVLiKIeDMFaUleq eKWUZMxRy75dPpObyd+i/YzYpdHybQ/Kt+QrBq1LRgdxQiKyEg9xc7azW4HEWsrw9w9V iNVBte+vWllZnnshB8v2zRaFrw/CEVML9v2kNXaF1gXBvrGQVDXv/AQ6EUF7m0Osvtcp WRvs2MZjFTWINnkQxVIIFnE3MlemL4p/C2qX84quMadnMywW5uxtmHV2pSQRrGAo/n1c ytYA== 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=/Ue+Yi5BSuWHL73As4IgNa1h3wnsUcXSPGJd4miskBA=; b=xEigsjASf1x6OdapO/mb4cC9oEXUEgJE3VFL+tpQ/8yA3Cyh7My8m6vFeZiUhGYT0Y 0rtUG+2ZMq3RJdsHGKoT/6oTBxXf8dbujw0PkKbRjDWNsb4XnOu24FNIHlCDiEESBtt2 RrNsT9X2PMnqOwQyKpu1XBIDQqPimW35YTgHuohWjW113tKBu2/XIz2zDrWxokF45uPS cmehTnfstVMBNBadYQZVfn8IlHTlkVGaBVyfo+oPVIUPtLPuVQNtGRr9LSDj7FX1UF2M zW+fFSMk5aI2zFaT4YCBpKhsbEj0es0Kvqfkcq3iZlDMeqFCUw+6+HitvzIg+EV47Gnz 2CoA== X-Received: by 10.50.26.71 with SMTP id j7mr642485igg.1.1401171156834; Mon, 26 May 2014 23:12:36 -0700 (PDT) X-BeenThere: lojban@googlegroups.com Received: by 10.50.67.2 with SMTP id j2ls192331igt.36.gmail; Mon, 26 May 2014 23:12:36 -0700 (PDT) X-Received: by 10.50.142.104 with SMTP id rv8mr73698igb.13.1401171156015; Mon, 26 May 2014 23:12:36 -0700 (PDT) Date: Mon, 26 May 2014 23:12:34 -0700 (PDT) From: guskant To: lojban@googlegroups.com Cc: guskant , mbays@sdf.org Message-Id: In-Reply-To: <20140527025346.GJ885@gonzales> References: <750f9b01-a747-4b12-80ba-e31b7e7bd20e@googlegroups.com> <570dae9f-cda3-42c4-a861-1c7974fe5bfd@googlegroups.com> <20140525194906.GA885@gonzales> <20140527025346.GJ885@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_251_28026554.1401171154938" X-Spam-Score: -0.1 (/) X-Spam_score: -0.1 X-Spam_score_int: 0 X-Spam_bar: / ------=_Part_251_28026554.1401171154938 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Le mardi 27 mai 2014 11:53:50 UTC+9, Martin Bays a =C3=A9crit : > > * Monday, 2014-05-26 at 08:01 -0700 - guskant >:=20 > > > > Le lundi 26 mai 2014 04:49:09 UTC+9, Martin Bays a =C3=A9crit :=20 > > >=20 > > > * Monday, 2014-05-19 at 06:04 -0700 - guskant >:=20 > > > >=20 > > >=20 > > > > Le mardi 8 avril 2014 10:09:19 UTC+9, guskant a =C3=A9crit :=20 > > >=20 > http://www.lojban.org/tiki/gadri%3A+an+unofficial+commentary+from+a+logic= al+point+of+view&no_bl=3Dy=20 > > >=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 > >=20 > > Thank you for the question. Here is my answer. I will add this topic to= =20 > the=20 > > commentary.=20 > >=20 > > 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.=20 > >=20 > > For example, we may freely say:=20 > >=20 > > S1- {ro mlatu cu jbena}.=20 > >=20 > > According to CLL 7.7, it has the same meaning as=20 > >=20 > > S2- {ro mlatu cu jbena zo'e zo'e zo'e}.=20 > > (I omit x2 of {mlatu} for simplicity.)=20 > >=20 > > Unless all cats in this universe of discourse were born to common=20 > 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:=20 > >=20 > > S3- {roda zo'u ganai da mlatu gi da jbena zo'e zo'e zo'e},=20 > > that is=20 > > Ax ~M(x) v J(x,f(x),g(x),h(x)),=20 > > where x corresponds to {da}, and is a singular variable bound by a=20 > > universal quantifier A,=20 > > ~ is negation,=20 > > v is OR,=20 > > M and J are predicates.=20 > >=20 > > S3 is a Skolemized form of a statement=20 > >=20 > > S4- {roda su'oidexipa su'oidexire su'oidexici zo'u=20 > > ganai da mlatu gi da jbena dexipa dexire dexici},=20 > > that is=20 > > Ax EY1 EY2 EY3 ~M(x) v J(x,Y1,Y2,Y3),=20 > > where Y1 Y2 Y3 are plural variables bound by existential quantifiers E.= =20 > > I don't know of any clear problem with this solution - which, when=20 > applied to {lo}, corresponds to CLL-{lo} (modulo the difference between= =20 > su'o and su'oi). But as I understand it, xorlo solves the problem rather= =20 > differently - by having the {zo'e}s there refer to generics, constant=20 > with respect to {da}.=20 > > Martin=20 > > The interpretation of {zo'e} as Skolem function rather reinforces xorlo,=20 and makes clear that the CLL-interpretation of gadri is problematic. Skolem functions f(x),g(x),h(x) of S3 are constants for every referent in= =20 the domain of Ax, because they depend on no variable except x. It does not= =20 contradict xorlo. On the other hand, any sumti of CLL-lo are bound by any= =20 singular quantifier, and cannot express Skolemized form. If a statement includes no universal quantifier after transformed into=20 prenex normal form, the statement can be Skolemized into a statement in=20 which all Skolem functions are Skolem constants. xorlo can precisely=20 express these constants. CLL-lo cannot. xorlo can make explicit the difference of meaning between S3 and S6.1 for= =20 any sumti in a simple way like S6. CLL-lo restricts the outer quantifier=20 according to sumti, and makes it difficult to express the difference of=20 meaning between S3 and S6.1. As for the example in my commentary that you pointed out: {su'o da zo'u loi re lo'i ro mokca noi sepli py noi mokca ku'o da cu=20 relcuktai}, the quantifier in the prenex is not universal A but existential E: it is=20 not a Skolemized form.=20 It is expressed in predicate logic as Ex R(m,p,x), where x is a singular variable bound by an existential quantifier E, R is a predicate, m and p are constants. Because this statement contains no other outer quantifier, it is a prenex= =20 normal form that contains no universal quantifier. It is therefore=20 Skolemized into {loi re lo'i ro mokca noi sepli py noi mokca ku'o zo'e cu relcuktai}, that is=20 R(m,p,z), where z is a Skolem constant.=20 There is no problem for interpreting it as "two sets of points that are=20 equidistant from a point P is a double circle." =20 --=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_251_28026554.1401171154938 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable


