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The paper considers extensions of a normal bimodal logic KL in which the two necessity operators are mutual one-sided inverses. A continuum of maximal consistent normal extensions of KL is constructed, each of which has infinitely many quasi-normal Post complete extensions. Some syntactic properties of maximal consistent normal bimodal logics and in particular of such extentions of KL are investigated.N.B. Prof Williamson is now based at the Faculty of Philosophy, University of Oxford

Continuum Many Maximal Consistent Normal Bimodal Logics with Inverses