Differences
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| Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
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sav08:non-ground_instantiation_and_resolution [2008/04/01 16:21] vkuncak |
sav08:non-ground_instantiation_and_resolution [2008/04/01 16:34] vkuncak |
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| Line 42: | Line 42: | ||
| \[ | \[ | ||
| \frac{C \cup \{\lnot A_1\}\ \ \ D \cup \{A_2\}} | \frac{C \cup \{\lnot A_1\}\ \ \ D \cup \{A_2\}} | ||
| - | {subst(\sigma,C \cup D)} | + | {subst(\sigma_1)(C) \cup subst(\sigma_2)(D)} |
| \] | \] | ||
| - | such that $subst(\sigma)(A_1) = subst(\sigma)(A_2)$. | + | such that $subst(\sigma_1)(A_1) = subst(\sigma_2)(A_2)$. |
| 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 $\{A_1,A_2\}$. | ||
| Line 51: | Line 51: | ||
| \[ | \[ | ||
| \frac{C \cup \{A_1, A_2\}} | \frac{C \cup \{A_1, A_2\}} | ||
| - | {subst(\sigma,C \cup D)} | + | {subst(\sigma)(C)} |
| \] | \] | ||
| where $subst(\sigma)(A_1)=subst(\sigma)(A_2)$. | where $subst(\sigma)(A_1)=subst(\sigma)(A_2)$. | ||