[jabowery]

Learning theory is the attempt to formalize natural science up to decision. Natural science's unstated assumption is that a sufficiently sophisticated algorithmic world model can be used to predict future observations from past observations. Since this is the same assumption as Solomonoff's assumption in his proof of inductive inference, you have to start there: with Turing complete coding rather than Rissanen's so-called "universal" coding.

It's ok* to depart from that starting point in creating subtheories but if you don't start there you'll end up with garbage like the last 50 years of confusion over what "The Minimum Description Length Principle" really means.

*It is, however, _not_ "ok" if what you are trying to do is come up with causal models. You can't get away from Turing complete codes if you're trying to model dynamical systems even though dynamical systems can be thought of as finite state machines with very large numbers of states. In order to make optimally compact codes you need Turing complete semantics that execute on a finite state machine that just so happens to have a really large but finite number of flipflops or other directed cyclic graph of universal (eg NOR, NAND, etc.) gates.