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• W1963857568 abstract "The aim of this paper is to investigate the expressibility of classical propositional monomodal logics. To this end, a notion of embedding of one logic into another is introduced, which is a translation preserving theoremhood. Each translation trF is induced by a formula F(p) of one variable p; it respects boolean connectives and translates a formula of a form □A into F(trF(A)). This notion enables to measure the expressibility of a logic by a (finite or infinite) number of logics embeddable into it. This measure is calculated here for a large family of modal logics including K, K4, KB, K5, GL, GL.3, T, S4, B, S5, Grz, Grz.3, and provability logics. It is also shown that some of these logics (e.g., all normal logics containing the symmetry axiom except for the logics Triv, Ver, and the intersection of these two) are not embeddable into some others (e.g., K, K4, K5, GL, GL.3, T, S4, Grz, Grz.3, and most of provability logics)." @default.
• W1963857568 created "2016-06-24" @default.
• W1963857568 creator A5064444221 @default.
• W1963857568 date "2000-11-01" @default.
• W1963857568 modified "2023-09-26" @default.
• W1963857568 title "Embeddings of propositional monomodal logics" @default.
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• W1963857568 doi "https://doi.org/10.1093/jigpal/8.6.861" @default.
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