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This article shows how derivations in the deep inference system  SKS  for classical propositional logic can be translated into proof nets. Since an  SKS  derivation contains more information about a proof than the corresponding proof net, we observe a loss of information which can be understood as ‘eliminating bureaucracy’. Technically, this is achieved by cut reduction on proof nets. As an intermediate step between the two extremes,  SKS  derivations and proof nets, we will see proof graphs representing derivations in ‘Formalism A’.

From Deep Inference to Proof Nets via Cut Elimination