1.  97
    The Modal Logic of Gödel Sentences.Hirohiko Kushida - 2010 - Journal of Philosophical Logic 39 (5):577 - 590.
    The modal logic of Gödel sentences, termed as GS, is introduced to analyze the logical properties of 'true but unprovable' sentences in formal arithmetic. The logic GS is, in a sense, dual to Grzegorczyk's Logic, where modality can be interpreted as 'true and provable'. As we show, GS and Grzegorczyk's Logic are, in fact, mutually embeddable. We prove Kripke completeness and arithmetical completeness for GS. GS is also an extended system of the logic of 'Essence and Accident' proposed by Marcos (...)
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  2.  23
    A Proof Theory for the Logic of Provability in True Arithmetic.Hirohiko Kushida - 2020 - Studia Logica 108 (4):857-875.
    In a classical 1976 paper, Solovay proved the arithmetical completeness of the modal logic GL; provability of a formula in GL coincides with provability of its arithmetical interpretations of it in Peano Arithmetic. In that paper, he also provided an axiomatic system GLS and proved arithmetical completeness for GLS; provability of a formula in GLS coincides with truth of its arithmetical interpretations in the standard model of arithmetic. Proof theory for GL has been studied intensively up to the present day. (...)
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  3.  28
    Applicability of Motohashi's method to modal logics.Hirohiko Kushida - 2005 - Bulletin of the Section of Logic 34 (3):121-134.