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Mexitl: Multimedia in Executable Interval Temporal Logic

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Abstract

This paper explores a formalism for describing a wide class of multimedia document constraints, based on an interval temporal logic. We describe the requirements that arise from the multimedia documents application area, and we illustrate these requirements using several examples. Then we present the temporal logic formalism that we use. This logic extends existing interval temporal logic with a number of new features: actions, framing of actions, past operators, a projection-like operator called filter and a new handling of interval length. The notation is applied to the specification of the examples, and in particular a set of logical manipulations, providing feedback to an author, is presented. A model theory, logic and satisfaction relation are defined for the notation.

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References

  1. J.F. Allen, “Maintaining knowledge about temporal intervals,” Communications of the ACM, Vol. 26, No. 1, pp. 832–843, 1983.

    Google Scholar 

  2. Y.Y. Al-Salqan and C.K. Chang, “Temporal relations and synchronization agents,” IEEE Multimedia, Vol. 3, No. 2, pp. 30–39, 1996.

    Google Scholar 

  3. A.F. Ates, M. Bilgic, S. Saito, and B. Sarikaya, “Using timed CSP for specification, verification and simulation of multimedia synchronization,” Journal on Selected Areas in Communications, Vol. 14, No. 1, 1996.

  4. H. Barringer, M. Fisher, D. Gabbay, G. Gough, and R. Owens, “METATEM: A framework for programming in temporal logic,” in Lecture Notes in Artificial Intelligence, Vol. 430, Springer-Verlag, Berlin, 1989.

    Google Scholar 

  5. G. Berry and G. Gonthier, “The Esterel synchronous programming language: Design, semantics, implementation,” Science of Computer Programming, Vol. 19, No. 2, pp. 87–152, 1992.

    Google Scholar 

  6. H. Bowman, H. Cameron, P. King, and S. Thompson, “Specification and prototyping of structured multimedia documents using interval temporal logic,” in Howard Barringer et al. (Eds.), Advances in Temporal Logic, Kluwer Academic Publishers, Dordrecht, 2000.

    Google Scholar 

  7. H. Bowman and S. Thompson, “A tableau method for interval temporal logic with projection,” in Harrie de Swart (Ed.), Automated Reasoning with Analytic Tableaux and Related Methods: TABLEAUX '98, Lecture Notes in Computer Science, Vol. 1397, Springer-Verlag, Berlin, 1998.

    Google Scholar 

  8. H. Bowman and S.J. Thompson, “A decision procedure and complete axiomatisation of finite interval temporal logic with projection,” Journal of Logic and Computation, Vol. 13, No. 2, 2003.

  9. M.C. Buchanan and P.T. Zellweger, “Automatic temporal mechanisms,” in Proc. Multimedia '93, ACM Press, New York, 1993.

    Google Scholar 

  10. D.C.A. Bulterman and L. Hardman, “Multimedia authoring tools: State of the art and research challenges,” in J. van Leeuwen (Ed.), Computer Science Today: Recent Trends and Developments, Lecture Notes in Computer Science, Vol. 1000, Springer-Verlag, Berlin, 1995, pp. 575–591.

    Google Scholar 

  11. H. Cameron, P.R. King, and S.J. Thompson, “Modelling reactive multimedia: Events and behaviours,” Multimedia Tools and Applications, to appear.

  12. Z.H. Duan, “An extended interval temporal logic and a framing technique for temporal logic programming,” Ph.D. Thesis, University of Newcastle Upon Tyne, May 1996.

  13. R. Erfle, “Specification of temporal constraints in multimedia documents using HyTime,” Electronic Publishing, Vol. 6, No. 4, pp. 397–411, 1993.

    Google Scholar 

  14. D. Gabbay, “The declarative past and imperative future,” in H. Barringer (Ed.), Proceedings of the Colloquim on Temporal Logic and Specifications, Lecture Notes In Computer Science, Vol. 398, Springer-Verlag, Berlin, 1989, pp. 409–448.

    Google Scholar 

  15. R. Hale, “Using temporal logic for prototyping: The design of a lift controller,” in Lecture Notes in Computer Science, Vol. 379, Springer-Verlag, Berlin, 1989, pp. 375–408.

    Google Scholar 

  16. L. Hardman, J. Van Ossenbruggen, K.S. Mullender, L. Rutledge, and D. Bulterman, “Do you have the time? Composition and linking in time-base hypermedia,” in Proc. Hypertext '99, ACM Press, 1999.

  17. L. Hardman, G. van Rossum, and D.C.A. Bulterman, “Structured multimedia authoring,” ACM Multimedia 'S93, pp. 283–289, 1993.

  18. C.M. Huang, J.S. Chen, C.H. Lin, and C. Wang, “MING-I: A distributed interactive multimedia document development mechanism,” Multimedia Systems, Vol. 6, pp. 316–333, 1998.

