Definition:Gentzen Proof System

Definition
Gentzen proof systems are a class of proof systems for propositional and predicate logic.

Their characteristics include:

Specific instances may deviate from this general scheme at some points.
 * The presence of few axioms and many rules of inference.
 * Use of formal, sequent-like notation involving the turnstile $\vdash$.
 * Proofs whose structure can be viewed as rooted trees.