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Inclusion Relationship between Pseudo-Euclidean Logics

Hashimoto Y., Maruyama A.

Reports on Mathematical Logic

2011

Vol. 46

133-142

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 lozenge k fi rightarrow box m lozenge n fi, where k greater-than or equal to 0. 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.