Continuum many maximal consistent normal bimodal logics with inverses

Abstract

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 extensions of KL are investigated. © 1998 by the University of Notre Dame. All rights reserved.