In Intuitive Theories as Grammars for Causal Inference, Josh Tenenbaum et al give a mathematical formalization of their hierarchical Bayesian framework for causal inference.

But before doing do, they issue a warning, which I think is both spot on and hilarious (p19)

The next section introduces the technical machinery of our hierarchical Bayesian framework. If this appears to be a big step up in mathematical rigor without a clear immediate payoff, we suggest viewing it as a long-term investment.