Abstract
In this paper, we introduce a new logic, which we call AM3. It is a connexive logic that has several interesting properties, among them being strongly connexive and validating the Converse Boethius Thesis. These two properties are rather characteristic of the difference between, on the one hand, Angell and McCall’s CC1 and, on the other, Wansing’s C. We will show that in other aspects, as well, AM3 combines what are, arguably, the strengths of both CC1 and C. It also allows us an interesting look at how connexivity and the intuitionistic understanding of negation relate to each other. However, some problems remain, and we end by pointing to a large family of weaker logics that AM3 invites us to further explore.
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Acknowledgements
We would like to thank Francesco Paoli for extremely fruitful discussions in Bochum in December, 2021. We would also like to thank Heinrich Wansing for reading our draft very carefully and providing us with some helpful comments. Also, we received very helpful notes by two anonymous referees. The research by Hitoshi Omori has been supported by a Sofja Kovalevskaja Award of the Alexander von Humboldt-Foundation, funded by the German Ministry for Education and Research. Moreover, the research by Andreas Kapsner has been supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Project 436508789.
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Special Issue: Frontiers of Connexive Logic Edited by: Hitoshi Omori and Heinrich Wansing.
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Omori, H., Kapsner, A. Angell and McCall Meet Wansing. Stud Logica 112, 141–165 (2024). https://doi.org/10.1007/s11225-023-10083-0
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DOI: https://doi.org/10.1007/s11225-023-10083-0