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  1. Rosser Provability and Normal Modal Logics.Taishi Kurahashi - 2020 - Studia Logica 108 (3):597-617.
    In this paper, we investigate Rosser provability predicates whose provability logics are normal modal logics. First, we prove that there exists a Rosser provability predicate whose provability logic is exactly the normal modal logic \. Secondly, we introduce a new normal modal logic \ which is a proper extension of \, and prove that there exists a Rosser provability predicate whose provability logic includes \.
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  • Arithmetical Soundness and Completeness for $$\varvec{\Sigma }_{\varvec{2}}$$ Numerations.Taishi Kurahashi - 2018 - Studia Logica 106 (6):1181-1196.
    We prove that for each recursively axiomatized consistent extension T of Peano Arithmetic and \, there exists a \ numeration \\) of T such that the provability logic of the provability predicate \\) naturally constructed from \\) is exactly \ \rightarrow \Box p\). This settles Sacchetti’s problem affirmatively.
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