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  1. A cut-free Gentzen formulation of basic propositional calculus.Kentaro Kikuchi & Katsumi Sasaki - 2003 - 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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  • Avicenna on Syllogisms Composed of Opposite Premises.Behnam Zolghadr - 2021 - In Mathematics, Logic, and their Philosophies. pp. 433-442.
    This article is about Avicenna’s account of syllogisms comprising opposite premises. We examine the applications and the truth conditions of these syllogisms. Finally, we discuss the relation between these syllogisms and the principle of non-contradiction.
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