Completeness

$\Phi \models \psi \Rightarrow \Phi ⊢\psi$

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

So whenever $A\models B$ we also have $A{⊢}_{\mathcal{C}}B$.

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