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Trends in Logic pp 193–228Cite as

Substructural Logics and Residuated Lattices — an Introduction

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Part of the book series: Trends in Logic ((TREN,volume 21))

Abstract

This is an introductory survey of substructural logics and of residuated lattices which are algebraic structures for substructural logics. Our survey starts from sequent systems for basic substructural logics and develops the proof theory of them. Then, residuated lattices are introduced as algebraic structures for substructural logics, and some recent developments of their algebraic study are presented. Based on these facts, we conclude at the end that substructural logics are logics of residuated structures, and in this way explain why sequent systems are suitable for formalizing substructural logics.

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Author information

Authors and Affiliations

  1. Japan Advanced Institute of Science and Technology, School of Information Science, 1-1 Asahidai, Tatsunokuchi Ishikawa, 923-1292, Japan

    Hiroakira Ono

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  1. Hiroakira Ono
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Editor information

Editors and Affiliations

  1. Department of Philosophy and Science Studies, Roskilde University, Denmark

    Vincent F. Hendricks

  2. Institute of Philosophy and Sociology, The Polish Academy of Sciences, Poland

    Jacek Malinowski

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© 2003 Springer Science+Business Media Dordrecht

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Ono, H. (2003). Substructural Logics and Residuated Lattices — an Introduction. In: Hendricks, V.F., Malinowski, J. (eds) Trends in Logic. Trends in Logic, vol 21. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3598-8_8

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  • DOI: https://doi.org/10.1007/978-94-017-3598-8_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6414-1

  • Online ISBN: 978-94-017-3598-8

  • eBook Packages: Springer Book Archive

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