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sav08:proof_rule_for_equality [2008/04/02 20:11] vkuncak |
sav08:proof_rule_for_equality [2012/05/08 14:59] vkuncak |
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\[ | \[ | ||
- | \frac{D \cup \{ s = t \}\ \ \ \ C[s'] \}} | + | \frac{D \cup \{ s = t \}\ \ \ \ C[s'] } |
{subst(\sigma)(D \cup C[t])} | {subst(\sigma)(D \cup C[t])} | ||
\] | \] | ||
where $\sigma$ is [[Unification|mgu]] of $\{s,s'\}$. | where $\sigma$ is [[Unification|mgu]] of $\{s,s'\}$. | ||
+ | |||
+ | Here $C[s']$ means that $s'$ occurs somewhere in $C$; then $C[t]$ results from replacing that occurrence of $s'$ with $t$. | ||
=== Equality Resolution === | === Equality Resolution === | ||
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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 === |