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Interpretation (cont’)

    Quantified Formula (relative to Valuation function)

      I [∃x:α] true if α is true with V’(x)=d for some d∈D where V’ is otherwise identical to the prior V.
      I [∀x:α] true if α is true with V’(x)=d for all d∈D and where V’ is otherwise identical to the prior V.

    Note: ∀x∃y: α is different from ∃y∀x: α

    In the first case ∀x∃y:α , we go through all value assignments V'(x), and for each value assignment V'(x) of x, we have to find a suitable value V'(y) for y.

    In the second case ∃y∀x:α, we have to find one value V'(y) for y, such that all value assignments V'(x) make α true.


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