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Logica Universalis

, Volume 3, Issue 1, pp 95–124 | Cite as

What is a Logic Translation?

  • Till Mossakowski
  • Răzvan Diaconescu
  • Andrzej Tarlecki
Article

Abstract

We study logic translations from an abstract perspective, without any commitment to the structure of sentences and the nature of logical entailment, which also means that we cover both proof- theoretic and model-theoretic entailment. We show how logic translations induce notions of logical expressiveness, consistency strength and sublogic, leading to an explanation of paradoxes that have been described in the literature. Connectives and quantifiers, although not present in the definition of logic and logic translation, can be recovered by their abstract properties and are preserved and reflected by translations under suitable conditions.

Mathematics Subject Classification (2000)

03B20 03B22 03B70 03G30 18C50 68Q65 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Till Mossakowski
    • 1
    • 2
  • Răzvan Diaconescu
    • 3
  • Andrzej Tarlecki
    • 4
    • 5
  1. 1.DFKI GmbHBremenGermany
  2. 2.Universität BremenBremenGermany
  3. 3.Institute of Mathematics “Simion Stoilow”BucharestRomania
  4. 4.Institute of InformaticsThe University of WarsawWarsawPoland
  5. 5.Institute of Computer SciencePolish Academy of SciencesWarsawPoland

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