Talk:Herbrandization

Skolemization paragraph
The formula given is not actually in Skolem normal form since it contains an existence quantifier. It should be:
 * $$ F^S = \forall y \forall z [R(y,f_x(y)) \wedge \neg S(f_x(y),z)]. $$

Step by step:
 * $$F := \forall y \exists x [R(y,x) \wedge \neg\exists z S(x,z)]$$ (original formula)
 * $$F := \forall y \exists x [R(y,x) \wedge \forall z \neg S(x,z)]$$ (replace negated existence with all quantor with negated statement)
 * $$F := \forall y \exists x \forall z [R(y,x) \wedge \neg S(x,z)]$$ (move all quantifier to begin to formula to get prenex normal form)
 * $$F := \forall y \forall z [R(y,f_x(y)) \wedge \neg S(f_x(y),z)]$$ (replace variable bound by existence quantifier with function depending on preceding all quantors)

79.212.0.144 (talk) 18:22, 12 April 2016 (UTC)