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Semi De Morgan Logic Properly Displayed

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Abstract

In the present paper, we endow semi De Morgan logic and a family of its axiomatic extensions with proper multi-type display calculi which are sound, complete, conservative, and enjoy cut elimination and subformula property. Our proposal builds on an algebraic analysis of the variety of semi De Morgan algebras, and applies the guidelines of the multi-type methodology in the design of display calculi.

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Authors and Affiliations

  1. School of Philosophy and Social Development, Shandong University, Jinan, China

    Fei Liang

  2. Department of Languages, Literature and Communication, Utrecht University, Utrecht, The Netherlands

    Giuseppe Greco

  3. Chapman University, Orange, USA

    M. Andrew Moshier

  4. Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg, South Africa

    Alessandra Palmigiano

  5. School of Business and Economics, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands

    Alessandra Palmigiano

Authors
  1. Giuseppe Greco
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  2. Fei Liang
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  3. M. Andrew Moshier
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  4. Alessandra Palmigiano
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Correspondence to Fei Liang.

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Greco, G., Liang, F., Moshier, M.A. et al. Semi De Morgan Logic Properly Displayed. Stud Logica 109, 1–45 (2021). https://doi.org/10.1007/s11225-020-09898-y

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