Logical Induction
The article is basic mathematical research and is not intended to be implemented, but rather to guide further applied research.<p>The deeper motivation for this article is to allow future Artificial General Intelligences to prove facts about themselves; specifically, the fact that the AGI, or a next-gen that it developers, has the same (safe) utility function that the designers originally specified.<p>A formal system cannot achieve this by simulating itself.<p>A formal system cannot in general prove that it is reliable, i.e. that if it proves statement P then P is true.  <a href="http:&#x2F;&#x2F;intelligence.org&#x2F;files&#x2F;lob-notes-IAFF.pdf" rel="nofollow">http:&#x2F;&#x2F;intelligence.org&#x2F;files&#x2F;lob-notes-IAFF.pdf</a><p>But with this article, the hope is that a formal system can show that the statement about itself is <i>probably</i> true.