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# Lab for Automated Reasoning and Analysis LARA

# Differences

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

sav08:proof_rule_for_equality [2009/05/20 12:07] piskac |
sav08:proof_rule_for_equality [2015/04/21 17:30] (current) |
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=== Paramodulation === | === Paramodulation === | ||

- | \[ | + | \begin{equation*} |

\frac{D \cup \{ s = t \}\ \ \ \ C[s'] } | \frac{D \cup \{ s = t \}\ \ \ \ C[s'] } | ||

{subst(\sigma)(D \cup C[t])} | {subst(\sigma)(D \cup C[t])} | ||

- | \] | + | \end{equation*} |

where $\sigma$ is [[Unification|mgu]] of $\{s,s'\}$. | where $\sigma$ is [[Unification|mgu]] of $\{s,s'\}$. | ||

Line 13: | Line 13: | ||

=== Equality Resolution === | === Equality Resolution === | ||

- | \[ | + | \begin{equation*} |

\frac{C \cup \{ s \neq s' \}} | \frac{C \cup \{ s \neq s' \}} | ||

{subst(\sigma)(C)} | {subst(\sigma)(C)} | ||

- | \] | + | \end{equation*} |

where $\sigma$ is [[Unification|mgu]] of $\{s,s'\}$. | where $\sigma$ is [[Unification|mgu]] of $\{s,s'\}$. | ||

+ | **Superposition:** a closely related technique to paramodulation, also meant for dealing with equality. | ||

=== Completeness of Rules === | === Completeness of Rules === |