Abstract
Following the so-called inversion principle of Gentzen-Prawitz, we demonstrate that multiple-conclusion system of classical logic can be naturally regarded as a communication calculus. For the motivation, we first introduce a hierarchical structure for representing an abstract structure of classical proofs. The hierarchical structure describes that classical proofs consist of intuitionistic proofs as the components and the structural connections between those elements. We next provide proof term assignment rules based on the the hierarchical structure. The resulting term calculus is a natural extension of λ-calculus and can be considered as a communication calculus. It is found that the hierarchical structure can be regarded as a network structure for the communication, based on which a term can be passed on to distributed terms.
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