> On 6/8/06, cedricstjl <cedricstjl@> wrote:

This is a useful technique. I've also seen it called currifying in

> couldn't it be achieved equivalently by reifying functions and

> predicates?

other papers, however it doesn't let you achieve the full power of

second-order logic, much less higher-order logic.

A basic first-order logic result is that finiteness is not

expressible. That is there is no sentence P such that M is a model of

P iff. M is finite. However, in second order logic one can express

finiteness. Specifically, if P is the statement that all injective

functions are surjective, then M is a model of P iff. M is finite.

The wikipedia article on second-order logic discusses some of the

differences between first-order and second-order logic at more length

than this email.

Joe- Hmmm, I've got a hard time translating your example, or those from the

Wikipedia article into logical sentences (I have no idea how to

express that a model is finite, for instance). I guess I should pick

up a book on the subject; my only background in logic is from AIMA and

Hofstadter's book.

Thanks for the info!

Cedric

--- In aima-talk@yahoogroups.com, Joe Hendrix <jhendrix@...> wrote:

>

> > On 6/8/06, cedricstjl <cedricstjl@> wrote:

> > couldn't it be achieved equivalently by reifying functions and

> > predicates?

>

> This is a useful technique. I've also seen it called currifying in

> other papers, however it doesn't let you achieve the full power of

> second-order logic, much less higher-order logic.

>

> A basic first-order logic result is that finiteness is not

> expressible. That is there is no sentence P such that M is a model of

> P iff. M is finite. However, in second order logic one can express

> finiteness. Specifically, if P is the statement that all injective

> functions are surjective, then M is a model of P iff. M is finite.

>

> The wikipedia article on second-order logic discusses some of the

> differences between first-order and second-order logic at more length

> than this email.

>

> Joe

>