Re: [lojban-beginners] Re: [lojban] Tags and bridi operators

[Ian Johnson <blindbravado@gmail.com>]

On Sat, May 25, 2013 at 10:18 AM, Betsemes <betsemes@gmail.com> wrote:

On Tue, May 21, 2013 at 8:39 PM, selpa'i <seladwa@gmx.de> wrote:
> We know that na(ku), quantifiers, connectives and tenses are bridi
> operators, but what about non-tense tags?

As I follow the conversation on the main lojban list, I think I more
or less understand what's a bridi operator.

But I'm having difficulties on seeing how a quantifier is a bridi
operator. Could someone please explain it to me in mathematical and/or
computer languages terms? Or maybe point me to the appropriate
webpage.

mu'o mi'e betsemes

It depends on how you look at it, really. Essentially you have the syntax of a proposition, i.e. a relation between variables, some of which may be unbound, and then the quantifiers bind the variables. 

Suppose there are no constants, and consider the sentence P(x,y). Since there are no constants, x and y are unbound. So this doesn't say anything, but it has the syntax of a proposition. Then when you add quantifiers you take the same sentence and get an actual proposition with bound variables. For example, forall x: exists y: P(x,y).

A more clear "bridi operator" way of looking at it is actually that the quantifiers act on the bridi from the innermost quantifier out. That is, my previous example has the proposition P(x,y), which is acted on by the existential quantifier to give "exists y: P(x,y)". Then the existentially quantified statement is acted on by the universal quantifier to give "forall x: exists y: P(x,y)".

*Sorry that although I am a math student, I am not a logic student, so this is not at all a formal term. Hopefully it is still understandable. 

mi'e la latro'a mu'o

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