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sav08:instantiation_plus_ground_resolution [2008/04/01 16:20] vkuncak |
sav08:instantiation_plus_ground_resolution [2008/04/01 18:19] vkuncak |
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| The proof system has two rules: ground instantiation and ground resolution. | The proof system has two rules: ground instantiation and ground resolution. | ||
| - | **Ground Instantiation Rule** | + | === Ground Instantiation Rule === |
| \[ | \[ | ||
| Line 18: | Line 18: | ||
| Ground substitution is of the form $\{x_1 \mapsto t_1,\ldots,x_n \mapsto t_n\}$ where each $t_i$ is a ground term. | Ground substitution is of the form $\{x_1 \mapsto t_1,\ldots,x_n \mapsto t_n\}$ where each $t_i$ is a ground term. | ||
| - | **Ground Resolution Rule** | + | === Ground Resolution Rule === |
| 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 | ||
| Line 27: | Line 27: | ||
| 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). | ||
| - | |||
| - | **Ground Factoring** | ||
| - | |||
| - | If $A$ is a ground atom and $C$ are ground clauses, | ||
| - | \[ | ||
| - | \frac{C \cup \{\lnot A, A\}} | ||
| - | {C} | ||
| - | \] | ||
| - | (It is a necessary simplification rule in propositional resolution.) | ||
| ==== Example ==== | ==== Example ==== | ||