  The logical depth of a graph $G$ is the minimum quantifier depth of a first
order sentence defining $G$ up to isomorphism in the language of the adjacency
and the equality relations. We consider the case that $G$ is a dissection of a
convex polygon or, equivalently, a biconnected outerplanar graph. We bound the
logical depth of a such $G$ from above by a function of combinatorial
parameters of the dual tree of $G$.
