  We study the relationship between cartesian bicategories and a specialisation
of Lawvere's hyperdoctrines, namely elementary existential doctrines. Both
provide different ways of abstracting the structural properties of logical
systems: the former in algebraic terms based on a string diagrammatic calculus,
the latter in universal terms using the fundamental notion of adjoint functor.
We prove that these two approaches are related by an adjunction, which can be
strengthened to an equivalence by imposing further constraints on doctrines.
