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Re: TECH: Quantifiers (was: cukta)



la kau,n. tu'a mi di'e spuda
> > I suppose {lo klama be ro da} must be one who goes to every destination,
> > and {lo klama be da}, assuming {da} is currently unbound, is one who goes
> > to some destination (no matter which).  So the {da} becomes implicitly
> > bound *inside* the description, and {ro klama be da} are the members of
> > the set {x: exists(y): klama(x,y,...)}.

> I think this is all entirely correct,

... so you say ...

> PROVIDED that you keep in mind the
> fundamental difference between "standard" quantifier scope and Lojban
> quantifier scope.

> First of all, there are no free variables in Lojban: all are quantified
> as soon as they appear.  The default quantification is existential.
> (This makes Lojban transcriptions of Prolog annoying.)

> 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;

... 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.

> up to:

>         the appearance of an "appropriate" number of NIhO cmavo, where
>         "appropriate" is usually 1-2 but may depend on context;

> or:

>         a single "da'o" cmavo, which cancels all bindings;

> or:

>         another appearance of the same variable with explicit quantifier
>         prepended.

> It follows from these rules that Lojban is "fully alpha-converted": there
> are no inner-scope rebindings.

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

mi'e .i,n.