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• W4313591815 abstract "Abstract We consider the relationship between the algorithmic properties of the validity problem for a modal or superintuitionistic propositional logic and the size of the smallest Kripke countermodels for non-theorems of the logic. We establish the existence, for every degree of unsolvability, of a propositional logic whose validity problem belongs to the degree and whose every non-theorem is refuted on a Kripke frame that validates the logic and has the size linear in the length of the non-theorem. Such logics are obtained among the normal extensions of the propositional modal logics $textbf {KTB}$, $textbf {GL}$ and $textbf {Grz}$ as well as in the lattice of superintuitionistic propositional logics. This shows that the computational complexity of a modal or superintuitionistic propositional logic is, in general, not related to the size of the countermodels for its non-theorems." @default.
• W4313591815 created "2023-01-06" @default.
• W4313591815 creator A5028473449 @default.
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• W4313591815 date "2023-01-03" @default.
• W4313591815 modified "2023-09-27" @default.
• W4313591815 title "Complexity function and complexity of validity of modal and superintuitionistic propositional logics" @default.
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• W4313591815 doi "https://doi.org/10.1093/logcom/exac085" @default.
• W4313591815 hasPublicationYear "2023" @default.
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