  This article contributes in that it clarifies and indeed completes an
approach (initiated by Dunn and this author several years ago and again pursued
by the present author over the last three years or so) to the relational
semantics of logics that may lack distribution (Dunn's non-distributive
gaggles). The approach uses sorted frames with an incidence relation on sorts
(polarities), equipped with additional sorted relations, but, in the spirit of
Occam's razor principle, it drops the extra assumptions made in the generalized
Kripke frames approach, initiated by Gehrke, that the frames be separated and
reduced (RS-frames). We show in this article that, despite rejecting the
additional frame restrictions, all the main ideas and results of the RS-frames
approach relating to the semantics of non-distributive logics are captured in
this simpler framework. This contributes in unifying the research field, and,
in an important sense, it complements and completes Dunn's gaggle theory
project for the particular case of logics that may drop distribution.
