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sav08:non-ground_instantiation_and_resolution [2008/04/01 20:08] vkuncak |
sav08:non-ground_instantiation_and_resolution [2008/04/02 10:49] vkuncak |
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| such that $subst(\sigma_1)(A_1) = subst(\sigma_2)(A_2)$. | such that $subst(\sigma_1)(A_1) = subst(\sigma_2)(A_2)$. | ||
| - | This rule generalizes resolution and ground resolution. | + | This rule generalizes the above non-ground resolution and ground resolution. |
| 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: 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 | ||
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| 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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| + | Note: a //renaming// is substitution whose domain and codomain are variables and which is injective. That, is, it renames variables without clashing variable names. | ||
| Further step: do we need to consider all possible unifiers? | Further step: do we need to consider all possible unifiers? | ||