Received: from mail-vc0-f183.google.com ([209.85.220.183]:38739) by stodi.digitalkingdom.org with esmtps (TLSv1:RC4-SHA:128) (Exim 4.80.1) (envelope-from ) id 1WpTUp-0000Bv-Ms for lojban-list-archive@lojban.org; Tue, 27 May 2014 19:21:53 -0700 Received: by mail-vc0-f183.google.com with SMTP id lf12sf2855053vcb.10 for ; Tue, 27 May 2014 19:21:33 -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=ArSakNl4zdHy1TdYq9D/NQ6CgWrKu3KrysmpFsxT6T0=; b=U3MayKppQG82B3un3UG5UvAwQEka61ETeI3t1fMEZvj8L3Wp17s6YjDaUvubgGF8Us pvv0L3z5RytIGWpKtrkee3Vqdo9a7MYh71Y5H4FIaM82ZMDALZ607fpeT54iLXN0BoSM 4ly3YPQ1GkcD/ad2ayqGnBE+bFz6yQDGLkTo5Dexav/gMS0Fwzh+qf6Dacczr+T51NGn 6vxikVeTtysJ2pvlAtHu4wJ9/kbRswMLpnIvFh26JsnC9iNikVbaRQqYN30DNtK8d+l7 4086uCXrFim9PkXdDWVLZVemthgrPblveu7ECDU7CE7LAkXo8rlHftaBVcSQEQ9KDXzE AWtw== 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=ArSakNl4zdHy1TdYq9D/NQ6CgWrKu3KrysmpFsxT6T0=; b=LR5vHbapzrwY5OBJPfnxSfjMRzKEe6kqMXnp8n8ktQj0E+19dkOxsdoDMSFv1msdz/ et+xpmkGpqOpsQ+Tk1Qob75n+I6hO8QbIw7gBs9J85/SVyoDpbA1RUq6hp7q3NT8MLBj ZHDLpZZLYAuocjrdTkX7X2YOBw+loMFhTli0BkRfNTpjCo9d2UqnQws7CBx2wmetRonA mAAyZfsFVAyzH0Wz/VsmeFnD6BFDdcgtpFfOqAWTxS2WoSuGuz81DVxStA6fj186xHso y57dGpWpRxKNWT7EF7fw7WQZLsoS8EUZb+ErZR2/Ar2f1WuLW92T7WbClJ799OAcuFBj u0Vw== X-Received: by 10.50.61.100 with SMTP id o4mr742622igr.7.1401243693464; Tue, 27 May 2014 19:21:33 -0700 (PDT) X-BeenThere: lojban@googlegroups.com Received: by 10.50.253.74 with SMTP id zy10ls2584146igc.26.canary; Tue, 27 May 2014 19:21:32 -0700 (PDT) X-Received: by 10.50.128.108 with SMTP id nn12mr744778igb.1.1401243692837; Tue, 27 May 2014 19:21:32 -0700 (PDT) Date: Tue, 27 May 2014 19:21:31 -0700 (PDT) From: guskant To: lojban@googlegroups.com Cc: guskant Message-Id: <462524b8-28de-49f3-a938-4cc42543c28f@googlegroups.com> In-Reply-To: <20140527204250.GL885@gonzales> References: <750f9b01-a747-4b12-80ba-e31b7e7bd20e@googlegroups.com> <570dae9f-cda3-42c4-a861-1c7974fe5bfd@googlegroups.com> <20140525194906.GA885@gonzales> <20140527025346.GJ885@gonzales> <20140527204250.GL885@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_4371_28401645.1401243691437" X-Spam-Score: -0.1 (/) X-Spam_score: -0.1 X-Spam_score_int: 0 X-Spam_bar: / ------=_Part_4371_28401645.1401243691437 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Le mercredi 28 mai 2014 05:42:53 UTC+9, Martin Bays a =C3=A9crit : > > * Monday, 2014-05-26 at 23:12 -0700 - guskant >:=20 > > > > Le mardi 27 mai 2014 11:53:50 UTC+9, Martin Bays a =C3=A9crit :=20 > > > * 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 > > > > > * 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 > > > > >=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=20 > really=20 > > > > > enough to explain how they work, because of cases where a=20 > description=20 > > > > > includes a bound variable, e.g.=20 > > > > > {ro da poi verba cu prami lo rirni be da} .=20 > > > > Generally, all {zo'e} in a statement that contains one or more boun= d=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)= =20 > 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 > > > >=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 > > > >=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 quantifier= s=20 > E.=20 > > >=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=20 > between=20 > > > su'o and su'oi). But as I understand it, xorlo solves the problem=20 > rather=20 > > > differently - by having the {zo'e}s there refer to generics, constant= =20 > > > with respect to {da}.=20 > >=20 > > The interpretation of {zo'e} as Skolem function rather reinforces xorlo= ,=20 > > and makes clear that the CLL-interpretation of gadri is problematic.=20 > >=20 > > Skolem functions f(x),g(x),h(x) of S3 are constants for every referent= =20 > in=20 > > the domain of Ax, because they depend on no variable except x. It does= =20 > not=20 > > contradict xorlo. On the other hand, any sumti of CLL-lo are bound by= =20 > any=20 > > singular quantifier, and cannot express Skolemized form.=20 > > Although I don't actually consider myself qualified to pronounce on what= =20 > xorlo is, my understanding is that the intention and common=20 > understanding of xorlo have {lo} and {zo'e} constant in the sense of=20 > being outside the scope of any quantifier, except when absolutely forced= =20 > to be inside. So e.g. in {ro da broda lo brode}, the (plural) referent=20 > of {lo brode} is constant with respect to {da} under xorlo, whereas it=20 > is not in CLL-lojban.=20 > > Regarding {zo'e} as the outmost constant in a prenex of a statement is a=20 special case of {zo'e} as Skolem functions. As for the example {ro da broda lo brode}, that is=20 Ax B(x,f(x)), it says nothing about whether {lo brode} as a Skolem function f(x) is=20 constant for all x or not. That is to say, xorlo allows both=20 interpretations "EYAx B(x,Y)" and "AxEY B(x,Y)" as a statement before=20 Skolemization, while CLL-lo restricts the interpretation to "AxEy B(x,y)"= =20 (small y is a singular variable). If xorlo did not allow this=20 interpretation, CLL 7.7 must have been abandoned. As long as both xorlo and= =20 CLL 7.7 are kept true, a constant {zo'e} is not always out of bound=20 variables. =20 > > 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.