Abstract
Kapsner strong logics, originally studied in the context of connexive logics, are those in which all formulas of the form \(A\rightarrow \lnot A\) or \(\lnot A\rightarrow A\) are unsatisfiable, and in any model at most one of \(A\rightarrow B, A\rightarrow \lnot B\) is satisfied. In this paper, such logics are studied algebraically by means of algebraic structures in which negation is modeled by an operator \(\lnot \) s.t. any element a is incomparable with \(\lnot a\). A range of properties which are (in)compatible with such operators are studied, and examples are given; finally, the question of which further operators can be added to such structures is broached.
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Acknowledgements
Thanks are due to Petr Cintula, Davide Fernandez Duque, Nicholas Ferenz, Andreas Kapsner, Teresa Kouri-Kissel, Shay Allen Logan, Franci Mangraviti, Tommaso Moraschini, Eileen Nutting, Hrafn Oddsson, Grace Paterson, Jamie Wannenburg, and Heinrich Wansing for helpful discussion, as well as other members of audiences at the Ruhr University Bochum, University of Cagliari, and the Czech Academy of Sciences. In addition, recommendations by two anonymous referees were very helpful in improving the paper. I gratefully acknowledge fellowship funding from the Alexander von Humboldt foundation.
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Tedder, A. Kapsner Complementation: An Algebraic Take on Kapsner Strong Logics. Stud Logica 111, 321–352 (2023). https://doi.org/10.1007/s11225-022-10025-2
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DOI: https://doi.org/10.1007/s11225-022-10025-2