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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.