Rosser provability and normal modal logics

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 $\mathsf{KDR}$.

19 pages

Cited by in corpus (1)

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