Abstract
The term ‘hyperconnexive logic’ (or ‘hyperconnexivity’ in general) in relation to a certain logical system was coined by Sylvan to indicate that not only do Boethius’ theses hold in such a system, but also their converses. The plausibility of the latter was questioned by some connexive logicians. Without going into the discussion regarding the plausibility of hyperconnexivity and the converses of Boethius’ theses, this paper proposes a quite simple way to escape the hyperconnexivity within the semantic framework of Wansing-style constructive connexive logics. In particular, we present a working method for escaping hyperconnexivity of constructive connexive logic \({{\textbf{C}}}\), discuss the problem that creates an obstacle to using the same method in the case of logic \({{\textbf{C3}}}\) and provide a possible solution to this problem that allows us to construct a logical theory which is similar to \({{\textbf{C3}}}\) and free from hyperconnexivity. All new logics introduced in this paper are equipped with sound and complete Hilbert-style calculi, and their relationships with other well-known connexive logics are discussed.
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Acknowledgements
An earlier version of this paper has been presented at the conference ‘Frontiers of connexive logic’ (the 21st ‘Trends in logic’ international conference), Bochum, December 2021. I would like to thank the audience of this conference for helpful feedback. In particular, I want to thank Heinrich Wansing and Hitoshi Omori for their comments and suggestions. I am extremely grateful to two anonymous referees for reading this paper carefully and providing me with very helpful suggestions. This research has been supported by the Interdisciplinary Scientific and Educational School of Moscow University ‘Brain, Cognitive Systems, Artificial Intelligence’.
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Belikov, A. A Simple Way to Overcome Hyperconnexivity. Stud Logica 112, 69–94 (2024). https://doi.org/10.1007/s11225-023-10056-3
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DOI: https://doi.org/10.1007/s11225-023-10056-3