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The ubiquity of conservative translations
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SYSNO ASEP 0384231 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The ubiquity of conservative translations Author(s) Jeřábek, Emil (MU-W) RID, SAI, ORCID Source Title Review of Symbolic Logic. - : Cambridge University Press - ISSN 1755-0203
Roč. 5, č. 4 (2012), s. 666-678Number of pages 12 s. Language eng - English Country GB - United Kingdom Keywords conservative translation ; deductive system ; nonclassical logic Subject RIV BA - General Mathematics R&D Projects IAA100190902 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) 1M0545 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) Institutional support MU-W - RVO:67985840 UT WOS 000311684800006 DOI 10.1017/S1755020312000226 Annotation We study the notion of conservative translation between logics introduced by Feitosa and D'Ottaviano. 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2013
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