Ultimate Cognition à la Gödel

Jürgen Schmidhuber
<span title="2009-03-05">2009</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fyqcejpxl5gdvbw7yq7x2x5abu" style="color: black;">Cognitive Computation</a> </i> &nbsp;
All life is problem solving," said Popper. To deal with arbitrary problems in arbitrary environments, an ultimate cognitive agent should use its limited hardware in the "best" and "most efficient" possible way. Can we formally nail down this informal statement, and derive a mathematically rigorous blueprint of ultimate cognition? Yes, we can, using Kurt Gödel's celebrated self-reference trick of 1931 in a new way. Gödel exhibited the limits of mathematics and computation by creating a formula
more &raquo; ... at speaks about itself, claiming to be unprovable by an algorithmic theorem prover: either the formula is true but unprovable, or math itself is flawed in an algorithmic sense. Here we describe an agent-controlling program that speaks about itself, ready to rewrite itself in arbitrary fashion once it has found a proof that the rewrite is useful according to a user-defined utility function. Any such a rewrite is necessarily globally optimal-no local maxima!-since this proof necessarily must have demonstrated the uselessness of continuing the proof search for even better rewrites. Our self-referential program will optimally speed up its proof searcher and other program parts, but only if the speed up's utility is indeed provable-even ultimate cognition has limits of the Gödelian kind.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s12559-009-9014-y">doi:10.1007/s12559-009-9014-y</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yctnndvu7verhoac6zmyh3jdim">fatcat:yctnndvu7verhoac6zmyh3jdim</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20090713130616/http://www.idsia.ch/~juergen/ultimatecognition.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/79/67/7967805e138d87346211aa7686abfa163b4895cc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s12559-009-9014-y"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>