# sound,, complete

If $Th$ and $Pr$ are two sets of facts (in particular, a theory of some language and the set of things provable by some method) we say $Pr$ is sound for $Th$ if $Pr\subseteq Th$. Typically we have a theory and set of rules for constructing proofs, and we say the set of rules are sound (which theory is intended is usually clear from context) since everything they prove is true (in $Th$).

If $Th\subseteq Pr$ we say $Pr$ is complete for $Th$. Again, we usually have a theory and a set of rules for constructing proofs, and say that the set of rules is complete since everything true (in $Th$) can be proven.

Title sound,, complete SoundComplete 2013-03-22 13:02:33 2013-03-22 13:02:33 Henry (455) Henry (455) 7 Henry (455) Definition msc 03F03 sound complete