TECH: Quantifiers (was: cukta)

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

la xorxes. cusku di'e

> > This brings up a (totally unrelated) question that I made myself some time
> > ago, and I had forgotten about it.
>
> > {ro lo klama} means the same as {ro lo klama be ?ma}
>
> > Is {zo'e} the right answer?

la i,n. cusku di'e

> I think it has to be -

I agree.

> but this raises in my mind the question of the meaning
> of constructions such as {lo klama be ro da} and {lo klama be da},
> or conversely how you talk about "all goers, irrespective of destination".
> How does the quantification work inside a description?
>
> 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, 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;

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.

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