2001
DOI: 10.1016/s0168-0072(00)00046-4
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Conservative translations

Abstract: In this paper we introduce the concept of conservative translation between logics. We present some necessary and su cient conditions for a translation to be conservative and study some general properties of logical systems, these properties being characterized by the existence of conservative translations between the systems. We prove that the class constituted by logics and conservative translations between them determines a co-complete subcategory of the bi-complete category constituted by logics and transla… Show more

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Cited by 28 publications
(29 citation statements)
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“…By its turn, Gödel's ones are translations only in Prawitz' sense (cf. Feitosa and D'Ottaviano [17]). …”
Section: Interpretations Transformations Translationsmentioning
confidence: 99%
See 3 more Smart Citations
“…By its turn, Gödel's ones are translations only in Prawitz' sense (cf. Feitosa and D'Ottaviano [17]). …”
Section: Interpretations Transformations Translationsmentioning
confidence: 99%
“…An important subclass of translations, the conservative translations, is investigated by D'Ottaviano and Feitosa in [16], [17] and [10]. Definition 2.5.…”
Section: Running Definitions Of (Conservative) Translationmentioning
confidence: 99%
See 2 more Smart Citations
“…Some of them are only conservative mappings, others are conservative translations. 1 A conservative mapping of a logic L 1 into a logic L 2 is a function that preserves valid formulas in both ways: 1 We take over Feitosa and D'Ottaviano's [8] terminology. They also provide a review of a variety of notions of translations of one logic into another logic and a discussion of the historical translations of the 1930s [8, pp.…”
Section: Introductionmentioning
confidence: 99%