Abstract
The Komori–Kashima problem, that asks whether (or not) the implicational intermediate logics axiomatizable by formulas minimal in classical logic are only intuitionistic logic and classical logic, has stood for over a decade. In this paper, we give a counter-example to this problem. Additionally, we also give some open problems derived from this result.
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Acknowledgements
We would like to thank Yuichi Komori and Ryo Kashima for proposing this problem and presenting valuable comments. We also would like to thank Yoichi Hirai for presenting a counter-example to the problem for full formulas. This work was supported by JSPS KAKENHI Grant Number 21K13828.
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Presented by Hiroakira Ono
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Nakamura, Y., Matsuda, N. On Implicational Intermediate Logics Axiomatizable by Formulas Minimal in Classical Logic: A Counter-Example to the Komori–Kashima Problem. Stud Logica 109, 1413–1422 (2021). https://doi.org/10.1007/s11225-021-09955-0
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DOI: https://doi.org/10.1007/s11225-021-09955-0