1. bookVolume 12 (2021): Issue 1 (January 2021)
Journal Details
License
Format
Journal
eISSN
1946-0163
First Published
23 Nov 2011
Publication timeframe
2 times per year
Languages
English
access type Open Access

Measuring Intelligence and Growth Rate: Variations on Hibbard’s Intelligence Measure

Published Online: 19 Jan 2021
Page range: 1 - 25
Received: 16 Oct 2020
Accepted: 08 Jan 2021
Journal Details
License
Format
Journal
eISSN
1946-0163
First Published
23 Nov 2011
Publication timeframe
2 times per year
Languages
English
Abstract

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 for measuring function growth rates, and exhibit the resulting Hibbard-like intelligence measures and taxonomies. Of particular interest, we obtain intelligence taxonomies based on Big-O and Big-Theta notation systems, which taxonomies are novel in that they challenge conventional notions of what an intelligence measure should look like. We discuss how intelligence measurement of sequence predictors can indirectly serve as intelligence measurement for agents with Artificial General Intelligence (AGIs).

Alexander, S. A. 2019a. Intelligence via ultrafilters: structural properties of some intelligence comparators of deterministic Legg-Hutter agents. Journal of Artificial General Intelligence 10(1):24–45.10.2478/jagi-2019-0003 Search in Google Scholar

Alexander, S. A. 2019b. Measuring the intelligence of an idealized mechanical knowing agent. In CIFMA.10.1007/978-3-030-57506-9_13 Search in Google Scholar

Alexander, S. A. 2020a. AGI and the Knight-Darwin Law: why idealized AGI reproduction requires collaboration. In ICAGI.10.1007/978-3-030-52152-3_1 Search in Google Scholar

Alexander, S. A. 2020b. The Archimedean trap: Why traditional reinforcement learning will probably not yield AGI. Journal of Artificial General Intelligence 11(1):70–85.10.2478/jagi-2020-0004 Search in Google Scholar

Bostrom, N. 2003. Ethical issues in advanced artificial intelligence. In Schneider, S., ed., Science fiction and philosophy: from time travel to superintelligence. John Wiley and Sons. 277–284. Search in Google Scholar

Chaitin, G. 2011. Metaphysics, Metamathematics and Metabiology. In Hector, Z., ed., Randomness through computation. World Scientific.10.1142/9789814327756_0006 Search in Google Scholar

Conway, J. H. 2000. On Numbers and Games. CRC Press, 2nd edition.10.1201/9781439864159 Search in Google Scholar

Ehrlich, P. 2012. The absolute arithmetic continuum and the unification of all numbers great and small. Bulletin of Symbolic Logic 18:1–45.10.2178/bsl/1327328438 Search in Google Scholar

Girard, J.-Y. 1981. 21 \prod\nolimits_2^1 {} -logic, Part 1: Dilators. Annals of Mathematical Logic 21(2-3):75–219. Search in Google Scholar

Goldblatt, R. 2012. Lectures on the hyperreals: an introduction to nonstandard analysis. Springer. Search in Google Scholar

Good, I. J. 1969. Gödel’s theorem is a red herring. The British Journal for the Philosophy of Science 19(4):357–358.10.1093/bjps/19.4.357 Search in Google Scholar

Hardy, G. H. 1904. A theorem concerning the infinite cardinal numbers. Quarterly Journal of Mathematics 35:87–94. Search in Google Scholar

Hibbard, B. 2008. Adversarial sequence prediction. In ICAGI, 399–403. Search in Google Scholar

Hibbard, B. 2011. Measuring agent intelligence via hierarchies of environments. In ICAGI, 303–308. Search in Google Scholar

Hrbacek, K., and Katz, M. G. 2020. Infinitesimal analysis without the axiom of choice. Preprint.10.1016/j.apal.2021.102959 Search in Google Scholar

Hutter, M. 2004. Universal artificial intelligence: Sequential decisions based on algorithmic probability. Springer. Search in Google Scholar

Kirman, A. P., and Sondermann, D. 1972. Arrow’s theorem, many agents, and invisible dictators. Journal of Economic Theory 5(2):267–277.10.1016/0022-0531(72)90106-8 Search in Google Scholar

Knuth, D. E. 1974. Surreal numbers: a mathematical novelette. Addison-Wesley. Search in Google Scholar

Knuth, D. E. 1976. Big Omicron and big Omega and big Theta. ACM Sigact News 8(2):18–24.10.1145/1008328.1008329 Search in Google Scholar

Legg, S. 2006. Is there an elegant universal theory of prediction? In International Conference on Algorithmic Learning Theory, 274–287. Springer.10.1007/11894841_23 Search in Google Scholar

Liu, S.-C. 1960. An enumeration of the primitive recursive functions without repetition. Tohoku Mathematical Journal 12(3):400–402.10.2748/tmj/1178244403 Search in Google Scholar

Robinson, A. 1974. Non-standard analysis. Princeton University Press. Search in Google Scholar

Wainer, S., and Buchholz, W. 1987. Provably computable functions and the fast growing hierarchy. In Simpson, S. G., ed., Logic and Combinatorics. AMS.10.1090/conm/065/891248 Search in Google Scholar

Wainer, S. 1989. Slow growing versus fast growing. The Journal of Symbolic Logic 54(2):608–614.10.2307/2274873 Search in Google Scholar

Wang, P. 2019. On Defining Artificial Intelligence. Journal of Artificial General Intelligence 10(2):1–37.10.2478/jagi-2019-0002 Search in Google Scholar

Weiermann, A. 1997. Sometimes slow growing is fast growing. Annals of Pure and Applied Logic 90(1-3):91–99.10.1016/S0168-0072(97)00033-X Search in Google Scholar

Weiermann, A. 2002. Slow versus fast growing. Synthese 133:13–29.10.1023/A:1020899506400 Search in Google Scholar

Yampolskiy, R. V. 2012. AI-complete, AI-hard, or AI-easy–classification of problems in AI. In The 23rd Midwest Artificial Intelligence and Cognitive Science Conference.10.5402/2012/271878 Search in Google Scholar

Yampolskiy, R. V. 2013. Turing test as a defining feature of AI-completeness. In Artificial intelligence, evolutionary computing and metaheuristics. Springer. 3–17. Search in Google Scholar

Yampolskiy, R. V. 2020. On Controllability of Artificial Intelligence. Technical report. Search in Google Scholar

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