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When Thinking Never Comes to a Halt: Using Formal Methods in Making Sure Your AI Gets the Job Done Good Enough

  • Tarek R. BesoldEmail author
  • Robert Robere
Chapter
Part of the Synthese Library book series (SYLI, volume 376)

Abstract

The recognition that human minds/brains are finite systems with limited resources for computation has led researchers in cognitive science to advance the Tractable Cognition thesis: Human cognitive capacities are constrained by computational tractability. As also human-level AI in its attempt to recreate intelligence and capacities inspired by the human mind is dealing with finite systems, transferring this thesis and adapting it accordingly may give rise to insights that can help in progressing towards meeting the classical goal of AI in creating machines equipped with capacities rivaling human intelligence. Therefore, we develop the “Tractable Artificial and General Intelligence Thesis” and corresponding formal models usable for guiding the development of cognitive systems and models by applying notions from parameterized complexity theory and hardness of approximation to a general AI framework. In this chapter we provide an overview of our work, putting special emphasis on connections and correspondences to the heuristics framework as recent development within cognitive science and cognitive psychology.

Keywords

Cognitive systems Complexity theory Parameterized complexity Approximation theory Tractable AI Approximable AI Heuristics in AI 

References

  1. Besold, T. R. (2013). Formal limits to heuristics in cognitive systems. In Proceedings of the Second Annual Conference on Advances in Cognitive Systems (ACS) 2013, Baltimore.Google Scholar
  2. Besold, T. R., & Robere, R. (2013a). A note on tractability and artificial intelligence. In K. U. Kühnberger, S. Rudolph, & P. Wang (Eds.), Artificial General Intelligence – 6th International Conference, AGI 2013, Proceedings, Beijing (Lecture Notes in Computer Science, Vol. 7999, pp. 170–173). Springer.Google Scholar
  3. Besold, T. R., & Robere, R. (2013b). When almost is not even close: remarks on the approximability of HDTP. In K. U. Kühnberger, S. Rudolph, & P. Wang (Eds.), Artificial General Intelligence – 6th International Conference, AGI 2013, Proceedings, Beijing (Lecture Notes in Computer Science, Vol. 7999, pp. 11–20). Springer.Google Scholar
  4. Blokpoel, M., Kwisthout, J., Wareham, T., Haselager, P., Toni, I., & van Rooij, I. (2011). The computational costs of recipient design and intention recognition in communication. In Proceedings of the 33rd Annual Meeting of the Cognitive Science Society, Boston (pp. 465–470)Google Scholar
  5. Cai, L., & Chen, J. (1997). On fixed-parameter tractability and approximability of {NP} optimization problems. Journal of Computer and System Sciences, 54(3), 465–474. doi:http://dx.doi.org/10.1006/jcss.1997.1490.
  6. Cai, L., & Huang, X. (2006). Fixed-parameter approximation: Conceptual framework and approximability results. In H. Bodlaender & M. Langston (Eds.), Parameterized and exact computation (Lecture Notes in Computer Science, Vol. 4169, pp. 96–108). Berlin/Heidelberg: Springer. doi:10.1007/11847250_9.CrossRefGoogle Scholar
  7. Chapman, D. (1987). Planning for conjunctive goals. Artificial Intelligence, 32(3), 333–377.CrossRefGoogle Scholar
  8. Cooper, G. (1990). The computational complexity of probabilistic inference using Bayesian belief networks. Artificial Intelligence, 42, 393–405.CrossRefGoogle Scholar
  9. Cummins, R. (2000). “How does it work?” vs. “What are the laws?” two conceptions of psychological explanation. In F. Keil & R. Wilson (Eds.), Explanation and cognition (pp. 117–145). Cambridge: MIT.Google Scholar
  10. Czerlinski, J., Goldstein, D., & Gigerenzer, G. (1999). How good are simple heuristics? In G. Gigerenzer, P. Todd, & the ABC Group (Eds.), Simple heuristics that make us smart. New York: Oxford University Press.Google Scholar
  11. Downey, R. G., & Fellows, M. R. (1999). Parameterized complexity. New York: Springer.CrossRefGoogle Scholar
  12. Downey, R. G., Fellows, M. R., & Stege, U. (1997). Parameterized complexity: A framework for systematically confronting computational intractability. In Contemporary Trends in Discrete Mathematics: From DIMACS and DIMATIA to the Future. Providence: AMS.Google Scholar
  13. Evans, T. G. (1964). A heuristic program to solve geometric-analogy problems. In Proceedings of the April 21–23, 1964, Spring Joint Computer Conference AFIPS ’64 (Spring) (pp. 327–338). New York: ACM. doi:http://doi.acm.org/10.1145/1464122.1464156
