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sav08:definition_of_resolution_for_fol [2008/04/02 10:59] vkuncak |
sav08:definition_of_resolution_for_fol [2015/04/21 17:30] (current) |
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| This is the definition of resolution rule for first-order logic clauses. | This is the definition of resolution rule for first-order logic clauses. | ||
| - | \[ | + | \begin{equation*} |
| \frac{C \cup \{\lnot A_1\}\ \ \ D \cup \{A_2\}} | \frac{C \cup \{\lnot A_1\}\ \ \ D \cup \{A_2\}} | ||
| {subst(\sigma)(C' \cup D')} | {subst(\sigma)(C' \cup D')} | ||
| - | \] | + | \end{equation*} |
| where $\sigma_1$, $\sigma_2$ are renamings, $\sigma = mgu(\{subst(\sigma_1)(A_1),subst(\sigma_2)(A_2)\})$, | where $\sigma_1$, $\sigma_2$ are renamings, $\sigma = mgu(\{subst(\sigma_1)(A_1),subst(\sigma_2)(A_2)\})$, | ||
| where $C' = subst(\sigma_1)(C)$ and $D' = subst(\sigma_2)(D)$. | where $C' = subst(\sigma_1)(C)$ and $D' = subst(\sigma_2)(D)$. | ||