I am trying to show that the logic $K4.3$ is canonical, i.e., its canonical frame is transitive and weakly connected.
For reference, the logic $K4.3$ is the smallest normal logic containing $K$ and the formulae ${\Box A\implies \Box\Box A}$, ${\Box ((A\wedge\Box A)\implies B)\vee\Box ((B\wedge\Box B)\implies A)}$.
Weak connectedness of a relation $R$ is characterized by the first order formula $\forall x\forall y\forall z ((xRy \wedge xRz)\implies (yRz\vee zRy\vee y=z))$.
Is there an efficient approach here? Thanks in advance!