Journal ArticleDOI
Paraconsistent logics and translations
TLDR
Some conservative translations involving classical logic, Lukasiewicz three-valued system L3, the intuitionistic system I1 and several paraconsistent logics are presented.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.read more
Citations
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Journal ArticleDOI
New Dimensions on Translations Between Logics
TL;DR: Three paradigms of translations between logics are concentrated on: (conservative) translations, transfers and contextual translations, compared and assessed against questions about the meaning of a translation and about comparative strength and extensibility of a logic with respect to another.
Journal ArticleDOI
Bochvar's Three-Valued Logic and Literal Paralogics: Their Lattice and Functional Equivalence
TL;DR: In this article, various features of the class of propositional literal paralogics are considered, including paraproperties such as paraconsistence, paracompleteness and paranormality.
Journal ArticleDOI
The ubiquity of conservative translations
TL;DR: It is shown that one can take instead of CPC a broad class of logics including most nonclassical logics studied in the literature, hence in a sense, (almost) any two reasonable deductive systems can be conservatively translated into each other.
Journal ArticleDOI
The ubiquity of conservative translations
TL;DR: The notion of conservative translation between logics introduced by Feitosa and D'Ottaviano as discussed by the authors has been studied in the context of propositional logic, and it has been shown that for a broad class of logics (extensions of a certain fragment of full Lambek calculus FL) including most non-classical logics studied in literature, it is possible to conservatively translate them into each other.
A weakly-intuitionistic logic I1
TL;DR: In 1995, Sette and Carnielli presented a calculus, I1, which is intended to be dual to the paraconsistent calculus P1, but the authors do not explicitly define what they mean by ‘duality’ between the calculi.
References
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TL;DR: The fundamental texts of the great classical period in modern logic, some of them never before available in English translation, are here gathered together for the first time as discussed by the authors, and they are presented with a note that sets it in perspective, explains its importance, and points out difficulties in interpretation.
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TL;DR: A non-woven fabric adapted for use in footwear is impregnated with a polymer prepared by polymerizing acrylic acid or methacrylic acid, mixtures thereof, or mixtures with other vinyl monomers in the presence of polyethylene oxide to improve its water absorption characteristics.
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