What is a logic translation?

Logica Universalis 3 (1):95-124 (2009)
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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DOI 10.1007/s11787-009-0005-2
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References found in this work BETA
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2002 - Cambridge University Press.
Mathematical Logic.Joseph R. Shoenfield - 1967 - Reading, Mass., Addison-Wesley Pub. Co..
The Mathematics of Metamathematics.Helena Rasiowa - 1963 - Warszawa, Państwowe Wydawn. Naukowe.
The Collected Papers of Gerhard Gentzen.Gerhard Gentzen - 1969 - Amsterdam: North-Holland Pub. Co..
Introduction to Higher Order Categorical Logic.J. Lambek & P. J. Scott - 1989 - Journal of Symbolic Logic 54 (3):1113-1114.

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Citations of this work BETA
The Ubiquity of Conservative Translations.Emil Jeřábek - 2012 - Review of Symbolic Logic 5 (4):666-678.

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