Re: TECH: Quantifiers (was: cukta)

[Logical Language Group <lojbab@ACCESS.DIGEX.NET>]

mi pu cusku di'e

> > The scope of a quantified variable extends from:
>
> >         the most recent place where a "prenex" grammatical construct
> >         could have occurred, viz. the innermost relative clause,
> >         abstraction, GEK-GIK-connected subsentence, main sentence,
> >         TUhE-TUhU supersentence, or whole text containing the variable;
>
> > or:
>
> >         the most recent appearance of this variable with an explicit
> >         quantifier prepended;

la i,n. cusku di'e

> ... but there is no place in such a description where a prenex could have
> occurred.  If it had been {ro da poi [de zo'u:]  da klama de}, fair enough,
> but it appears from this that {ro klama be de} refers to all goers to one
> specific place, since {de} is quantified *outside* the description, in
 whatever
> bridi it occupies.

Yes, it is.  However, "ro klama" means "ro lo klama", which can be transformed
WLG into "ro DA poi klama", where DA is an otherwise-unique member of the
da-series.  The quantification of this "DA" precedes that of "de", so the
fully explicit prenex-normal-form is:

        ro DA [su'o] DE zo'u co'e DA poi klama de

where the "co'e" represents the whole selbri in which this description is
embedded.  Every quantified expression in Lojban can be transformed into
a form in which the quantifier is attached to a variable.  Therefore,
even though "de" is quantified outside the description, so is the implicit
"ro DA", and the "ro DA" is outside the "de".

> Is this the same as saying that there are no nested scopes?

There are no nested scopes in which the same variable is rebound.  There
are nested scopes in the sense that within a given prenex, the variables which
appear first have longer scope than those which appear later.  This is not
explicit or implicit in my previously-stated rules, but should have been.
Likewise, when variables (actual or created by transformation) don't appear in a
prenex, they are moved to the prenex in the same order in which they appear
(or would appear) in the actual text.

Keep asking these questions!  They help concretize my ideas for a paper on
the predicate logic of Lojban, one of the last unwritten papers in the
reference grammar.

--
John Cowan              sharing account <lojbab@access.digex.net> for now
                e'osai ko sarji la lojban.