Abstract
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 \(\mathsf{KD}\). Secondly, we introduce a new normal modal logic \(\mathsf{KDR}\) which is a proper extension of \(\mathsf{KD}\), and prove that there exists a Rosser provability predicate whose provability logic includes \(\mathsf{KDR}\).
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Acknowledgements
This work was partly supported by JSPS KAKENHI Grant Number 16K17653. The author would like to thank the referees for their valuable comments and suggestions.
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Kurahashi, T. Rosser Provability and Normal Modal Logics. Stud Logica 108, 597–617 (2020). https://doi.org/10.1007/s11225-019-09865-2
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DOI: https://doi.org/10.1007/s11225-019-09865-2