If we require that both the geometry of spacetime and matter canonically evolve together, we are left with only few options to provide diffeomorphism-invariant dynamics to the gravitational degrees of free- dom. Concretely, as we will show in this thesis, it is possible to derive the gravitational dynamics from any matter theory, which fulfils three physically essential conditions and is formulated on a tensorial geom- etry. For this, one solves a countable set of linear partial differential equations, the gravitational closure equations, and obtains the gravitational action functional in a constructive fashion. As demonstrated in this thesis, one can obtain general relativity starting from the matter fields of the standard model of par- ticle physics by solving this system of partial differential equations. In applications where the behaviour of weak fields is of interest, this system further simplifies to linear algebraic equations for the expansion coefficients of the action functional. This was used in this thesis to derive the linear equations of motion of a gravitational theory that allows for birefringence of light in vacuo.