# First order logic

1. Jun 21, 2012

### D_Miller

I have a problem I can't quite figure out:

I have a first order system $S$, and an interpretation $I$ of $S$. I have to show that a closed well formed formula $B$ is true in $I$ if and only if there exists a valuation in $I$ which satisfies $B$.

I've done one of the two implications, but I still have problems with the part in which I have to show the existence of the valuation. I'm thinking that perhaps the wff being closed along with the property of the valuation which says that the valuation $v$ satisfies $(\forall x_i)\mathcal{B}$ if every valuation $v'$ which is $i$-equivalent to $v$ satisfies $\mathcal{B}$. Is this idea way off? I can't seem to get started on the proof.