Completeness

ΦψΦψ\Phi \models \psi \Rightarrow \Phi \vdash \psi

A Calculus is called complete when given a formula AA entailing BB can be used to derive BB.

So whenever ABA\models B we also have ACBA\vdash_{\mathcal{C}}B.

In the sense of an Evaluation Criteria for Knowledge Representation:

  • Can I do all the inferences that I want to do
  • Can I do reasoning with incomplete knowledge