Re: free variables in FOL

Jim Spriggs wrote:
>
> I'm not sure what a sentential formula is, but one way to understand a
> formula with free variables in it is to imagine that all the free
> variables are bound by a prefix of universal quantifiers. So
>
> F(x, y)
>
> with x and y both free means one of these:
>
> (all x)(all y) F(x, y)
>
> (all y)(all x) F(x, y)
>
> Since they are provably materially equivalent it doesn't matter which,
> but for the sake of definiteness you could require that the variables in
> the prefix are in alphabetical order.

(I think a sentential formula is simply a wff in FOL)

That makes sense, but howcum Mathworld has these rules of inference:

if G=>F(x)
then G=>AxF(x)

if F(x)=>G
then ExF(x)=>G

with Ex in the second?

Thanks.

Ken

.

Relevant Pages

  • Re: free variables in FOL
    ... Ken Quirici wrote: ... > Jim Spriggs wrote: ... >> variables are bound by a prefix of universal quantifiers. ... > (I think a sentential formula is simply a wff in FOL) ...
    (sci.logic)
  • Re: free variables in FOL
    ... > Ken Quirici wrote: ... >> Jim Spriggs wrote: ... >>> variables are bound by a prefix of universal quantifiers. ... >> (I think a sentential formula is simply a wff in FOL) ...
    (sci.logic)