=20 > >=20 > > xorlo can make explicit the difference of meaning between S3 and S6.1= =20 > for=20 > > any sumti in a simple way like S6. CLL-lo restricts the outer quantifie= r=20 > > according to sumti, and makes it difficult to express the difference of= =20 > > meaning between S3 and S6.1.=20 > > > > S6- {cy zo'u ro mlatu cu jbena fo cy},=20 > > > > S6.1- Ax ~M(x) v J(x,f(x),g(x),h),=20 > > You're right, the semantics you're suggesting aren't really CLL-lo. But= =20 > they share the scope-sensitivity of CLL-lo; that's all I really meant.=20 > > CLL-lo cannot express S3 precisely for the same reason above. S3 of xorlo= =20 says nothing about whether the Skolem functions f(x),g(x),h(x) are Skolem= =20 constants or not. In other words, S3 of xorlo does not say the order of=20 bound variables of a statement before Skolemization. Regarding it as S4 is= =20 the most general case. Any of the statements with prenex "EY2 Ax EY1 EY3"= =20 "EY1 EY2 Ax EY3" etc may be Skolemized into S3, because a Skolen function= =20 {zo'e} does not indicate whether it is a Skolem constant or not. On the other hand, according to CLL-lo, speaker must always select the=20 order of Ax, EY1, EY2 and EY3 of a statement before Skolemization. =20 > > As for the example in my commentary that you pointed out:=20 > >=20 > > {su'o da zo'u loi re lo'i ro mokca noi sepli py noi mokca ku'o da cu=20 > > relcuktai},=20 > >=20 > > the quantifier in the prenex is not universal A but existential E: it i= s=20 > > not a Skolemized form.=20 > > It is expressed in predicate logic as=20 > >=20 > > Ex R(m,p,x),=20 > > where x is a singular variable bound by an existential quantifier E,=20 > > R is a predicate,=20 > > m and p are constants.=20 > >=20 > > Because this statement contains no other outer quantifier, it is a=20 > prenex=20 > > normal form that contains no universal quantifier. It is therefore=20 > > Skolemized into=20 > >=20 > > {loi re lo'i ro mokca noi sepli py noi mokca ku'o zo'e cu relcuktai},= =20 > > that is=20 > > R(m,p,z),=20 > > where z is a Skolem constant.=20 > >=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 > > But you seem to have jumped the existential through the {re} quantifier.= =20 > The radii are meant to be allowed to be different for the two circles,=20 > but in the original sentence the radii are quantified with outermost=20 > scope.=20 > > I was also confused because the english reads like a definition, whereas= =20 > the lojban has no hint of that (and I'm not sure that adding a {ca'e}=20 > would do it).=20 > > Martin=20 > {re} in this example is an inner quantifier, and it does not affect the=20 order of outer quantifier.=20 {zo'e} in the statement {loi re lo'i ro mokca noi sepli py noi mokca ku'o= =20 zo'e cu relcuktai} is a plural constant. Precisely saying, this {zo'e} is= =20 {lo re zo'e} in this context. This statement does not make clear if each=20 individual of the referent of {zo'e} distributively satisfies {sepli}, but= =20 such an interpretation is allowed. I used rather a bound singular variable= =20 {su'oda} in the original example because I wanted to make explicit that the= =20 radii distributively satisfy {sepli}. When I created the example, I did not= =20 consider Skolem functions, but if I wanted to make scopes of the arguments= =20 explicit, I should have been said {py lu'a loi re lo'i ro mokca su'o da lo'i ro mokca zo'u loi re lo'i ro=20 mokca noi sepli py noi mokca ku'o da cu relcuktai}, where I added {lu'a} in order to draw each of {lo se gunma} in the=20 loi-sumti. This trick allows inner quantification to behave as if outer=20 quantification in the prenex. However, I don't think such a precision by prenex is not necessary for an= =20 example of repeating inner quantification. As a summary, xorlo can express the scopes of arguments without outer=20 quantifier unambiguously as well as ambiguously, while CLL-lo must always= =20 do unambiguously.=20 If we take the interpretation like S7, the scopes of the outmost terbri=20 sumti of a statement become unambiguous also in xorlo, though I think this= =20 idea should be at most a plausible interpretation, not a restriction. In=20 general, there are many cases where the order of arguments out of prenex is= =20 restricted by grammar, like that example of relcuktai. xorlo allows Lojban= =20 users to select the most likely interpretation among some possible ones,=20 while CLL-lo definitely requires prenex even for such a simple example. The= =20 idea of xorlo made the language closer to natural expressions, while it=20 reserves also the unambiguity of logic in expressions with prenex. =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_4371_28401645.1401243691437 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable


