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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 === |