    Google Scholar 

  19. ISO 10744, “Information Technology—Hypermedia/Time-Based Structuring Language (HyTime), 1992.

  20. M. Jourdan, N. Layada, and C. Roisin, A Survey on Authoring Techniques for Temporal Scenarios of Multimedia Documents, Handbook of Internet and Multimedia Systems and Applications, Part 1: Tools and Standards. CRC Press, Boca Raton, FL, 1998.

    Google Scholar 

  21. C. Keramane and A. Duda, “Interval expressions, a functional model for interactive dynamic multimedia presentations,” in Proc. Conf. Multimedia '96, IEEE, 1996.

  22. P.R. King, “Modelling multimedia documents,” Electronic Publishing, Vol. 8, No. 2/3, pp. 95–110, 1996.

    Google Scholar 

  23. P.R. King, “A logic based formalism for temporal constraints in multimedia documents,” in Principles of Document Processing PODP96, Lecture Notes in Computer Science, Vol. 1293, Springer-Verlag, Berlin, 1997, pp. 87–100.

    Google Scholar 

  24. S. Kono, “A combination of clausal and non-clausal temporal logic programs,” in Lecture Notes in Artificial Intelligence, Vol. 897, Springer-Verlag, Berlin, 1993, pp. 40–57.

    Google Scholar 

  25. R. Koymans, “Specifying real-Time properties with metric temporal logic,” Real-Time Systems, Vol. 2, No. 4, pp. 255–299, 1990.

    Google Scholar 

  26. W. Liao and V.O.K. Li, “Synchronization of distributed multimedia systems with user interactions,” Multimedia Systems, Vol. 6, pp. 196–205, 1998.

    Google Scholar 

  27. Z. Manna and A. Pnueli, The Temporal Logic of Reactive and Concurrent Systems, Springer-Verlag, Berlin, 1992.

    Google Scholar 

  28. L.E. Moser, Y.S. Ramakrishna, G. Kutty, P.M. Melliar-Smith, and L.K. Dillon, “A graphical environment for the design of concurrent real-time systems,” ACM Transactions on Software Engineering and Methodology, Vol. 6, No. 1, pp. 31–79, 1997.

    Google Scholar 

  29. B. Moszkowski, Executing Temporal Logic, Cambridge University Press, 1986.

  30. B. Moszkowski, “Some very compositional temporal properties,” in Proc. Programming Concepts, Methods and Calculi, IFIP Trans. A-56, North-Holland, Amsterdam, 1994, pp. 307–326.

    Google Scholar 

  31. B.C. Moszkowski, “A complete axiomatisation of interval temporal logic with infinite time,” in LICS 2000, 2000.

  32. B.C. Moszkowski, “An automata theoretic completeness proof for interval temporal logic,” in ICALP 2000, 2000.

  33. J. Peterson, C. Elliott, and G.S. Ling, Fran Users' Manual, 1997. Available at http://research.microsoft.com/~conal/Fran/UsersMan.htm.

  34. B. Prabhakaran and S.V. Raghavan, “Synchronization models for multimedia presentation with user participation,” in Multimedia' 93. ACM Press, New York, 1993.

    Google Scholar 

  35. P. Sénac, M. Diaz, A. Léger, and P. de Saqui-Sannes, “Modeling logical and temporal synchronization in hypermedia systems,” IEEE Journal on Selected Areas in Communications, Vol. 14, No. 1, pp. 84–103, 1996.

    Google Scholar 

  36. T.K. Shih, L.-J. Hwang, and J.-Y. Tsai, “Formal model of temporal properties underlying multimedia presentations,” in Courtiat et al. (Eds.), Multimedia Modeling: Towards the Information Superhighway. World Scientific Publishing, Singapore, 1996.

    Google Scholar 

  37. P.D. Stotts, R. Furuta, and C.R. Cabarrus, “Hyperdocuments as automata: Verification of trace-based browsing properties by model checking,” ACM Trans. Information Systems, Vol. 16, No. 1, pp. 1–30, 1993.

    Google Scholar 

  38. P.D. Stotts, R. Furuta, and J.C. Ruiz, “Hyperdocuments as automata: Trace-based browsing property verification,” in D. Lucarella, J. Nanard, M. Nanard, and P. Paolini (Eds.), Proc. the ACM Conf. Hypertext break (ECHT '92), ACM Press, New York, 1992, pp. 272–281 (Nov. 30-Dec. 4, 1992, Milan, Italy).

    Google Scholar 

  39. S. Thompson, “Constructive interval temporal logic in Alf,” in Howard Barringer et al. (Eds.), Advances in Temporal Logic. Kluwer Academic Publishers, Dordrecht, 2000.

    Google Scholar 

  40. T. Wahl and K. Rothermel, “Representing time in multimedia systems,” in Proc. Int. Conf. Multimedia Computing and Systems, 1994.

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Bowman, H., Cameron, H., King, P. et al. Mexitl: Multimedia in Executable Interval Temporal Logic. Formal Methods in System Design 22, 5–38 (2003). https://doi.org/10.1023/A:1021736013555

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