In this chapter, we continue the study of two-dimensional frames. Here we look at these frames from a slightly different perspective, namely apart from taking the states in the two-dimensional frames to be just pairs *(u*,*v)*, we will view them as *arrows* leading from *u* to *v*. We will study a similarity type which, interpreted on squares, is very expressive. This similarity type consists of the following three modalities, a dyadic ○ a monadic ⊗ and a constant ι δ. All of these were discussed before; we recall their definitions on squares,
$$\begin{array}{*{20}{l}}
{\mathfrak{M}, (u,\upsilon ) \Vdash \varphi \circ \psi }&{\mathop \Leftrightarrow \limits^{def} }&{(\exists w) : \mathfrak{M}, (u,w) \Vdash \varphi \& \mathfrak{M},(w,\upsilon ) \Vdash \psi } \\
{\mathfrak{M},(u,\upsilon ) \Vdash \otimes \varphi }&{\mathop \Leftrightarrow \limits^{def} }&{\mathfrak{M},(\upsilon ,u) \Vdash \varphi } \\
{\mathfrak{M},(u,\upsilon ) \Vdash \iota \delta }&{\mathop \Leftrightarrow \limits^{def} }&{u = \upsilon .}
\end{array}$$