This volume examines the notion of an analytic proof as a natural deduction, suggesting that the proof's value may be understood as its normal form--a concept with significant implications to proof-theoretic semantics.

N. Tennant; XI*—Entailment and Proofs, Proceedings of the Aristotelian Society, Volume 79, Issue 1, 1 June 1979, Pages 167–190, https://doi.org/10.1093/aristote.