Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I

By K. Gödel. 1931

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Citations in the corpus

Deep learning in neural networks: An overview (2014, background): “A general approach (Schmidhuber, 1997) for both SL and RL seeks to compactly encode weights of large NNs (Schmidhuber, 1997) through programs written in a universal programming language (Church, 1936; Gödel, 1931; Post, 1936; Turing, 1936).”
PowerPlay: Training an Increasingly General Problem Solver by Continually Searching for the Simplest Still Unsolvable Problem (2011, background): “All such problem solvers can be uniquely encoded (Gödel, 1931) or implemented on universal computers (Church, 1936; Post, 1936; Turing, 1936) such as universal Turing Machines (TM).”
First Experiments with PowerPlay (2012, background): “All problem solvers can be uniquely encoded [7] or implemented on universal computers such as universal Turing Machines (TM) [31].”
Optimal Ordered Problem Solver (2002, background): “The primitives of Section A collectively embody a universal programming language, computationally as powerful as the one of G¨odel (1931) or Forth or Ada or C.”
One Big Net For Everything (2018, background): “To become a general problem solver that is able to run arbitrary problem-solving programs, the controller of a robot or an artiﬁcial agent must be a general-purpose computer [15, 7, 92, 44].”
Computational psychiatry (2011, background): “This notion implies key constraints on mental phenomena – in particular constraints on computational complexity that limit the power of any device, neural or mechanical, to solve a wide range of problems [14].”
Reinforcement Learning Upside Down: Don't Predict Rewards - Just Map Them to Actions (2019, background): “To become a general problem solver that is able to run arbitrary problem-solving programs, the controller C of an artificial agent must be a general-purpose computer [14, 7, 68, 35].”
Locus Solum: From the rules of logic to the logic of rules (2001, background): “…for formal Arithmetic – the key theory for finitistic foundationalism – these remarks may now be understood in the light of Gödel’s Representation Lemma (Gödel 1931): by this very technical result, one may encode the metatheory of arithmetic into arithmetic itself, and thus the ‘rules of the…”