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Accepted Manuscript

The provability logic of all provability predicates

English (英語)

Journal of Logic and Computation

34(6)

1108-1135

Oxford University Press

2023-09-25

2024-09-25

We prove that the provability logic of all provability predicates is exactly Fitting, Marek, and Truszczyński’s pure logic of necessitation N⁠. Moreover, we introduce three extensions N4⁠, NR and NR4 of N and investigate the arithmetical semantics of these logics. In fact, we prove that N4⁠, NR and NR4 are the provability logics of all provability predicates satisfying the third condition D3 of the derivability conditions, all Rosser provability predicates and all Rosser provability predicates satisfying D3⁠, respectively.

学術雑誌論文

This is a pre-copyedited, author-produced version of an article accepted for publication in Journal of Logic and Computation following peer review. The version of record Taishi Kurahashi, The provability logic of all provability predicates, Journal of Logic and Computation, 2023;, exad060. is available online at: https://doi.org/10.1093/logcom/exad060.