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Paraconsistent Logics and Translations |
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| Authors: | D’Ottaviano Itala M. Loffredo Feitosa Hércules de Araújo |
| Affiliation: | 1.The Group for Theoretical and Applied Logic – CLE/IFCH, Epistemology and the History of Science Philosophy Department State University of Campinas – UNICAMP, S?o Paulo, Brazil ;2.Mathematics Department Faculty of Sciences, S?o Paulo State University - UNESP, S?o Paulo, Brazil ; |
| Abstract: | In 1999, da Silva, D'Ottaviano and Sette proposed a general definition for the term translation between logics and presented an initial segment of its theory. Logics are characterized, in the most general sense, as sets with consequence relations and translations between logics as consequence-relation preserving maps. In a previous paper the authors introduced the concept of conservative translation between logics and studied some general properties of the co-complete category constituted by logics and conservative translations between them. In this paper we present some conservative translations involving classical logic, Lukasiewicz three-valued system L 3, the intuitionistic system I 1 and several paraconsistent logics, as for instance Sette's system P 1, the D'Ottaviano and da Costa system J 3 and da Costa's systems C n, 1≤ n≤ω. |
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