How is FAI a math problem?

In the same sense AIXI is a mathematical formulation of a solution to the AGI problem, we don't have a good idea of what FAI is supposed to be. As a working problem statement, I'm thinking of how to define "preference" for a given program (formal term), with this program representing an agent that imperfectly implements that preference, for example a human upload could be such a program. This "preference" needs to define criteria for decision-making on the unknown-physics real world from within a (temporary) computer environment with known semantics, in the same sense that a human could learn about what could/should be done in the real world while remaining inside a computer simulation, but having an I/O channel to interact with the outside, without prior knowledge of the physical laws.

I'm gradually writing up the idea of this direction of research on my blog. It's vague, but there is some hope that it can put people into a more constructive state of mind about how to approach FAI.