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  1. Kentaro Kikuchi (2008). Call-by-Name Reduction and Cut-Elimination in Classical Logic. Annals of Pure and Applied Logic 153 (1):38-65.
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  2. Kentaro Kikuchi & Katsumi Sasaki (2003). A Cut-Free Gentzen Formulation of Basic Propositional Calculus. Journal of Logic, Language and Information 12 (2):213-225.
    We introduce a Gentzen style formulation of Basic Propositional Calculus(BPC), the logic that is interpreted in Kripke models similarly tointuitionistic logic except that the accessibility relation of eachmodel is not necessarily reflexive. The formulation is presented as adual-context style system, in which the left hand side of a sequent isdivided into two parts. Giving an interpretation of the sequents inKripke models, we show the soundness and completeness of the system withrespect to the class of Kripke models. The cut-elimination theorem isproved (...)
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  3. Kentaro Kikuchi (2001). Relationships Between Basic Propositional Calculus and Substructural Logics. Bulletin of the Section of Logic 30 (1):15-20.
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  4. Kentaro Kikuchi & Ryo Kashima (2001). Sequent Calculi for Visser's Propositional Logics. Notre Dame Journal of Formal Logic 42 (1):1-22.
    This paper introduces sequent systems for Visser's two propositional logics: Basic Propositional Logic (BPL) and Formal Propositional Logic (FPL). It is shown through semantical completeness that the cut rule is admissible in each system. The relationships with Hilbert-style axiomatizations and with other sequent formulations are discussed. The cut-elimination theorems are also demonstrated by syntactical methods.
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