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Proof-graphs: a Thorough Cycle Treatment, Normalization and Subformula Property

Alve G.V., Oliveira A.G.,de, Queiroz R., de

Fundamenta Informaticae

2011

Vol. 106, nr 2-4

119-147

A normalization procedure is presented for a classical natural deduction (ND) proof system. This proof system, called N-Graphs, has a multiple conclusion proof structure, where cycles are allowed. With this, we have developed a thorough treatment of cycles, including cycles normalization via an algorithm. We also demonstrate the usefulness of the graphical framework of N-Graphs, where derivations are seen as digraphs. We use geometric perspective techniques to establish the normalization mechanism, thus giving a direct normalization proof. Moreover, the subformula and separation properties are determined.