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sav08:instantiation_plus_ground_resolution [2009/05/14 13:40] vkuncak |
sav08:instantiation_plus_ground_resolution [2015/04/21 17:30] (current) |
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| Line 11: | Line 11: | ||
| === Ground Instantiation Rule === | === Ground Instantiation Rule === | ||
| - | \[ | + | \begin{equation*} |
| \frac{C}{subst(\sigma)(C)} | \frac{C}{subst(\sigma)(C)} | ||
| - | \] | + | \end{equation*} |
| where $C$ is a clause and $\sigma$ is a ground substitution. | where $C$ is a clause and $\sigma$ is a ground substitution. | ||
| Line 21: | Line 21: | ||
| If $A$ is a ground atom and $C,D$ are ground claues, then | If $A$ is a ground atom and $C,D$ are ground claues, then | ||
| - | \[ | + | \begin{equation*} |
| \frac{C \cup \{\lnot A\}\ \ \ D \cup \{A\}} | \frac{C \cup \{\lnot A\}\ \ \ D \cup \{A\}} | ||
| {C \cup D} | {C \cup D} | ||
| - | \] | + | \end{equation*} |
| Note that this is propositional resolution where propositional variables have "long names" (they are ground atoms). | Note that this is propositional resolution where propositional variables have "long names" (they are ground atoms). | ||