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- W3149031245 abstract "In this paper, we discuss a proof system $mathsf{NGL}$ with an $omega$-rule, which axiomatize the logic $mathbf{GL}$ of provability. We show the three classes of transitive Kripke frames, the class which strongly validate the $omega$-rule, the class which weakly validate the $omega$-rule, and the class which is defined by the L{o}b formula, are mutually different, while all of them define $mathbf{GL}$. This gives an example of a proof system $P$ and a class $C$ of Kripke frames such that $P$ is sound with respect to $C$ but the soundness cannot be proved by the induction on the height of the derivation in $P$. We also show Kripke completeness $mathsf{GL}$ in an algebraic manner." @default.
- W3149031245 created "2021-04-13" @default.
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- W3149031245 date "2021-03-31" @default.
- W3149031245 modified "2023-10-14" @default.
- W3149031245 title "An $omega$-rule for the logic of provability and its models" @default.
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- W3149031245 doi "https://doi.org/10.48550/arxiv.2103.16857" @default.
- W3149031245 hasPublicationYear "2021" @default.
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