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sav08:substitutions_for_first-order_logic [2008/03/19 00:11] vkuncak |
sav08:substitutions_for_first-order_logic [2008/03/19 00:12] vkuncak |
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\] | \] | ||
then for formulas: | then for formulas: | ||
- | \[ | + | \[\begin{array}{rcl} |
nsubst(\sigma)(R(t_1,\ldots,t_n)) &=& R(nsubst(\sigma)(t_1),\ldots,nsubst(\sigma)(t_n)) \\ | nsubst(\sigma)(R(t_1,\ldots,t_n)) &=& R(nsubst(\sigma)(t_1),\ldots,nsubst(\sigma)(t_n)) \\ | ||
nsubst(\sigma)(t_1 = t_2) &=& (nsubst(\sigma)(t_1) = nsubst(\sigma)(t_n)) \\ | nsubst(\sigma)(t_1 = t_2) &=& (nsubst(\sigma)(t_1) = nsubst(\sigma)(t_n)) \\ | ||
nsubst(\sigma)(\lnot F) &=& \\ | nsubst(\sigma)(\lnot F) &=& \\ | ||
nsubst(\sigma)(F_1 \land F_2) &=& \\ | nsubst(\sigma)(F_1 \land F_2) &=& \\ | ||
- | nsubst(\sigma)(\forall x.F) &=& | + | nsubst(\sigma)(\forall x.F) &=& \\ |
nsubst(\sigma)(\forall x.F) &=& | nsubst(\sigma)(\forall x.F) &=& | ||
\] | \] |