Rosser provability and normal modal logics

Taishi Kurahashi

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arXiv · 1812.09735

Rosser provability and normal modal logics

Taishi Kurahashi

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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 ${\sf KD}$. Secondly, we introduce a new normal modal logic ${\sf KDR}$ which is a proper extension of ${\sf KD}$, and prove that there exists a Rosser provability predicate whose provability logic includes ${\sf KDR}$.

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Taishi Kurahashi. 2018-12-23. Rosser provability and normal modal logics. https://arxiv.org/abs/1812.09735

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