Skip to main content
SpringerLink
Log in

Some Considerations on Branching Areas of Time

  • Published:
Journal of Logic, Language and Information Aims and scope Submit manuscript

Abstract

In this paper we show that properties of non-linear time structures have not been studied enough. Axioms forcing the existence of a branching point in a branching area of a structure are presented for various classes of structures. We show also that the classical Dedekind continuity axiom does not work well in non-linear structures and we suggest stronger versions. Finally, some interdependencies between the axioms presented are proved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • van Benthem, J.F.A.K., 1983, The Logic of Time, Dordrecht: D. Reidel.

    Google Scholar 

  • Emerson, E.A, 1991, “Real time and mucalculus,” pp. 176–194 in Proceedings on REX Workshop on Real Time: Theory in Practice, Mook, The Netherlands, J.W. Bakker, C. Huizing, W.P. Roever, and G. Rozenberg, eds., LNCS 600, Berlin/Heidelberg/New York: SpringerVerlag.

    Google Scholar 

  • Fikes, R. and Nilsson N.J., 1971, “STRIPS: A new approach to application of theorem proving to problem solving,' Artificial Intelligence 2, 189-208.

  • Gabbay, D.M., Pnueli, A., Shelah, S., and Stavi, J., 1980, “On the temporal analysis of fairness,” pp. 163–173 in Seventh Annual ACM Symposium on Principles of Programming Languages, Las Vegas, NV.

  • Haugh, B.A., 1987, “Non-standard semantics for the method of temporal arguments,” pp. 449–455 in Proceedings of the Tenth International Joint Conference on Artificial Intelligence, Milan, Italy, J. McDermott, ed., Los Altos, CA: Morgan Kaufmann Publishers.

    Google Scholar 

  • Kahn, K. and Gorry, G.A., 1977, “Mechanizing temporal knowledge,' Artificial Intelligence 9, 87–108.

    Google Scholar 

  • Lamport, L., 1980, “'sometime' is sometimes 'not never',” pp. 174–184 in Seventh Annual ACM Symposium on Principles of Programming Languages, Las Vegas, NV.

  • Manna, Z. and Pnueli, A., 1981, “Verification of concurrent programs: The temporal framework,” pp. 215–273 in The Correctness Problems in Computer Science, R.S. Boyer and J.S. Moore, eds., New York: Academic Press.

    Google Scholar 

  • Manna, Z. and Pnueli, A., 1982, “Verification of concurrent programs: Temporal proof principles,” pp. 200–252 in Proceedings of the Workshop on Logics of Programs, Yorktown Heights, NY, D. Kozen, ed., LNCS 131, Berlin/Heidelberg/New York: SpringerVerlag.

    Google Scholar 

  • McDermott, D., 1982, “A temporal logic for reasoning about processes and plans,” Cognitive Science 6, 101–155.

    Google Scholar 

  • Moszkowski, B. and Manna, Z., 1984, “Reasoning in interval temporal logic,” pp. 371–382 in Proceedings the Workshop on Logics of Programs, Pittsburgh, PA, E. Clarke and D. Kozen, eds., LNCS 164, Berlin/Heidelberg/New York: SpringerVerlag.

    Google Scholar 

  • Penczek, W., 1995, “Branching time and partial order in temporal logics,” pp. 179–228 in Logic and Time, L. Bolc and A. Szałas, eds., London: UCL Press.

    Google Scholar 

  • Pinter, S.S. and Wolper, P., 1984, “A temporal logic for reasoning about partialy ordered computations,' pp. 28–37 in Proceedings of the Third Symposium on Principles of Distributed Computing.

  • Rodriguez, R., Anger, F., and Ford, K., 1991, “Temporal reasoning: A relativistic model,” International Journal of Intelligent Systems 6, 237–254.

    Google Scholar 

  • Rodriguez, R.V., 1993, “A relativistic temporal algebra for efficient design of distributed systems,” Applied Intelligence: The International Journal of Artificial Intelligence, Neural Networks and Complex Problem-Solving Technologies 3, 31–45.

    Google Scholar 

  • Sacerdoti, E.D., 1977, A Structure for Time and Behaviour, Amsterdam: Elsevier/NorthHolland.

    Google Scholar 

  • Shoham, Y., 1987, “Reasoning about change: Time and causation from the standpoint of artificial intelligence,” Ph.D. Thesis, Yale University, New Haven, CT.

    Google Scholar 

  • Shoham, Y., 1989, “Time for action: On the relation between time, knowledge and action,” pp. 954–959 in Proceedings of the Eleventh International Joint Conference on Artificial Intelligence, Detroit, MI, N.S. Sridharan, ed., San Mateo, CA: Morgan Kaufmann.

    Google Scholar 

  • Song, F. and Cohen R., 1988, “The interpretation of temporal relations in narratives,” pp. 745–750 in Proceedings of the Seventh AAAI Conference, Saint Paul, MN, R.G. Smith and T.M. Mitchell, eds., San Mateo, CA: Morgan Kaufmann.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science, Polish Academy of Sciences, 01-237, Warsaw, Ordona 21, Poland

    ElŻbieta Hajnicz

Authors
  1. ElŻbieta Hajnicz
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hajnicz, E. Some Considerations on Branching Areas of Time. Journal of Logic, Language and Information 8, 17–43 (1999). https://doi.org/10.1023/A:1008229020082

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008229020082

Search

Navigation