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Conservative Translations Revisited

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Abstract

We provide sufficient conditions for the existence of a conservative translation from a consequence system to another one. We analyze the problem in many settings, namely when the consequence systems are generated by a deductive calculus or by a logic system including both proof-theoretic and model-theoretic components. We also discuss reflection of several metaproperties with the objective of showing that conservative translations provide an alternative to proving such properties from scratch. We discuss soundness and completeness, disjunction property and metatheorem of deduction among others. We provide several illustrations of conservative translations.

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Acknowledgements

The authors would like to acknowledge the support of Instituto de Telecomunicações Research Unit ref. UIDB/50008/2020 funded by Fundação para a Ciência e a Tecnologia (FCT) and the Department of Mathematics of Instituto Superior Técnico, Universidade de Lisboa. The authors acknowledge the suggestions and comments of the two anonymous reviewers that helped to shape the final version of the paper.

Funding

The authors would like to acknowledge the support of Instituto de Telecomunicações, Research Unit ref. UIDB/50008/2020 funded by Fundação para a Ciência e a Tecnologia (FCT) and the Department of Mathematics of Instituto Superior Técnico, Universidade de Lisboa.

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Correspondence to C. Sernadas.

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Ramos, J., Rasga, J. & Sernadas, C. Conservative Translations Revisited. J Philos Logic 52, 889–913 (2023). https://doi.org/10.1007/s10992-022-09691-3

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