* 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 écrit :
> > * Monday, 2014-05-26 at 08:01 -0700 - guskant <gusni...@gmail.com<javascript:>>:
> > > Le lundi 26 mai 2014 04:49:09 UTC+9, Martin Bays a écrit :
> > > > * Monday, 2014-05-19 at 06:04 -0700 - guskant <gusni...@gmail.com<javascript:>>:
> > > > > Le mardi 8 avril 2014 10:09:19 UTC+9, guskant a écrit :
> > > >
> > http://www.lojban.org/tiki/gadri%3A+an+unofficial+commentary+from+a+logical+point+of+view&no_bl=y
> > > >
> > > > 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} .
> > > 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 official 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
> > >
> > > S2- {ro mlatu cu jbena zo'e zo'e zo'e}.
> > >
> > > 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)),
> > >
> > > S3 is a Skolemized form of a statement
> > >
> > > S4- {roda su'oidexipa su'oidexire su'oidexici zo'u
> > > ganai da mlatu gi da jbena 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 by existential quantifiers 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 rather
> > differently - by having the {zo'e}s there refer to generics, constant
> > with respect to {da}.
>
> 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 domain of Ax, because they depend on no variable except x. It does not
> contradict xorlo. On the other hand, any sumti of CLL-lo are bound by any
> 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
> prenex normal form, the statement can be Skolemized into a statement in
> which all 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 makes it difficult to express the difference of
> 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:
>
> {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 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
> normal form that contains no universal quantifier. It is therefore
> Skolemized into
>
> {loi re lo'i ro mokca noi sepli py noi mokca ku'o zo'e cu relcuktai},
> that is
> R(m,p,z),
> where z is a Skolem constant.
>
> There is no problem for interpreting it as "two sets of points that are
> 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
Attachment:
signature.asc
Description: Digital signature