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ON NON FINITE AXIOMATIZABILITY OF n-MODAL LOGICS BETWEEN Kn AND S5n FOR FINITE n >= 3
Journal article

ON NON FINITE AXIOMATIZABILITY OF n-MODAL LOGICS BETWEEN Kn AND S5n FOR FINITE n >= 3

Tarek Sayed Ahmed
JP journal of algebra, number theory and applications, Vol.47(1), pp.99-119
01/07/2020
DOI: https://doi.org/10.17654/NT047010099

Abstract

Mathematics Physical Sciences Science & Technology
Let 2 < n < omega. We show that any n-modal logic between K-n and S5(n) is not axiomatizable by a set of modal formulas containing finitely many propositional formulas. This is proved algebraically by showing that the corresponding variety of modal algebras, namely, that of diagonal free cylindric algebras of dimension n (RDf(n)) has no equational axiomatization using finitely many variables.

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