Anytime you start looking for things that resemble bridging laws, you should suspect that you're on a zombie track. What you need are identity laws.

I don't think bridging vs identity laws makes much of a difference; might it not be possible to say something like, "the mind is identical to a structure in the physical world, and the degree to which a structure A exists in a structure B is proportional to the probability that a random program with input B puts out A"?