  The logic of Dependence and Independence Bunched Implications (DIBI) is a
logic to reason about conditional independence (CI); for instance, DIBI
formulas can characterise CI in probability distributions and relational
databases, using the probabilistic and relational DIBI models, respectively.
Despite the similarity of the probabilistic and relational models, a uniform,
more abstract account remains unsolved. The laborious case-by-case verification
of the frame conditions required for constructing new models also calls for
such a treatment. In this paper, we develop an abstract framework for
systematically constructing DIBI models, using category theory as the unifying
mathematical language. In particular, we use string diagrams -- a graphical
presentation of monoidal categories -- to give a uniform definition of the
parallel composition and subkernel relation in DIBI models. Our approach not
only generalises known models, but also yields new models of interest and
reduces properties of DIBI models to structures in the underlying categories.
Furthermore, our categorical framework enables a logical notion of CI, in terms
of the satisfaction of specific DIBI formulas. We compare it with string
diagrammatic approaches to CI and show that it is an extension of string
diagrammatic CI under reasonable conditions.
