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sav08:substitutions_for_first-order_logic [2008/03/19 10:27] vkuncak |
sav08:substitutions_for_first-order_logic [2008/03/19 10:31] vkuncak |
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| We define naive substitution recursively, first for terms: | We define naive substitution recursively, first for terms: | ||
| + | |||
| \[ | \[ | ||
| \begin{array}{rcl} | \begin{array}{rcl} | ||
| Line 31: | Line 32: | ||
| \end{array} | \end{array} | ||
| \] | \] | ||
| + | |||
| then for formulas: | then for formulas: | ||
| \[\begin{array}{rcl} | \[\begin{array}{rcl} | ||
| Line 39: | Line 41: | ||
| nsubst(\sigma)(\forall x.F) &=& \\ | nsubst(\sigma)(\forall x.F) &=& \\ | ||
| nsubst(\sigma)(\exists x.F) &=& | nsubst(\sigma)(\exists x.F) &=& | ||
| + | \end{array} | ||
| \] | \] | ||