On the axiomatization of finiteK-frames |
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Authors: | Fabio Bellissima Massimo Mirolli |
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Institution: | 1. Università di Siena, Via del Capitano 15, 53100, Siena, Italy
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Abstract: | We find a short way to construct a formula which axiomatizes a given finite frame of the modal logicK, in the sense that for each finite frameA, we construct a formula ωA which holds in those and only those frames in which every formula true inA holds. To obtain this result we find, for each finite model \(\mathfrak{A}\) and each natural numbern, a formula ω \(\mathfrak{A}\) which holds in those and only those models in which every formula true in \(\mathfrak{A}\) , and involving the firstn propositional letters, holds. |
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