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Date: Tue, 27 May 2014 13:42:50 -0700
From: Martin Bays <mbays@sdf.org>
To: lojban@googlegroups.com
Cc: guskant <gusni.kantu@gmail.com>
Subject: Re: [lojban] Individuals and xorlo
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* Monday, 2014-05-26 at 23:12 -0700 - guskant <gusni.kantu@gmail.com>:

> Le mardi 27 mai 2014 11:53:50 UTC+9, Martin Bays a =E9crit :
> > * Monday, 2014-05-26 at 08:01 -0700 - guskant <gusni...@gmail.com<javas=
cript:>>:=20
> > > Le lundi 26 mai 2014 04:49:09 UTC+9, Martin Bays a =E9crit :=20
> > > > * Monday, 2014-05-19 at 06:04 -0700 - guskant <gusni...@gmail.com<j=
avascript:>>:=20
> > > > > Le mardi 8 avril 2014 10:09:19 UTC+9, guskant a =E9crit :=20
> > > >=20
> > http://www.lojban.org/tiki/gadri%3A+an+unofficial+commentary+from+a+log=
ical+point+of+view&no_bl=3Dy=20
> > > >=20
> > > > Saying that {zo'e} and {lo broda} introduce "constants" isn't reall=
y=20
> > > > enough to explain how they work, because of cases where a descripti=
on=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 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 difference between=
=20
> > su'o and su'oi). But as I understand it, xorlo solves the problem rathe=
r=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
> 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 no=
t=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 what
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 forced
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.

> 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
> 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.
> > > 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.

> As for 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 relcuktai},
> 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 that 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, whereas
the lojban has no hint of that (and I'm not sure that adding a {ca'e}
would do it).

Martin

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