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First order logic

  1. Jun 21, 2012 #1
    I have a problem I can't quite figure out:

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

    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 [itex]v[/itex] satisfies [itex](\forall x_i)\mathcal{B}[/itex] if every valuation [itex]v'[/itex] which is [itex]i[/itex]-equivalent to [itex]v[/itex] satisfies [itex]\mathcal{B}[/itex]. Is this idea way off? I can't seem to get started on the proof.
     
  2. jcsd
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