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THE UBIQUITY OF CONSERVATIVE TRANSLATIONS

Published online by Cambridge University Press:  05 September 2012

EMIL JEŘÁBEK
EMIL JEŘÁBEK*
Affiliation:
Academy of Sciences of the Czech Republic
*
*INSTITUTE OF MATHEMATICS AS CR, ŽITNÁ 25, 115 67 PRAHA 1, CZECH REPUBLIC, E-mail: [email protected], URL: http://math.cas.cz/~jerabek
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Abstract

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 nonclassical logics studied in the literature, hence in a sense, (almost) any two reasonable deductive systems can be conservatively translated into each other. We also provide some counterexamples, in particular the paraconsistent logic LP is not universal.

Type
Research Articles
Information
The Review of Symbolic Logic , Volume 5 , Issue 4 , December 2012 , pp. 666 - 678
Copyright
Copyright © Association for Symbolic Logic 2012

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