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International Journal of Theoretical Physics

, Volume 48, Issue 5, pp 1290–1299 | Cite as

Logic of Simultaneity

  • Kenji Tokuo
Article
  • 61 Downloads

Abstract

A logical model of spatiotemporal structures is pictured as a succession of processes in time. One usual way to formalize time structure is to assume the global existence of time points and then collect some of them to form time intervals of processes. Under this set-theoretic approach, the logic that governs the processes acquires a Boolean structure. However, in a distributed computer system or a relativistic universe where the message-passing time between different locations is not negligible, the logic has no choice but to accept time interval instead of time point as a primitive concept. The resulting logico-algebraic structure matches that of orthologic, which is known as the most simplified version of quantum logic, and the conventionality of simultaneity claim is reduced to the non-distributivity of the logic.

Keywords

Conventionality of simultaneity Special relativity Orthologic Quantum logic 

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References

  1. 1.
    Baeten, J.C.M.: A brief history of process algebra. Theor. Comput. Sci. 335(2–3), 131–146 (2005) MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Birkhoff, G.: Lattice Theory, 3rd edn. American Mathematical Society Colloquium Publications, vol. XXV. American Mathematical Society, Providence (1967) MATHGoogle Scholar
  3. 3.
    Dalla Chiara, M.L.: Quantum Logic. In: Gabbay, D.M., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 6, 2nd edn., pp. 129–228. Kluwer, Dordrecht (2001) Google Scholar
  4. 4.
    Galton, A.: Time and continuity in philosophy, mathematics, and artificial intelligence. Ars Semiot. 19(1–2), 101–119 (1996) Google Scholar
  5. 5.
    Goldblatt, R.: Logic of Time and Computation. CSLI Lecture Notes, No. 7, Stanford (1987) Google Scholar
  6. 6.
    Goranko, V., Montanari, A., Sciavicco, G.: A road map on interval temporal logics and duration calculi. J. Appl. Non-Class. Log. 14(1–2), 9–54 (2004) CrossRefGoogle Scholar
  7. 7.
    Grünbaum, A.: Philosophical Problems of Space and Time, 2nd edn. Reidel, Boston (1973) Google Scholar
  8. 8.
    Halpern, J.Y., Shoham, Y.: A propositional modal logic of time intervals. J. ACM 38(4), 935–962 (1991) MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Humberstone, I.L.: Interval semantics for tense logic: some remarks. J. Philos. Log. 8, 171–196 (1979) MATHMathSciNetGoogle Scholar
  10. 10.
    Lamport, L.: Time, clocks and the ordering of events in a distributed system. Commun. ACM 21(7), 558–565 (1978) MATHCrossRefGoogle Scholar
  11. 11.
    Malament, D.: Causal theories of time and the conventionality of simultaneity. Noûs 11, 293–300 (1977) CrossRefGoogle Scholar
  12. 12.
    Norton, J.D.: Philosophy of space and time. In: Salmon, et al. (eds.) Introduction to the Philosophy of Science. Prentice-Hall, New York (1992) Google Scholar
  13. 13.
    Pierce, B.C.: Foundational calculi for programming languages. In: Tucker, A.B. (ed.) The Computer Science and Engineering Handbook, pp. 2190–2207. CRC Press, Boca Raton (1997) Google Scholar
  14. 14.
    Redhead, M.: The conventionality of simultaneity. In: Earman, J., Janis, A.I., Massey, G.I., Rescher, N. (eds.) Philosophical Problems of Internal and External Worlds: Essays on the Philosophy of Adolf Grünbaum, pp. 103–128. University of Pittsburgh, Pittsburgh (1993) Google Scholar
  15. 15.
    Reichenbach, H.: The Philosophy of Space and Time. Dover, New York (1957). English translation by M. Reichenbach and J. Freund Google Scholar
  16. 16.
    Russell, B.: Our Knowledge of the External World as a Field for Scientific Method in Philosophy. Allen and Unwin, London (1926) MATHGoogle Scholar
  17. 17.
    Taylor, E.F., Wheeler, J.A.: Spacetime Physics: An Introduction to Special Relativity, 2nd edn. Freeman, New York (1992) Google Scholar

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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Computer and Control EngineeringOita National College of TechnologyOitaJapan

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