Le mercredi 28 mai 2014 05:42:53 UTC+9, Martin Bay= s a =C3=A9crit :
* Monday,= 2014-05-26 at 23:12 -0700 - guskant <gusni...@gmail.com>:

> Le mardi 27 mai 2014 11:53:50 UTC+9, Martin Bays a =C3=A9crit :
> > * Monday, 2014-05-26 at 08:01 -0700 - guskant <gusni...= @gmail.com<javascript:>>:=20
> > > Le lundi 26 mai 2014 04:49:09 UTC+9, Martin Bays a =C3= =A9crit :=20
> > > > * Monday, 2014-05-19 at 06:04 -0700 - guskant <<= a>gusni...@gmail.com<javascript:>>:=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+commenta= ry+from+a+logical+point+of+view&no_bl=3Dy=20
> > > >=20
> > > > Saying that {zo'e} and {lo broda} introduce "consta= nts" isn't really=20
> > > > enough to explain how they work, because of cases w= here a description=20
> > > > includes a bound variable, e.g.=20
> > > >     {ro da poi verba cu prami lo rirni be= da} .=20
> > > Generally, all {zo'e} in a statement that contains one o= r 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
> > >=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
> > >
> > > 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 differen= ce between=20
> > su'o and su'oi). But as I understand it, xorlo solves the pro= blem rather=20
> > differently - by having the {zo'e}s there refer to generics, = constant=20
> > with respect to {da}.=20
>=20
> The interpretation of {zo'e} as Skolem function rather reinforces = xorlo,=20
> and makes clear that the CLL-interpretation of gadri is problemati= c.
>=20
> Skolem functions f(x),g(x),h(x) of S3 are constants for every refe= rent 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.

Although I don't actually consider myself qualified to pronounce on wha= t
xorlo is, my understanding is that the intention and common
understanding of xorlo have {lo} and {zo'e} constant in the sense of
being outside the scope of any quantifier, except when absolutely force= d
to be inside. So e.g. in {ro da broda lo brode}, the (plural) referent
of {lo brode} is constant with respect to {da} under xorlo, whereas it
is not in CLL-lojban.



Regarding {zo'e} as the= outmost constant in a prenex of a statement is a special case of {zo'e} as= Skolem functions. As for the example

{ro da broda= lo brode},
that is 
Ax B(x,f(x)),

<= /div>
it says nothing about whether {lo brode} as a Skolem function f(x= ) is constant for all x or not. That is to say, xorlo allows both interpret= ations "EYAx B(x,Y)" and "AxEY B(x,Y)" as a statement before Skolemization,= while CLL-lo restricts the interpretation to "AxEy B(x,y)" (small y is a s= ingular variable). If xorlo did not allow this interpretation, CLL 7.7 must= have been abandoned. As long as both xorlo and CLL 7.7 are kept true, a co= nstant {zo'e} is not always out of bound variables.


