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sav08:definition_of_resolution_for_fol [2008/04/01 18:11] vkuncak created |
sav08:definition_of_resolution_for_fol [2015/04/21 17:30] (current) |
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| ====== Definition of Resolution for First-Order Logic ====== | ====== Definition of Resolution for First-Order Logic ====== | ||
| - | \[ | + | This is the definition of resolution rule for first-order logic clauses. |
| + | \begin{equation*} | ||
| \frac{C \cup \{\lnot A_1\}\ \ \ D \cup \{A_2\}} | \frac{C \cup \{\lnot A_1\}\ \ \ D \cup \{A_2\}} | ||
| {subst(\sigma)(C' \cup D')} | {subst(\sigma)(C' \cup D')} | ||
| - | \] | + | \end{equation*} |
| - | where $C'$ is renaming of $C$, where $D'$ is renaming of $D$, and where $\sigma = mgu(\{C',D'\})$. | + | 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 $D' = subst(\sigma_2)(D)$. | ||
| + | |||
| + | We will call the above rule //mgu-resolution// if we need to differentiate it from [[Non-Ground Instantiation and Resolution|instantiation followed by resolution]]. | ||