 To render the notions of proof and validity more systematized, Prawitz has introduced the notion of a canonical proof. A sentence might be proved in several different ways, but it is the direct, or canonical proof that is constitutive of its meaning. A canonical proof is a proof whose last step is an application of an introduction rule, and its immediate subproofs are canonical (unless they have free variables or undischarged assumptions—for details see Prawitz 2005). A canonical proof is conceived as giving direct evidence for the sentence proved, as it establishes the truth of the sentence by the rule constitutive of the meaning of its connectives. For more on canonical proofs and the ways other proofs can be reduced to them, see the entry on  proof-theoretic semantics.