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Date: Mon, 26 May 2014 19:53:46 -0700
From: Martin Bays <mbays@sdf.org>
To: guskant <gusni.kantu@gmail.com>
Cc: lojban@googlegroups.com
Subject: Re: [lojban] Individuals and xorlo
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* Monday, 2014-05-26 at 08:01 -0700 - guskant <gusni.kantu@gmail.com>:

> Le lundi 26 mai 2014 04:49:09 UTC+9, Martin Bays a =E9crit :
> >
> > * Monday, 2014-05-19 at 06:04 -0700 - guskant <gusni...@gmail.com<javas=
cript:>>:=20
> >
> >
> > > Le mardi 8 avril 2014 10:09:19 UTC+9, guskant a =E9crit :=20
> > http://www.lojban.org/tiki/gadri%3A+an+unofficial+commentary+from+a+log=
ical+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 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 t=
he=20
> commentary.
>=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
> 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 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}.

Martin

> In Skolemizing S4 into S3, {su'oidexipa}, {su'oidexire} and {su'oidexici}=
=20
> of S4 are replaced by {zo'e}s that are respectively equal to f(x), g(x) a=
nd=20
> h(x). If {zo'e} were not Skolem functions, we should have abandoned the=
=20
> interpretation "S1 =3D S2" so that the omitted sumti could have been boun=
d=20
> variables. (It would not be the case if we accepted the idea in "Section=
=20
> 4.3.1. If zo'e could be a bound plural variable" of my commentary, but it=
=20
> is another story.)
>=20
> If we want to make explicit that a Skolem function {zo'e} is a Skolem=20
> plural constant (that is, the referent of {zo'e} does not vary according =
to=20
> {da}), we should say the corresponding plural variable earlier than {roda=
}=20
> in the prenex of the statement before Skolemization.
> For example, in order to mean that {zo'e} at x4 of {jbena} refers to the=
=20
> Earth that is common to all cats, the statement before Skolemization shou=
ld=20
> be
>=20
> S5- {su'oidexici roda su'oidexipa su'oidexire zo'u
> ganai da mlatu gi da jbena dexipa dexire dexici},
> that is
> EY3 Ax EY1 EY2 ~M(x) v J(x,Y1,Y2,Y3).
>=20
> By skolemizing S5, we obtain a statement that is
> S6.1- Ax ~M(x) v J(x,f(x),g(x),h),
> where h is a Skolem plural constant: h does not depend on x because EY3 o=
f=20
> S5 was said earlier than Ax in the prenex.=20
>=20
> Lojban expression of S6.1 might not officially be explained, but I would=
=20
> profit the property that Lojban prenex can include constants:
>=20
> S6- {cy zo'u ro mlatu cu jbena fo cy},
> which is the same as
> {cy roda poi mlatu zo'u da jbena fo cy}
> and
> {cy roda zo'u ganai da mlatu gi da jbena fo cy}.
>=20
> In S6, I used {cy} instead of {zo'e} for the constant, otherwise we could=
=20
> not distinguish which {zo'e} was on the prenex.
>=20
>=20
> Although it might be off-topic, the following thread on the order of tagg=
ed=20
> sumti and its scope suggests me of an idea:
> https://groups.google.com/d/topic/lojban/PhZD1fO64jc/discussion
>=20
> I suggest that not only the scope of tagged sumti but also that of terbri=
=20
> sumti reflects their order. For example, I suggest considering that S6.1=
=20
> and S6 are the same as=20
>=20
> S7- {fo cy fa ro mlatu cu jbena}.

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