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
Canonical name	SoundComplete
Date of creation	2013-03-22 13:02:33
Last modified on	2013-03-22 13:02:33
Owner	Henry (455)
Last modified by	Henry (455)
Numerical id	7
Author	Henry (455)
Entry type	Definition
Classification	msc 03F03
Defines	sound
Defines	complete