 
> If a statement includes no universal quantifier after transformed i= nto=20
> prenex normal form, the statement can be Skolemized into a stateme= nt in=20
> which all Skolem functions are Skolem constants. xorlo can precise= ly=20
> express these constants. CLL-lo cannot.
>=20
> xorlo can make explicit the difference of meaning between S3 and S= 6.1 for=20
> any sumti in a simple way like S6. CLL-lo restricts the outer quan= tifier=20
> according to sumti, and makes it difficult to express the differen= ce of=20
> meaning between S3 and S6.1.
> > > S6- {cy zo'u ro mlatu cu jbena fo cy},
> > > S6.1- Ax ~M(x) v J(x,f(x),g(x),h),

You're right, the semantics you're suggesting aren't really CLL-lo. But
they share the scope-sensitivity of CLL-lo; that's all I really meant.



CLL-lo cannot expr= ess S3 precisely for the same reason above. S3 of xorlo says nothing about = whether the Skolem functions f(x),g(x),h(x) are Skolem constants or not. In= other words, S3 of xorlo does not say the order of bound variables of a st= atement before Skolemization. Regarding it as S4 is the most general case. = Any of the statements with prenex "EY2 Ax EY1 EY3" "EY1 EY2 Ax EY3" etc may= be Skolemized into S3, because a Skolen function {zo'e} does not indicate = whether it is a Skolem constant or not.

On the oth= er hand, according to CLL-lo, speaker must always select the order of Ax, E= Y1, EY2 and EY3 of a statement before Skolemization.

 
> As f= or the example in my commentary that you pointed out:
>=20
> {su'o da zo'u loi re lo'i ro mokca noi sepli py noi mokca ku'o da = cu=20
> relcuktai},
>=20
> 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
>=20
> 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.
>=20
> 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
>=20
> {loi re lo'i ro mokca noi sepli py noi mokca ku'o zo'e cu relcukta= i},
> that is=20
> R(m,p,z),
> where z is a Skolem constant.=20
>=20
> There is no problem for interpreting it as "two sets of points tha= t are=20
> equidistant from a point P is a double circle."

But you seem to have jumped the existential through the {re} quantifier= .
The radii are meant to be allowed to be different for the two circles,
but in the original sentence the radii are quantified with outermost
scope.

I was also confused because the english reads like a definition, wherea= s
the lojban has no hint of that (and I'm not sure that adding a {ca'e}
would do it).

Martin


{re} in this examp= le is an inner quantifier, and it does not affect the order of outer quanti= fier. 

{zo'e} in the statement {loi re lo'i r= o mokca noi sepli py noi mokca ku'o zo'e cu relcuktai} is a plural constant= . Precisely saying, this {zo'e} is {lo re zo'e} in this context. This state= ment does not make clear if each individual of the referent of {zo'e} distr= ibutively satisfies {sepli}, but such an interpretation is allowed. I used = rather a bound singular variable {su'oda} in the original example because I= wanted to make explicit that the radii distributively satisfy {sepli}. Whe= n I created the example, I did not consider Skolem functions, but if I want= ed to make scopes of the arguments explicit, I should have been said
<= div>
{py lu'a loi re lo'i ro mokca su'o da lo'i ro mokca zo'u= loi re lo'i ro mokca noi sepli py noi mokca ku'o da cu relcuktai},

where I added {lu'a} in order to draw each of {lo se gunm= a} in the loi-sumti. This trick allows inner quantification to behave as if= outer quantification in the prenex.

However, I do= n't think such a precision by prenex is not necessary for an example of rep= eating inner quantification.


As a s= ummary, xorlo can express the scopes of arguments without outer quantifier = unambiguously as well as ambiguously, while CLL-lo must always do unambiguo= usly. 

If we take the interpretation like S7,= the scopes of the outmost terbri sumti of a statement become unambiguous a= lso in xorlo, though I think this idea should be at most a plausible interp= retation, not a restriction. In general, there are many cases where the ord= er of arguments out of prenex is restricted by grammar, like that example o= f relcuktai. xorlo allows Lojban users to select the most likely interpreta= tion among some possible ones, while CLL-lo definitely requires prenex even= for such a simple example. The idea of xorlo made the language closer to n= atural expressions, while it reserves also the unambiguity of logic in expr= essions with prenex.

 

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