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 PrTh. 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 ThPr we say Pr is completePlanetmathPlanetmath 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