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  1. Measuring Intelligence and Growth Rate: Variations on Hibbard's Intelligence Measure.Samuel Alexander & Bill Hibbard - 2021 - Journal of Artificial General Intelligence 12 (1):1-25.
    In 2011, Hibbard suggested an intelligence measure for agents who compete in an adversarial sequence prediction game. We argue that Hibbard’s idea should actually be considered as two separate ideas: first, that the intelligence of such agents can be measured based on the growth rates of the runtimes of the competitors that they defeat; and second, one specific (somewhat arbitrary) method for measuring said growth rates. Whereas Hibbard’s intelligence measure is based on the latter growth-rate-measuring method, we survey other methods (...)
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  • Short-Circuiting the Definition of Mathematical Knowledge for an Artificial General Intelligence.Samuel Alexander - forthcoming - Lecture Notes in Computer Science.
    We propose that, for the purpose of studying theoretical properties of the knowledge of an agent with Artificial General Intelligence (that is, the knowledge of an AGI), a pragmatic way to define such an agent’s knowledge (restricted to the language of Epistemic Arithmetic, or EA) is as follows. We declare an AGI to know an EA-statement φ if and only if that AGI would include φ in the resulting enumeration if that AGI were commanded: “Enumerate all the EA-sentences which you (...)
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  • The Archimedean Trap: Why Traditional Reinforcement Learning Will Probably Not Yield AGI.Samuel Allen Alexander - 2020 - Journal of Artificial General Intelligence 11 (1):70-85.
    After generalizing the Archimedean property of real numbers in such a way as to make it adaptable to non-numeric structures, we demonstrate that the real numbers cannot be used to accurately measure non-Archimedean structures. We argue that, since an agent with Artificial General Intelligence (AGI) should have no problem engaging in tasks that inherently involve non-Archimedean rewards, and since traditional reinforcement learning rewards are real numbers, therefore traditional reinforcement learning probably will not lead to AGI. We indicate two possible ways (...)
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