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- W4322754594 abstract "Abstract In this paper, the predicate counterparts, defined both axiomatically and semantically by means of Kripke frames, of the modal propositional logics $textbf {GL}$, $textbf {Grz}$, $textbf {wGrz}$ and their extensions are considered. It is proved that the set of semantical consequences on Kripke frames of every logic between $textbf {QwGrz}$ and $textbf {QGL.3}$ or between $textbf {QwGrz}$ and $textbf {QGrz.3}$ is $Pi ^1_1$-hard even in languages with three (sometimes, two) individual variables, two (sometimes, one) unary predicate letters, and a single proposition letter. As a corollary, it is proved that infinite families of modal predicate axiomatic systems, based on the classical first-order logic and the modal propositional logics $textbf {GL}$, $textbf {Grz}$, $textbf {wGrz}$ are not Kripke complete. Both $Pi ^1_1$-hardness and Kripke incompleteness results of the paper do not depend on whether the logics contain the Barcan formula." @default.
- W4322754594 created "2023-03-03" @default.
- W4322754594 creator A5028473449 @default.
- W4322754594 date "2023-02-28" @default.
- W4322754594 modified "2023-09-26" @default.
- W4322754594 title "Predicate counterparts of modal logics of provability: High undecidability and Kripke incompleteness" @default.
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- W4322754594 doi "https://doi.org/10.1093/jigpal/jzad002" @default.
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