  14. Falkenhainer, B., Forbus, K., & Gentner, D. (1989). The structure-mapping engine: Algorithm and examples. Artificial Intelligence, 41(1), 1–63. doi:10.1016/0004-3702(89)90077-5.CrossRefGoogle Scholar
  15. Flum, J., & Grohe, M. (2006). Parameterized complexity theory. Berlin: Springer.Google Scholar
  16. Frixione, M. (2001). Tractable competence. Minds and Machines, 11, 379–397.CrossRefGoogle Scholar
  17. Gentner, D. (1983). Structure-mapping: A theoretical framework for analogy. Cognitive Science, 7(2), 155–170.CrossRefGoogle Scholar
  18. Gentner, D., & Forbus, K. (1991). MAC/FAC: A model of similarity-based retrieval. Cognitive Science, 19, 141–205.Google Scholar
  19. Gigerenzer, G., Hertwig, R., & Pachur, T. (Eds.). (2011). Heuristics: The foundation of adaptive behavior. New York: Oxford University Press.Google Scholar
  20. Gottlob, G., & Szeider, S. (2008). Fixed-parameter algorithms for artificial intelligence, constraint satisfaction and database problems. The Computer Journal, 51(3), 303–325. doi:10.1093/comjnl/bxm056.CrossRefGoogle Scholar
  21. Hofstadter, D. (2001). Epilogue: Analogy as the core of cognition. In D. Gentner, K. Holyoak, & B. Kokinov (Eds.), The analogical mind: Perspectives from cognitive science (pp. 499–538). Cambridge: MIT.Google Scholar
  22. Kahneman, D., Slovic, P., & Tversky, A. (1982). Judgment under uncertainty: Heuristics and biases. Cambridge/New York: Cambridge University Press.CrossRefGoogle Scholar
  23. Krumnack, U., Schwering, A., Gust, H., & Kühnberger, K. (2007). Restricted higher-order anti-unification for analogy making. In Twentieth Australian Joint Conference on Artificial Intelligence. Berlin: Springer.Google Scholar
  24. Kwisthout, J., & van Rooij, I. (2012). Bridging the gap between theory and practice of approximate bayesian inference. In Proceedings of the 11th International Conference on Cognitive Modeling, Berlin (pp. 199–204).Google Scholar
  25. Levesque, H. (1988). Logic and the complexity of reasoning. Journal of Philosophical Logic, 17, 355–389.CrossRefGoogle Scholar
  26. Marr, D. (1982). Vision: A computational investigation into the human representation and processing visual information. San Francisco: Freeman.Google Scholar
  27. Nebel, B. (1996). Artificial intelligence: A computational perspective. In G. Brewka (Ed.), Principles of knowledge representation (pp. 237–266). Stanford: CSLI Publications.Google Scholar
  28. Pylyshyn, Z. (1980). Computation and cognition: Issues in the foundation of cognitive science. The Behavioral and Brain Sciences, 3, 111–132.CrossRefGoogle Scholar
  29. Reitman, W. R., Grove, R. B., & Shoup, R. G. (1964). Argus: An information-processing model of thinking. Behavioral Science, 9(3), 270–281. doi:10.1002/bs.3830090312.CrossRefGoogle Scholar
  30. Robere, R., & Besold, T. R. (2012). Complex analogies: Remarks on the complexity of HDTP. In Twentyfifth Australasian Joint Conference on Artificial Intelligence (Lecture Notes in Computer Science, Vol. 7691, pp. 530–542). Berlin/New York: Springer.Google Scholar
  31. Schwering, A., Krumnack, U., Kühnberger, K. U., & Gust, H. (2009a). Syntactic principles of heuristic-driven theory projection. Journal of Cognitive Systems Research, 10(3), 251–269.Google Scholar
  32. Schwering, A., Kühnberger, K. U., & Kokinov, B. (2009b). Analogies: Integrating multiple cognitive abilities – guest editorial. Journal of Cognitive Systems Research 10(3), 175–177.Google Scholar
  33. Simon, H. A. (1956). Rational choice and the structure of the environment. Psychological Review, 63, 129–138. doi:10.1037/h0042769.CrossRefGoogle Scholar
  34. Simon, H. A. (1957). Models of man: Social and rational. New York: Wiley.Google Scholar
  35. Turing, A. (1969). Intelligent machinery. In B. Meltzer & D. Michie (Eds.), Machine intelligence (Vol. 5, pp. 3–23). Edinburgh: Edinburgh University Press.Google Scholar
  36. van Rooij, I. (2008). The tractable cognition thesis. Cognitive Science, 32, 939–984.CrossRefGoogle Scholar
  37. Wareham, T., Kwisthout, J., Haselager, P., & van Rooij, I. (2011). Ignorance is bliss: A complexity perspective on adapting reactive architectures. In Proceedings of the First IEEE Conference on Development and Learning and on Epigenetic Robotics, Frankfurt am Main (pp. 465–470).Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.The KRDB Research Centre, Faculty of Computer ScienceFree University of Bozen-BolzanoBozen-BolzanoItaly
  2. 2.Department of Computer ScienceUniversity of TorontoTorontoCanada

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