The ubiquity of conservative translations

0384231 - MÚ 2013 RIV GB eng J - Journal Article
Jeřábek, Emil
The ubiquity of conservative translations.
Review of Symbolic Logic. Roč. 5, č. 4 (2012), s. 666-678. ISSN 1755-0203. E-ISSN 1755-0211
R&D Projects: GA AV ČR IAA100190902; GA MŠMT(CZ) 1M0545
Institutional support: RVO:67985840
Keywords : conservative translation * deductive system * nonclassical logic
Subject RIV: BA - General Mathematics
Impact factor: 0.500, year: 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.
Permanent Link: http://hdl.handle.net/11104/0215361