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Paraconsistent Logics and Translations

Itala M. Loffredo D’Ottaviano & Hércules de Araújo Feitosa

Synthese 125 (1-2):77-95 (2000)

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Conservative Translations Revisited.J. Ramos, J. Rasga & C. Sernadas - 2023 - Journal of Philosophical Logic 52 (3):889-913.details We provide sufficient conditions for the existence of a conservative translation from a consequence system to another one. We analyze the problem in many settings, namely when the consequence systems are generated by a deductive calculus or by a logic system including both proof-theoretic and model-theoretic components. We also discuss reflection of several metaproperties with the objective of showing that conservative translations provide an alternative to proving such properties from scratch. We discuss soundness and completeness, disjunction property and metatheorem of (...) Download Export citation Bookmark
The ubiquity of conservative translations.Emil Jeřábek - 2012 - Review of Symbolic Logic 5 (4):666-678.details We study the notion of conservative translation between logics introduced by (Feitosa & D’Ottaviano2001). We show that classical propositional logic (CPC) is universal in the sense that every finitary consequence relation over a countable set of formulas can be conservatively translated into CPC. The translation is computable if the consequence relation is decidable. More generally, we show that one can take instead of CPC a broad class of logics (extensions of a certain fragment of full Lambek calculus FL) including most (...) Download Export citation Bookmark 10 citations
Conservative translations.Hércules Feitosa & Itala Loffredo D'ottaviano - 2001 - Annals of Pure and Applied Logic 108 (1-3):205-227.details In this paper we introduce the concept of conservative translation between logics. We present some necessary and sufficient conditions for a translation to be conservative and study some general properties of logical systems, these properties being characterized by the existence of conservative translations between the systems. We prove that the class constituted by logics and conservative translations between them determines a co-complete subcategory of the bi-complete category constituted by logics and translations. Download Export citation Bookmark 13 citations
Conservative translations.Hércules A. Feitosa & Itala M. Loffredo D'Ottaviano - 2001 - Annals of Pure and Applied Logic 108 (1-3):205-227.details In this paper we introduce the concept of conservative translation between logics. We present some necessary and sufficient conditions for a translation to be conservative and study some general properties of logical systems, these properties being characterized by the existence of conservative translations between the systems. We prove that the class constituted by logics and conservative translations between them determines a co-complete subcategory of the bi-complete category constituted by logics and translations. Download Export citation Bookmark 14 citations

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