INCLUSIONS BETWEEN PSEUDO-EUCLIDEAN MODAL LOGICS

We describe properties of simply axiomatized modal logics, which are called pseudo-Euclidean modal logics. For fixed non-negative integers m and n, let Em,n k be the logic which is obtained from the smallest normal propositional modal logic K by adding the pseudo-Euclidean axiom. We will then give a complete description of the inclusion relationship among these logics by showing inclusion relationships for pairs of their logics with fixed m and n.