The cosmological constant and the deconstruction of gravity

Witten has presented an argument for the vanishing of the cosmological constant in 2+1 dimensions. This argument is crucially tied to the specific properties of (2+1)-dimensional gravity. We argue that this reasoning can be deconstructed to 3+1 dimensions under certain conditions. Our observation is also tied to a possibility that there exists a well-defined UV completion of (3+1)-dimensional gravity.