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What is a Logic Translation?

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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.

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Authors and Affiliations

  1. DFKI GmbH, Bremen, Germany

    Till Mossakowski

  2. Universität Bremen, Bremen, Germany

    Till Mossakowski

  3. Institute of Mathematics “Simion Stoilow”, Bucharest, Romania

    Răzvan Diaconescu

  4. Institute of Informatics, The University of Warsaw, Warsaw, Poland

    Andrzej Tarlecki

  5. Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland

    Andrzej Tarlecki

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  1. Till Mossakowski
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  2. Răzvan Diaconescu
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  3. Andrzej Tarlecki
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Correspondence to Till Mossakowski.

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In memoriam Joseph Goguen

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Mossakowski, T., Diaconescu, R. & Tarlecki, A. What is a Logic Translation?. Log. Univers. 3, 95–124 (2009). https://doi.org/10.1007/s11787-009-0005-2

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