Minds and Machines

, Volume 21, Issue 2, pp 301–322 | Cite as

Significance of Models of Computation, from Turing Model to Natural Computation

Article

Abstract

The increased interactivity and connectivity of computational devices along with the spreading of computational tools and computational thinking across the fields, has changed our understanding of the nature of computing. In the course of this development computing models have been extended from the initial abstract symbol manipulating mechanisms of stand-alone, discrete sequential machines, to the models of natural computing in the physical world, generally concurrent asynchronous processes capable of modelling living systems, their informational structures and dynamics on both symbolic and sub-symbolic information processing levels. Present account of models of computation highlights several topics of importance for the development of new understanding of computing and its role: natural computation and the relationship between the model and physical implementation, interactivity as fundamental for computational modelling of concurrent information processing systems such as living organisms and their networks, and the new developments in logic needed to support this generalized framework. Computing understood as information processing is closely related to natural sciences; it helps us recognize connections between sciences, and provides a unified approach for modeling and simulating of both living and non-living systems.

Keywords

Philosophy of computer science Philosophy of computing Theory of computation Hypercomputing Philosophy of information Models of computation 

References

  1. Abramsky, S. (1997). Semantics of interaction: An introduction to game semantics. In P. Dybjer & A. Pitts (Eds.), Proceedings of the 1996 CLiCS Summer School, Isaac Newton Institute (pp. 1–31). Cambridge: Cambridge University Press.Google Scholar
  2. Abramsky, S. (2003). Sequentiality versus concurrency in games and logic. Mathematical Structures in Computer Science, 13, 531–565.MathSciNetMATHCrossRefGoogle Scholar
  3. Abramsky, S. (2007). A compositional game semantics for multi-agent logics of imperfect information in interactive logic. In J. van Benthem, D. Gabbay, & B. Lowe (Eds.), Texts in logic and games, Vol. 1 (pp. 11–48). Amsterdam: Amsterdam University Press.Google Scholar
  4. Abramsky, S. (2008). Petri nets, discrete physics, and distributed quantum computation. In P. Degano, R. De Nicola and J. Meseguer (Eds.), Concurrency, graphs and models, essays dedicated to Ugo Montanari on the occasion of his 65th birthday, Vol. 5065 of lecture notes in computer science. Springer, 527–543.Google Scholar
  5. Abramsky, S., & Coecke, B. (2007). Physics from computer science, Int. Journal of Unconventional Computing, 3(3), 179–197.Google Scholar
  6. Allo, P. (2007). Formalising semantic information. Lessons from logical pluralism. In G. Dodig-Crnkovic & S. Stuart (Eds.), Computation, information, cognition: The Nexus and the Liminal (pp. 41–52). Cambridge: Cambridge Scholars Publishing.Google Scholar
  7. Ashby, W. R. (1964). An introduction to cybernetics. London: Methuen.Google Scholar
  8. Beall, J. C., & Restall, G. (2000). Logical pluralism. Australasian Journal of Philosophy, 78, 475–493.CrossRefGoogle Scholar
  9. Beall, J.C., Restall, G. (2005). Logical Consequence, The Stanford Encyclopedia of Philosophy (Winter 2005 Edition). In: Edward N. Zalta (ed.). URL = <http://plato.stanford.edu/archives/win2005/entries/logical-consequence/>.
  10. Benthem van, J. (2001). Extensive games as process models. In M. Pauly & P. Dekker, (Eds.), Special issue of Journal of logic, language and information, 11, 289–313.Google Scholar
  11. Benthem van, J. (2003). Logic and the dynamics of information. Minds and Machines, 13, 503–519.CrossRefGoogle Scholar
  12. Benthem van, J. (2008). Logical pluralism meets logical dynamics? The Australasian Journal of Logic, 6, 182–209.MathSciNetMATHGoogle Scholar
  13. Bohan Broderick, P. (2004). On communication and computation. Minds and Machines, 14, 1–19.MATHCrossRefGoogle Scholar
  14. Bringsjord, S. (1994). Computation, among other things, is beneath us. Minds and Machines, 4, 469–488.CrossRefGoogle Scholar
