- English only

# Lab for Automated Reasoning and Analysis LARA

# Differences

This shows you the differences between two versions of the page.

Both sides previous revision Previous revision Next revision | Previous revision | ||

sav08:definition_of_resolution_for_fol [2008/04/01 18:19] vkuncak |
sav08:definition_of_resolution_for_fol [2015/04/21 17:30] (current) |
||
---|---|---|---|

Line 2: | Line 2: | ||

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 $C'$ 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]]. | We will call the above rule //mgu-resolution// if we need to differentiate it from [[Non-Ground Instantiation and Resolution|instantiation followed by resolution]]. | ||