Formal System

We call $\langle\mathcal{L}, \mathcal{K}, \models, \vdash\rangle$ a formal system if $\mathcal{S}=\langle\mathcal{L}, \mathcal{K}, \models\rangle$ is a Logical System and the relation $\vdash$ is a Derivation Relation for $\mathcal{S}$.

We can use Calculus-Derivation to create proofs in such a system.

Logical System + Derivation Relation = Formal System