* Tuesday, 2014-05-27 at 19:21 -0700 - guskant <gusni.kantu@gmail.com>:
> Le mercredi 28 mai 2014 05:42:53 UTC+9, Martin Bays a écrit :
> > * Monday, 2014-05-26 at 23:12 -0700 - guskant <gusni...@gmail.com<javascript:>>:
> > > 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
> > > > > S1- {ro mlatu cu jbena}.
> > > > > 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},
> > > > > Ax ~M(x) v J(x,f(x),g(x),h(x)),
> > > > > S4- {roda su'oidexipa su'oidexire su'oidexici zo'u
> > > > > ganai da mlatu gi da jbena dexipa dexire dexici},
> > > > > Ax EY1 EY2 EY3 ~M(x) v J(x,Y1,Y2,Y3),
> > > > >
> > > > > If we want to make explicit that a Skolem function {zo'e} is
> > > > > a Skolem plural 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 the prenex of the
> > > > > statement before Skolemization.
> > > The interpretation of {zo'e} as Skolem function rather reinforces xorlo,
> > > and makes clear that the CLL-interpretation of gadri is problematic.
> > 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.
>
> 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)),
>
> 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
> interpretations "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 singular variable).
Assuming I understand you correctly as wanting {lo broda se broda ro da}
to have only the "EYAx" interpretation, this is in direct conflict with
the gadri BPFK section, which says
"Any term without an explicit outer quantifier is a constant, i.e. not
a quantified term. This means that it refers to one or more individuals,
and changing the order in which the constant term appears with respect
to a negation or with respect to a quantified term will not change the
meaning of the sentence.".
> 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 constant {zo'e} is not always out of bound
> variables.
>
> > > 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.
>
> CLL-lo cannot express 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 statement 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 other hand, according to CLL-lo, speaker must always select the
> order of Ax, EY1, EY2 and EY3 of a statement before Skolemization.
The statement "there exists a function f(x) such that for all x,
P(x,f(x))" is logically equivalent to "for all x, there exists y such
that P(x,y)". Now it might be that f is a constant function, which
corresponds to there being a uniform witness for the "exists y". The two
presentations are equivalent. So if Skolemisation were the only
difference between xor-lo and CLL-lo, there'd be no difference.
> > > {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).
>
> {re} in this example is an inner quantifier, and it does not affect the
> order of outer quantifier.
True.
> {zo'e} in the statement {loi re lo'i ro 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 statement does not make clear if each
> individual of the referent of {zo'e} distributively 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}.
I still don't see how to make sense of the original sentence. But never
mind.
Martin
> When I created the example, I did not consider Skolem functions, but
> if I wanted to make scopes of the arguments 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
> 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
> loi-sumti. This trick allows inner quantification to behave as if outer
> quantification in the prenex.
>
> However, I don't think such a precision by prenex is not necessary for an
> example of repeating inner quantification.
>
> As a summary, xorlo can express the scopes of arguments without outer
> quantifier unambiguously as well as ambiguously, while CLL-lo must always
> do unambiguously.
>
> If we take the interpretation like S7, the scopes of the outmost terbri
> sumti of a statement become unambiguous also in xorlo, though I think this
> idea should be at most a plausible interpretation, not a restriction. In
> general, there are many cases where the order of arguments out of prenex is
> restricted by grammar, like that example of relcuktai. xorlo allows Lojban
> users to select the most likely interpretation 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 natural expressions, while it
> reserves also the unambiguity of logic in expressions with prenex.
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