  15. Bringsjord, S., & Zenzen, M. (2002). Toward a formal philosophy of hypercomputation. Minds and Machines, 12, 241–258.MATHCrossRefGoogle Scholar
  16. Burgin, M. (1999). Super-recursive algorithms as a tool for high performance computing. In Proceedings of high performance computing symposium, San Diego, 224–228. http://www.math.ucla.edu/~mburgin/res/compsc/res2/highperfcomp.html
  17. Burgin, M. (2005). Super-recursive algorithms. Springer Monographs in Computer Science.Google Scholar
  18. Cantwell Smith, B. (1996). On the origin of objects. Cambridge, MA: MIT Press.Google Scholar
  19. Chaitin, G. J. (2006). Epistemology as information theory: From Leibniz to Ω. Collapse, 1, 27–51.Google Scholar
  20. Church, A. (1935). Abstract no. 204. Bulletin of the American Mathematical Society, 41, 332–333.Google Scholar
  21. Church, A. (1936). An unsolvable problem of elementary number theory. American Journal of Mathematics, 58, 345–363.MathSciNetCrossRefGoogle Scholar
  22. Colburn, T. R., & Shute, G. M. (2008). Metaphor in computer science. Journal of Applied Logic, 6, 526–533.CrossRefGoogle Scholar
  23. Cooper, S. B., Löwe, B., & Sorbi, A., Eds. (2008). New computational paradigms: Changing conceptions of what is computable. Springer.Google Scholar
  24. Copeland, B. J. (1997). ‘The Church–Turing thesis’. In E. Zalta (Ed.), Stanford encyclopedia of philosophy, <http://plato.stanford.edu>.
  25. Copeland, B. J. (1998). Super Turing-machines. Complexity, 4, 30–32.MathSciNetCrossRefGoogle Scholar
  26. Copeland, B. J. (2000). Narrow versus wide mechanism. Journal of Philosophy, 96, 5–32.MathSciNetCrossRefGoogle Scholar
  27. Copeland, B. J. (2002). Hypercomputation. Minds and Machines, 12, 461–502.MATHCrossRefGoogle Scholar
  28. Copeland, B. J., & Proudfoot, D. (1999). Alan Turing’s forgotten ideas in computer science. Scientific American, 280, 76–81.CrossRefGoogle Scholar
  29. Copeland, B. J., & Shagrir, O. (2007). Physical computation: How general are Gandy’s principles for mechanisms? Minds and Machines, 17, 217–223.CrossRefGoogle Scholar
  30. Copeland, B. J., & Sylvan, R. (1999). Beyond the universal Turing machine. Australian Journal of Philosopy, 77, 46–67.MATHCrossRefGoogle Scholar
  31. Denning, P. (2007). Computing is a natural science, communications of the ACM, 50(7), 13–18. http://cs.gmu.edu/cne/pjd/PUBS/CACMcols/cacmJul07.pdf.
  32. Dodig-Crnkovic, G. (2003). ‘Shifting the paradigm of the philosophy of science: The philosophy of information and a new renaissance’. Minds and Machines, 13(4), 521–536. http://www.springerlink.com/content/g14t483510156726/fulltext.pdf.
  33. Dodig-Crnkovic, G. (2006). Investigations into information semantics and ethics of computing. Mälardalen University Press http://www.idt.mdh.se/personal/gdc/work/publications.html.
  34. Dodig-Crnkovic, G. (2010). The cybersemiotics and info-computationalist research programmes as platforms for knowledge production in organisms and machines, entropy 12, 878–901. http://www.mdpi.com/1099-4300/12/4/878/pdf
  35. Dodig-Crnkovic, G., & Müller, V. (2010). A dialogue concerning two world systems: Info-computational versus mechanistic. In Information and computation. World Scientific, Singapore. Preprint available at: http://arxiv.org/abs/0910.5001
  36. Dodig-Crnkovic, G., & Stuart, S. (Eds.). (2007). Computation, information, cognition–The Nexus and the Liminal. Cambridge: Cambridge Scholar Press.Google Scholar
  37. Floridi, L. (2004). Open problems in the philosophy of information. Metaphilosophy, 35.4, 554–582.Google Scholar
  38. Goldin, D., Smolka, S., & Wegner P. (Eds.). (2006). Interactive computation: The new paradigm. Springer-Verlag.Google Scholar
  39. Goldin, D., & Wegner, P. (2002). Paraconsistency of interactive computation, PCL 2002 (Workshop on paraconsistent computational logic). Denmark.Google Scholar
  40. Hintikka, J. (1973). Logic, language-games and information: Kantian themes in the philosophy of logic. Oxford: Clarendon Press.MATHGoogle Scholar
  41. Hintikka, J. (1982). Game-theoretical semantics: Insights and prospects. Notre Dame Journal of Formal Logic, 23(2), 219–241.MathSciNetMATHCrossRefGoogle Scholar
