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

Authors:
Gleifer V. Alves;Anjolina G. de Oliveira;Ruy de Queiroz
Affiliations:
(Correspd.) (Thanks for the support of FACEPE/CAPES (Brazilian Federal Research Agency) by means of the doctoral scholarship) Centro de Informá/tica, Universidade Federal de Pernambuco, Recife ...;Centro de Informá/tica, Universidade Federal de Pernambuco, Recife, Brazil. gva@cin.ufpe.br/ ago@cin.ufpe.br/ ruy@cin.ufpe.br;Centro de Informá/tica, Universidade Federal de Pernambuco, Recife, Brazil. gva@cin.ufpe.br/ ago@cin.ufpe.br/ ruy@cin.ufpe.br
Venue:
Fundamenta Informaticae - Logic, Language, Information and Computation
Year:
2011

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Abstract

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.