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  1.  18
    Subminimal Logics in Light of Vakarelov’s Logic.Satoru Niki - 2020 - Studia Logica 108 (5):967-987.
    We investigate a subsystem of minimal logic related to D. Vakarelov’s logic \, using the framework of subminimal logics by A. Colacito, D. de Jongh and A. L. Vargas. In the course of it, the relationship between the two semantics in the respective frameworks is clarified. In addition, we introduce a sequent calculus for the investigated subsystem, and some proof-theoretic properties are established. Lastly, we formulate a new infinite class of subsystems of minimal logics.
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  2. Improving Strong Negation.Satoru Niki - forthcoming - Review of Symbolic Logic:1-27.
    Strong negation is a well-known alternative to the standard negation in intuitionistic logic. It is defined virtually by giving falsity conditions to each of the connectives. Among these, the falsity condition for implication appears to unnecessarily deviate from the standard negation. In this paper, we introduce a slight modification to strong negation, and observe its comparative advantages over the original notion. In addition, we consider the paraconsistent variants of our modification, and study their relationship with non-constructive principles and connexivity.
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  3.  8
    Empirical Negation, Co-Negation and Contraposition Rule I: Semantical Investigations.Satoru Niki - 2020 - Bulletin of the Section of Logic 49 (3):231-253.
    We investigate the relationship between M. De's empirical negation in Kripke and Beth Semantics. It turns out empirical negation, as well as co-negation, corresponds to different logics under different semantics. We then establish the relationship between logics related to these negations under unified syntax and semantics based on R. Sylvan's CCω.
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  4.  7
    Empirical Negation, Co-Negation and the Contraposition Rule II: Proof-Theoretical Investigations.Satoru Niki - 2020 - Bulletin of the Section of Logic 49 (4):359-375.
    We continue the investigation of the first paper where we studied logics with various negations including empirical negation and co-negation. We established how such logics can be treated uniformly with R. Sylvan's CCω as the basis. In this paper we use this result to obtain cut-free labelled sequent calculi for the logics.
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    Decidable Variables for Constructive Logics.Satoru Niki - 2020 - Mathematical Logic Quarterly 66 (4):484-493.
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