Completeness

Φ⊨ψ⇒Φ⊢ψ\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 A⊨BA\models B we also have A⊢CBA\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