is a subdiscipline of mathematical logic that treats proofs as formal mathematical objects to study their internal architecture and properties. Unlike traditional logic, which focuses on the truth of statements (semantics), structural proof theory focuses on the deductive process and the rules used to derive those statements. 1. Key Formalisms
: A direct consequence of cut-elimination, this property ensures that a normal proof of a formula only contains subformulas of Structural Proof Theory
: Designed to mirror "natural" human reasoning by using rules for introducing and eliminating logical constants. is a subdiscipline of mathematical logic that treats