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sav08:non-ground_instantiation_and_resolution [2008/04/01 16:34] vkuncak |
sav08:non-ground_instantiation_and_resolution [2008/04/01 16:43] vkuncak |
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| such that $subst(\sigma_1)(A_1) = subst(\sigma_2)(A_2)$. | such that $subst(\sigma_1)(A_1) = subst(\sigma_2)(A_2)$. | ||
| + | |||
| + | Resolution with instantiation generalizes resolution and ground resolution. | ||
| + | |||
| + | One complete proof system contains: | ||
| + | * instantiation | ||
| + | * resolution with instantiation | ||
| Note: $\sigma$ such that $subst(\sigma)(A_1) = subst(\sigma)(A_2)$ is called a **unifier** for $\{A_1,A_2\}$. | Note: $\sigma$ such that $subst(\sigma)(A_1) = subst(\sigma)(A_2)$ is called a **unifier** for $\{A_1,A_2\}$. | ||
| + | |||
| + | Further step: do we need to consider all unifiers? | ||
| + | |||
| + | Most general unifier. To compute it we can use the standard [[Unification]] algorithm. | ||
| + | |||
| + | ---- | ||
| + | |||
| **Factoring with instantiation** | **Factoring with instantiation** | ||
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| where $subst(\sigma)(A_1)=subst(\sigma)(A_2)$. | where $subst(\sigma)(A_1)=subst(\sigma)(A_2)$. | ||
| - | Further step: do we need to consider all unifiers? | ||
| - | |||
| - | Most general unifier. To compute it we can use the standard [[Unification]] algorithm. | ||