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The ubiquity of conservative translations

  1. 1. 0384231 - MU-W 2013 RIV GB eng J - Článek v odborném periodiku
    Jeřábek, Emil
    The ubiquity of conservative translations.
    Review of Symbolic Logic. Roč. 5, č. 4 (2012), s. 666-678 ISSN 1755-0203
    Grant CEP: GA AV ČR IAA100190902; GA MŠk(CZ) 1M0545
    Institucionální podpora: RVO:67985840
    Klíčová slova: conservative translation * deductive system * nonclassical logic
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 0.500, rok: 2012
    http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8757256

    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.
    Trvalý link: http://hdl.handle.net/11104/0215361
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