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On Implicational Intermediate Logics Axiomatizable by Formulas Minimal in Classical Logic: A Counter-Example to the Komori–Kashima Problem
Studia Logica 109 (6):1413-1422 (2021)
Abstract
The Komori–Kashima problem, that asks whether 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.My notes
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Citations of this work
On Implicational Intermediate Logics Axiomatizable by Formulas Minimal in Classical Logic: A Counter-Example to the Komori–Kashima Problem.Yoshiki Nakamura & Naosuke Matsuda - 2021 - Studia Logica 109 (6):1413-1422.
References found in this work
A propositional calculus with denumerable matrix.Michael Dummett - 1959 - Journal of Symbolic Logic 24 (2):97-106.
Contraction-free sequent calculi for intuitionistic logic.Roy Dyckhoff - 1992 - Journal of Symbolic Logic 57 (3):795-807.
On Implicational Intermediate Logics Axiomatizable by Formulas Minimal in Classical Logic: A Counter-Example to the Komori–Kashima Problem.Yoshiki Nakamura & Naosuke Matsuda - 2021 - Studia Logica 109 (6):1413-1422.
On the Extension of the Intuitionist Propositional Calculus to the Classical Calculus, and the Minimal Calculus to the Intuitionist Calculus.V. A. Jankov - 1973 - Journal of Symbolic Logic 38 (2):331-332.
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