Le mardi 27 mai 2014 11:53:50 UTC+9, Martin Bays a= =C3=A9crit :
* Monday, 20= 14-05-26 at 08:01 -0700 - guskant <= gusni...@gmail.com>:

> Le lundi 26 mai 2014 04:49:09 UTC+9, Martin Bays a =C3=A9crit :
> >
> > * Monday, 2014-05-19 at 06:04 -0700 - guskant <gusni...= @gmail.com<javascript:>>:=20
> >
> >
> > > Le mardi 8 avril 2014 10:09:19 UTC+9, guskant a =C3=A9cr= it :=20
> > http://www.lojban.org/tiki/gadri%3A+an+unofficial+commenta= ry+from+a+logical+point+of+view&no_bl=3Dy=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 des= cription=20
> > includes a bound variable, e.g.=20
> >     {ro da poi verba cu prami lo rirni be da} .=20
>=20
> Thank you for the question. Here is my answer. I will add this top= ic to the=20
> commentary.
>=20
> Generally, all {zo'e} in a statement that contains one or more bou= nd=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.
>=20
> For example, we may freely say:
>=20
> S1- {ro mlatu cu jbena}.
>=20
> According to CLL 7.7, it has the same meaning as
>=20
> S2- {ro mlatu cu jbena zo'e zo'e zo'e}.
> (I omit x2 of {mlatu} for simplicity.)
>=20
> 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.
>=20
> S3 is a Skolemized form of a statement
>=20
> 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 quantifie= rs E.

I don't know of any clear problem with this solution - which, when
applied to {lo}, corresponds to CLL-{lo} (modulo the difference between
su'o and su'oi). But as I understand it, xorlo solves the problem rathe= r
differently - by having the {zo'e}s there refer to generics, constant
with respect to {da}.

Martin



The interpretation of {= zo'e} as Skolem function rather reinforces xorlo, and makes clear that the = CLL-interpretation of gadri is problematic.

Skolem= functions f(x),g(x),h(x) of S3 are constants for every referent in the dom= ain of Ax, because they depend on no variable except x. It does not contrad= ict xorlo. On the other hand, any sumti of CLL-lo are bound by any singular= quantifier, and cannot express Skolemized form.

I= f a statement includes no universal quantifier after transformed into prene= x normal form, the statement can be Skolemized into a statement in which al= l Skolem functions are Skolem constants. xorlo can precisely express these = constants. CLL-lo cannot.

xorlo can make explicit = the difference of meaning between S3 and S6.1 for any sumti in a simple way= like S6. CLL-lo restricts the outer quantifier according to sumti, and mak= es it difficult to express the difference of meaning between S3 and S6.1.


As for the example in my commentary = that you pointed out:

{su'o da zo'u loi re lo'i ro= mokca noi sepli py noi mokca ku'o da cu relcuktai},

the quantifier in the prenex is not universal A but existential E: it is= not a Skolemized form. 
It is expressed in predicate logic = as

Ex R(m,p,x),
where x is a singular va= riable bound by an existential quantifier E,
R is a predicate,
m and p are constants.

Because this statem= ent contains no other outer quantifier, it is a prenex normal form that con= tains no universal quantifier. It is therefore Skolemized into
{loi re lo'i ro mokca noi sepli py noi mokca ku'o zo'e cu relc= uktai},
that is 
R(m,p,z),
where z is a = Skolem constant. 

There is no problem for int= erpreting it as "two sets of points that are equidistant from a point P is = a double circle."

 

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