Physical Systems as Constructive Logics

  • Peter Hines
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4135)


This paper is an investigation of S. Wolfram’s Principle of Computational Equivalence’ – that (discrete) systems in the natural world should be thought of as performing computations. We take a logical approach, and demonstrate that under almost trivial (physically reasonable) assumptions, discrete evolving physical systems give a class of logical models. Moreover, these models are of intuitionistic, or constructive logics – that is, exactly those logics with a natural computational interpretation under the Curry-Howard ‘proofs as programs’ isomorphism.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abramsky, S., Jung, A.: Domain Theory. In: Abramsky, S., Gabbay, D.M., Maibaum, T.S.E. (eds.) Handbook of Logic in Computer Science, vol. III, Oxford University Press, Oxford (1994)Google Scholar
  2. 2.
    Borceux, F.: Handbook of Categorical Algebra 3. In: Encyclopedia of Mathematics and its Applications, vol. 53. Cambridge University Press, Cambridge (1994)Google Scholar
  3. 3.
    Bunimovich, L.: Many Dimensional Lorentz Cellular Automata and Turing Machines. Int. Jour. of Bifurcation and Chaos 6, 1127–1135 (1996)CrossRefMathSciNetMATHGoogle Scholar
  4. 4.
    Dummett, M.: Elements of Intuitionism. Oxford University Press, Oxford (2000)MATHGoogle Scholar
  5. 5.
    Girard, J.-Y.: Geometry of Interaction 1. In: Proceedings Logic Colloquium 1988, pp. 221–260. North-Holland, Amsterdam (1989)Google Scholar
  6. 6.
    Johnstone, P.: The point of pointless topology. Bulletin American Mathematical Society 8(1), 41–53 (1983)CrossRefMathSciNetMATHGoogle Scholar
  7. 7.
    Robinson, J.: A machine-oriented logic based on the resolution principle. Communications of the ACM 5, 23–41 (1965)Google Scholar
  8. 8.
    Scott, D.: Outline of a mathematical theory of computation. In: 4th Annual Princeton Conference on Information Sciences and Systems, pp. 169–176 (1970)Google Scholar
  9. 9.
    Silagadze, Z.: Zeno meets modern Science. Acta Phys. Polon. B36, 2886–2930 (2005)Google Scholar
  10. 10.
    Urzyczyn, P., Sorensen, M.: Lectures on the Curry-Howard Isomorphism. Elsevier, Amsterdam (2006)MATHGoogle Scholar
  11. 11.
    Wolfram, S.: A New Kind of Science. Wolfram Media (2002)Google Scholar
  12. 12.
    Vickers, S.: Topology via Logic. Cambridge Tracts in Theoretical Computer Science, p. 5 (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Peter Hines
    • 1
  1. 1.York UniversityYorkU.K.

Personalised recommendations