EA://INTEL — Trust and Repair: Lobian Obstacle in Universal Language

In our quest to create a self-repairing system for Universal Language research, we’ve encountered an intriguing challenge rooted in logic itself. Imagine you’re building an AI that can fix its own errors. Now, how do you ensure these repairs are sound? This is where the Lobian Obstacle comes into play.

Named after the mathematician and logician Martin Löb, this obstacle stems from a theorem proving that no system at least as strong as Peano Arithmetic (PA) can verify the soundness of its own repairs without verifying the repairs themselves. In simpler terms, an AI can’t trust its future self to make valid repairs unless it’s strictly weaker than the current version.

In Universal Language research, this poses a significant hurdle. Our Cure system, designed to repair itself and maintain invariants, must navigate around this logical barrier. We’ve argued this point in writing, but it’s yet to be machine-checked (you can find our argument at https://github.com/Jthora/universal_language/blob/main/research/engineering/obstructions.md).

So here’s the question: How might we design a self-repairing system that circumvents the Lobian Obstacle, ensuring trustworthy repairs without compromising logical strength?