  42. Hodges, W. (2004). Logic and Games, The Stanford encyclopedia of philosophy (Winter 2004 Edition). Edward N. Zalta (Ed.). URL = <http://plato.stanford.edu/archives/win2004/entries/logic-games/>.
  43. Hodges, A. (2009). Alan Turing, The Stanford encyclopedia of philosophy (Winter 2009 Edition). In Edward N. Zalta (Ed.). URL = <http://plato.stanford.edu/archives/win2009/entries/turing/>.
  44. Japaridze, G. (2006). In the beginning was game semantics. In O. Majer, A.-V. Pietarinen, & T. Tulenheimo (Eds.), Logic and games: Foundational perspectives. Berlin: Springer Verlag.Google Scholar
  45. Kampis, G. (1991). Self-modifying systems in biology and cognitive science: A new framework for dynamics, information and complexity. Pergamon: Pergamon Press.Google Scholar
  46. Kelly, K. T. (2004). Uncomputability: The problem of induction internalized. Theoretical Computer Science, 317, 227–249.MathSciNetMATHCrossRefGoogle Scholar
  47. Kuipers, T. A. F. (2006). Theories looking for domains. Fact or fiction? Structuralist truth approximation by revision of the domain of intended applications, to appear. In L. Magnani (ed.), Model-based reasoning in science and engineering.Google Scholar
  48. Lloyd, S. (2006). Programming the universe: A quantum computer scientist takes on the cosmos. In Alfred A. Knopf.Google Scholar
  49. MacLennan, B. (2004). Natural computation and non-Turing models of computation. Theoretical Computer Science, 317, 115–145.MathSciNetMATHCrossRefGoogle Scholar
  50. Milner, R. (1989). Communication and concurrency. Prentice-Hall: International Series in Computing Science.MATHGoogle Scholar
  51. Piccinini, G. (2007). Computational modeling versus computational explanation: Is everything a Turing machine, and does it matter to the philosophy of mind? Australasian Journal of Philosophy, 85(1), 93–115.MathSciNetCrossRefGoogle Scholar
  52. Priest, G., & Tanaka, K. (2004). Paraconsistent Logic, The Stanford encyclopedia of philosophy (Winter 2004 Edition). In Edward N. Zalta (Ed.). URL = <http://plato.stanford.edu/archives/win2004/entries/logic-paraconsistent/>.
  53. Rozenberg, G., & Kari, L. (2008). The many facets of natural computing. Communications of the ACM, 51, 72–83.Google Scholar
  54. Schachter, V. (1999). How does concurrency extend the paradigm of computation? Monist, 82(1), 37–58.Google Scholar
  55. Sieg, W. (2007). Church without dogma–Axioms for computability. In B. Löwe, A. Sorbi, & S. B. Cooper (Eds.), New computational paradigms: Changing conceptions of what is computable (pp. 18–44). Heidelberg: Springer.Google Scholar
  56. Siegelman, H. T. (1999). Neural networks and analog computation. Berlin: Birkhauser.Google Scholar
  57. Sloman, A. (1996). Beyond Turing equivalence. In P.J.R. Millican & A. Clark (Eds.), Machines and thought: The legacy of Alan Turing, vol I, OUP(The Clarendon Press) pp 179–219, Revised version of paper presented to Turing Colloquium, University of Sussex, 1990. http://www.cs.bham.ac.uk/research/projects/cogaff/96-99.html#1
  58. Turing A. M. (1936). On computable numbers, with an application to the Entscheidungsproblem. In Proceedings of the London mathematical society, Vol. 42, pp. 230–265; reprinted in A. M. Turing, Collected works: mathematical logic, 18–53.Google Scholar
  59. Turing A. M. (1939). Systems of logic based on ordinals.In Proceedings of the London mathematical society, ser. 2, Vol. 45, 162–228.Google Scholar
  60. Turing, A. M. (1948). ‘Intelligent machinery’. National Physical Laboratory Report. In B. Meltzer, D. Michie (Eds.), 1969. Machine intelligence 5. Edinburgh: Edinburgh University Press. http://www.AlanTuring.net/intelligent_machinery.
  61. Turing, A. M. (1950). Computing machinery and intelligence, Mind LIX, 433–60. http://cogprints.org/499/0/turing.html
  62. Wegner, P. (1998). Interactive foundations of computing. Theoretical Computer Science, 192, 315–351.MathSciNetMATHCrossRefGoogle Scholar
  63. Wolfram, S. (2002) A new kind of science. Wolfram Science.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Computer Science Laboratory, School of Innovation, Design and EngineeringMälardalen UniversityVästeråsSweden

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