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See detailNormality, non-contamination and logical depth in classical natural deduction
D’Agostino, Marcello; Gabbay, Dov M. UL; Modgil, Sanjay

in Studia Logica (2020), 108(2), 291--357

In this paper we provide a detailed proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard ... [more ▼]

In this paper we provide a detailed proof-theoretical analysis of a natural deduction system for classical propositional logic that (i) represents classical proofs in a more natural way than standard Gentzen-style natural deduction, (ii) admits of a simple normalization procedure such that normal proofs enjoy the Weak Subformula Property, (iii) provides the means to prove a Non-Contamination Property of normal proofs that is not satisfied by normal proofs in the Gentzen tradition and is useful for applications, especially to formal argumentation, (iv) naturally leads to defining a notion of depth of a proof, to the effect that, for every fixed natural k, normal k-depth deducibility is a tractable problem and converges to classical deducibility as k tends to infinity. [less ▲]

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