A SEMANTICAL ANALYSIS OF CUT-FREE CALCULI FOR MODAL LOGICS.

We analyze semantically the logical inference rules in cut-free sequent calculi for the modal logics which are obtained from the least normal logic K by adding axioms from T, 4, 5, D and B. This implies Kripke completeness, as well as the cut- elimination property or the subformula property of the calculi. By slightly modifying the arguments, the finite model property of the logics also follows. [ABSTRACT FROM AUTHOR]