Labeled @-Calculus: Formalism for Time-Concerned Human Factors

  • Tetsuya Mizutani
  • Shigeru Igarashi
  • Yasuwo Ikeda
  • Masayuki Shio
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4120)


In the recent years it has come to be more and more important to analyze and verify systems which control complex external systems, like railways and airlines, whose serious accidents have been caused not only by bugs in software or hardware but also by human errors possibly involved in recognition or decision. This paper deals with an actual traffic accident widely known as “Shigaraki Kougen Railway accident” caused by a fatal decision based upon certain incorrect knowledge, as an example of systems involving human factor. In order to represent and analyze this accident, the formal system @-calculus is generalized into the “labeled” @-calculus so as to describe time-concerned recognition, knowledge, belief and decision of humans besides external physical or logical phenomena, while the word ‘time-concerned’ is used to express the property not only time-dependent mathematically but also distinctively featured by subtle and sophisticated sensitivity, interest or concern in exact time.

Topics: Artificial intelligence, logic, mathematical knowledge management.


Labeled @-calculus time-concerned knowledge and belief Shigaraki Kougen Railway accident 


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  1. 1.
    Alechina, N., Logan, B., Whitsey, M.: Modelling Communicating Agents in Timed Reasoning Logics. In: Alferes, J.J., Leite, J.A. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 95–107. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  2. 2.
    Aviation Safety Network: Aircraft accident description McDonnell Douglas DC-10-40 JA8546 - off Shizuoka Prefecture (2001),
  3. 3.
    Bennett, B., Dixon, C., Fisher, M., Hustadt, U., Franconi, E., Horrocks, I., de Rijke, M.: Combinations of Modal Logics. AI Review 17, 1–20 (2002)zbMATHGoogle Scholar
  4. 4.
    Damm, W., Hungar, H., Olderog, E.-R.: Verification of Cooperating Traffic Agents. International Journal of Control 79, 395–421 (2006)CrossRefMathSciNetzbMATHGoogle Scholar
  5. 5.
    Bereaved and Counselors of Shigaraki Accident (ed.): Shigaraki Kougen Railway Accident, Gendaijinbunsha (in Japanese) (2005)Google Scholar
  6. 6.
    Dixon, C., Nalon, C., Fisher, M.: Tableaux for Temporal Logics of Knowledge: Synchronous Systems of Perfect Recall or No Learning. In: The Proceedings of TIME-ICTL 2003, pp. 62–71 (2003)Google Scholar
  7. 7.
    Dixon, C., Gago, M.-C.F., Fisher, M., van der Hoek, W.: Using Temporal Logics of Knowledge in the Formal Verification of Security Protocols. In: Proceedings of TIME 2004, pp. 148–151 (2004)Google Scholar
  8. 8.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning About Knowledge. The MIT Press, Cambridge (1995)zbMATHGoogle Scholar
  9. 9.
    Gentzen, G.: Untersuchungen über das logische Schließen. Mathematische Zeitschrift 39, 176–210, 405–431 (1935); Investigations into Logical Deduction. In: Szabo, M. E. (ed.) The Collected Papers of Gerhard Gentzen, Series of Studies in Logic and the Foundations of Mathematics, pp. 68–131. North-Holland Publ. Co., Amsterdam (1969)Google Scholar
  10. 10.
    Halpern, J.Y., Vardi, M.Y.: The Complexity of Reasoning about Knowledge and Time. I. Lower Bounds. Journal of Computer and System Sciences 38, 195–237 (1989)CrossRefMathSciNetzbMATHGoogle Scholar
  11. 11.
    Hiraga, R., Igarashi, S.: Psyche: Computer Music Project. In: International Computer Music Conference, University of Tsukuba, pp. 297–300 (1997)Google Scholar
  12. 12.
    Igarashi, S., London, R., Luckhum, D.: Automatic Program Verification I: Logical Basis and its Application. Acta Informatica 4, 145–182 (1975)CrossRefGoogle Scholar
  13. 13.
    Igarashi, S.: The ν-Conversion and an Analytic Semantics. In: Mason, R.E.A. (ed.) Information Processing, vol. 83, pp. 769–774. Elsevier Sci. Publ. B. V., Amsterdam (1983)Google Scholar
  14. 14.
    Igarashi, S., Mizutani, T., Shirogane, T., Shio, M.: Formal Analysis for Continuous Systems Controlled by Programs. In: Jaffar, J., Yap, R.H.C. (eds.) ASIAN 1996. LNCS, vol. 1179, pp. 347–348. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  15. 15.
    Igarashi, S., Shirogane, T., Shio, M., Mizutani, T.: Tense Arithmetic I: Formalization of Properties of Programs in Rational Arithmetics. Tensor, N. S. 59, 132–152 (1998)MathSciNetGoogle Scholar
  16. 16.
    Igarashi, S.: Science of Music Expression, YAMAHA Music Media (in Japanese) (2000)Google Scholar
  17. 17.
    Igarashi, S., Mizutani, T., Ikeda, Y., Shio, M.: Tense Arithmetic II: @-calculus as an Adaptation for Formal Number Theory. Tensor, N. S. 64, 12–33 (2003)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Igarashi, S., Shio, M., Mizutani, T. and Ikeda, Y.: Specification and Verification of Cooperative Real-Timing Processes in @-Calculus (to appear)Google Scholar
  19. 19.
    Ikeda, Y.: Mathematics of Intellect and Sensibility: Logical System for Specifications. In: 2005 China-Japan Symposium on Advanced Science and Technology, Xiamen Univ. (2005)Google Scholar
  20. 20.
    McCarthy, J., Sato, M., Igarashi, S.: On the Model of Knowledge. Stanford Artificial Intelligence Lab. Memo. AIM-312, 1–11 (1977),
  21. 21.
    Machi, T., Ikeda, Y., Tomita, K., Hosono, C., Igarashi, S.: Tense Calculus and the Refinement without ∞. Tensor, N. S. 67, 79–93 (2006)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Mizutani, T., Igarashi, S., Tomita, K., Shio, M.: Representation of Discretely Controlled Continuous Systems in Software-Oriented Formal Analysis. In: Shyamasundar, R.K. (ed.) ASIAN 1997. LNCS, vol. 1345, pp. 110–120. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  23. 23.
    Mizutani, T., Igarashi, S., Shio, M.: Representation of a Discretely Controlled Continuous System in Tense Arithmetic. Electr. Notes in Theor. Comp. Sci. 42 (2001),
  24. 24.
    Mizutani, T.: Mathematics for Intellect and Sensibility: Case Study: Formal Representation of Shigaraki Kougen Railway Accident. In: 2005 China-Japan Symposium on Advanced Science and Technology, Xiamen Univ. (2005)Google Scholar
  25. 25.
    Shoenfield, J.R.: Mathematical Logic. Addison-Wesley Publishing Company, Massachusetts (1967)zbMATHGoogle Scholar
  26. 26.
    van Dalen, D.: Intuitionistic logic. In: Gabbay, D.M., Guenthner, F. (eds.) Handbook of Philosophical Logic, 2nd edn., vol. 5, pp. 1–114 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Tetsuya Mizutani
    • 1
  • Shigeru Igarashi
    • 2
  • Yasuwo Ikeda
    • 3
  • Masayuki Shio
    • 4
  1. 1.Department of Computer ScienceUniversity of Tsukuba 
  2. 2.Graduate School of Community DevelopmentTokiwa University 
  3. 3.Department of Computer & Media ScienceSaitama Junior College 
  4. 4.College of Community DevelopmentTokiwa University 

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