By the first two bullet points, do you mean you want to form formalized models of naturalized induction?

I've written an essay on the effects of interactive computation as an improvement for Solomonoff-like induction. (It was written in two all-nighters for an English class, so it probably still needs proofreading. It isn't well-sourced, either.) Do you mean things like that? I want to form a better formalization of naturalized induction than Solomonoff induction, one designed to be usable by space-, time-, and rate-limited agents, and interactive computation was a necessary first step. AIXI is by no means an ideal inductive agent.

I very much want to be hired for work like this.