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Conservative Expansions of Substructural Logics

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Hiroakira Ono on Substructural Logics

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 23))

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Abstract

In this paper we investigate several conservative expansions of substructural logics, and of fuzzy logics in particular. The most important are the expansion by \(\Delta \) and the expansion by propositional quantifiers, with applications to Craig interpolation. In the last part of the paper we show that in several expansions of MTL it is possible to add conservatively the Łukasiewicz connectives, as well as a new kind of product.

J. Amidei—This work was carried out during a Ph.D position at Scuola Normale Superiore di Pisa, Piazza dei Cavalieri, 7 56126 Pisa Italy.

F. Montagna—Sadly, Franco Montagna passed away in February 2015. He had sent to the editors a revised version of this paper in October 2014. Although he contributed in a definitive way to its writing, unfortunately he could not work on its last version. So, any imprecision should be attributed to the other authors.

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Acknowledgements

The authors thank an anonymous referee for his comments on a previous version of this paper.

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Authors and Affiliations

  1. The Open University, School of Computing and Communications, Milton Keynes, UK

    Jacopo Amidei

  2. CLE-UNICAMP, Rua Sérgio Buarque de Holanda, 251, Barão Geraldo, 13083-859, Campinas, SP, Brasil

    Rodolfo C. Ertola-Biraben

  3. Department of Information Engineering and Mathematics, Via Roma 56, 53100, Siena, Italy

    Franco Montagna

Authors
  1. Jacopo Amidei
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  2. Rodolfo C. Ertola-Biraben
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  3. Franco Montagna
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Corresponding author

Correspondence to Jacopo Amidei .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Denver, Denver, CO, USA

    Nikolaos Galatos

  2. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

    Kazushige Terui

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Amidei, J., Ertola-Biraben, R.C., Montagna, F. (2022). Conservative Expansions of Substructural Logics. In: Galatos, N., Terui, K. (eds) Hiroakira Ono on Substructural Logics. Outstanding Contributions to Logic, vol 23. Springer, Cham. https://doi.org/10.1007/978-3-030-76920-8_10

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