 Several normal modal logical systems weaker than S5 have been suggested in the literature. Here, we specify the logics by the set of their modal axioms. For example, the logic K is given by \(\{\text{K}\}\), while S5 is given by \(\{\text{K},\text{T},\text{B},\text{4}\}\). To establish nomenclature, the following table contains a selection of principles from the literature with the frame properties they characterize, cf. Aucher (2014) and Blackburn, de Rijke, &amp; Venema (2001), on the line below them. The frame conditions are not all straightforward.