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sav08:non-ground_instantiation_and_resolution [2008/04/01 16:43] vkuncak |
sav08:non-ground_instantiation_and_resolution [2008/04/01 17:39] vkuncak |
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| * instantiation | * instantiation | ||
| * resolution with instantiation | * resolution with instantiation | ||
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| + | Note: if we apply instantiation that renames variables in each clause, then $\sigma_1$ and $\sigma_2$ can have disjoint domains and we let $\sigma = \sigma_1 \cup \sigma_2$, obtaining | ||
| 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 $\{A_1,A_2\}$. | ||
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| Most general unifier. To compute it we can use the standard [[Unification]] algorithm. | Most general unifier. To compute it we can use the standard [[Unification]] algorithm. | ||
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| - | ---- | ||
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| - | **Factoring with instantiation** | ||
| - | \[ | ||
| - | \frac{C \cup \{A_1, A_2\}} | ||
| - | {subst(\sigma)(C)} | ||
| - | \] | ||
| - | where $subst(\sigma)(A_1)=subst(\sigma)(A_2)$. | ||
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