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Temporal Logic in Information Systems

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Part of the book series: The Springer International Series in Engineering and Computer Science ((SECS,volume 436))

Abstract

Temporal logic is obtained by adding temporal connectives to a logic language. Explicit references to time are hidden inside the temporal connectives. Different variants of temporal logic use different sets of such connectives. In this chapter, we survey the fundamental varieties of temporal logic and describe their applications in information systems.

Several features of temporal logic make it especially attractive as a query and integrity constraint language for temporal databases. First, because the references to time are hidden, queries and integrity constraints are formulated in an abstract, representation-independent way. Second, temporal logic is amenable to efficient implementation. Temporal logic queries can be translated to an algebraic language. Temporal logic constraints can be efficiently enforced using auxiliary stored information. More general languages, with explicit references to time, do not share these properties.

Recent research has proposed various implementation techniques to make temporal logic practically useful in database applications. Also, the relationships between different varieties of temporal logic and between temporal logic and other temporal languages have been clarified. We report on these developments and outline some of the remaining open research problems.

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References

  1. K.R. Apt and R.N. Bol. Logic Programming and Negation: A Survey. Journal of Logic Programming, 19-20:9–71, 1994.

    Article  MathSciNet  Google Scholar 

  2. R. Alur and T.A. Henzinger. Logics and Models of Real-Time: A Survey. In Real-Time: Theory in Practice, pp. 74–106. Springer-Verlag, LNCS 600, 1992.

    Google Scholar 

  3. S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison-Wesley, 1995.

    Google Scholar 

  4. S. Abiteboul, L. Herr, and J. Van den Bussche. Temporal Connectives versus Explicit Timestamps in Temporal Query Languages (preliminary report). In International Workshop of Temporal Databases, Zürich, Switzerland, September 1995. Springer-Verlag.

    Google Scholar 

  5. S. Abiteboul, L. Herr, and J. Van den Bussche. Temporal Versus First-Order Logic to Query Temporal Databases. In ACM Symposium on Principles of Database Systems, pp. 49–57, Montréal, Canada, June 1996.

    Google Scholar 

  6. J.F. Allen. Maintaining Knowledge about Temporal Intervals. Communications of the ACM, 26(11):832–843, November 1983.

    Article  MATH  Google Scholar 

  7. J.F. Allen. Towards a General Theory of Action and Time. Artificial Intelligence, 23:123–154, 1984.

    Article  MATH  Google Scholar 

  8. M. Abadi and Z. Manna. Temporal Logic Programming. Journal of Symbolic Computation, 8(3):277–295, September 1989.

    Article  MathSciNet  MATH  Google Scholar 

  9. L. Åqvist. A Conjectured Axiomatization of Two-Dimensional Reichenbachian Tense Logic. J. Philosophical Logic, 8:1–45, 1979.

    Article  MATH  Google Scholar 

  10. B. Alpern and F.B. Schneider. Defining Liveness. Information Processing Letters, 21:181–185, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  11. M. Baudinet. A Simple Proof of the Completeness of Temporal Logic Programming. In L. Farinas del Cerro and M. Penttonen, editors, Intensional Logics for Programming. Oxford University Press, 1992.

    Google Scholar 

  12. M. Baudinet. On the Expressiveness of Temporal Logic Programming. Information and Computation, 117(2):157–180, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  13. E. Baralis, S. Ceri, and S. Paraboschi. Declarative Specification of Constraint Maintenance. In International Conference on Entity-Relationship Approach, pp. 205–222. Springer-Verlag, LNCS 881, 1994.

    Google Scholar 

  14. M. Böhlen, J. Chomicki, R.T. Snodgrass, and D. Toman. Querying TSQL2 Databases with Temporal Logic. In International Conference on Extending Database Technology, pp. 325–341, Avignon, France, 1996. Springer Verlag, LNCS 1057.

    Google Scholar 

  15. M. Baudinet, J. Chomicki, and P. Wolper. Temporal Deductive Databases. In Tansel et al. [TCG+93], chapter 13, pp. 294–320.

    Google Scholar 

  16. C. Brzoska. Temporal Logic Programming and its Relation to Constraint Logic Programming. In V. Saraswat and K. Ueda, editors, International Logic Programming Symposium, pp. 661–677. MIT Press, 1991.

    Google Scholar 

  17. C. Brzoska. Temporal Logic Programming with Bounded Universal Modality Goals. In D.S. Warren, editor, International Conference on Logic Programming, pp. 239–256. MIT Press, 1993.

    Google Scholar 

  18. C. Brzoska. Temporal Logic Programming in Dense Time. In J.W. Lloyd, editor, International Logic Programming Symposium, pp. 303–317. MIT Press, 1995.

    Google Scholar 

  19. M. Böhlen, R.T. Snodgrass, and M.D. Soo. Coalescing in Temporal Databases. In International Conference on Very Large Data Bases, pp. 180–191, 1996.

    Google Scholar 

  20. F. Bacchus, J. Tenenberg, and J.A. Koomen. A Non-Reified Temporal Logic. Artificial Intelligence, 52(1):87–108, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  21. J. Chomicki, D. Goldin, and G. Kuper. Variable Independence and Aggregation Closure. In ACM Symposium on Principles of Database Systems, pp. 40–48, Montréal, Canada, June 1996.

    Google Scholar 

  22. J. Chomicki. Temporal Query Languages: A Survey. In D.M. Gabbay and H.J. Ohlbach, editors, Temporal Logic, First International Conference, pp. 506–534. Springer-Verlag, LNAI 827, 1994.

    Google Scholar 

  23. J. Chomicki. Efficient Checking of Temporal Integrity Constraints Using Bounded History Encoding. A CM Transactions on Database Systems, 20(2):149–186, June 1995.

    Article  Google Scholar 

  24. J. Chomicki and T. Imielinski. Temporal Deductive Databases and Infinite Objects. In ACM Symposium on Principles of Database Systems, pp. 61–73, Austin, Texas, March 1988.

    Google Scholar 

  25. J. Chomicki and D. Niwinski. On the Feasibility of Checking Temporal Integrity Constraints. Journal of Computer and System Sciences, 51(3):523–535, December 1995.

    Article  MathSciNet  MATH  Google Scholar 

  26. E.F. Codd. Relational Completeness of Data Base Sub-Languages. In R. Rustin, editor, Data Base Systems, pp. 33–64. Prentice-Hall, 1972.

    Google Scholar 

  27. J. Chomicki and D. Toman. Implementing Temporal Integrity Constraints Using an Active DBMS. IEEE Transactions on Knowledge and Data Engineering, 7(4):566–582, August 1995.

    Article  Google Scholar 

  28. S. Ceri and J. Widom. Deriving Production Rules for Constraint Maintenance. In D. McLeod, R. Sacks-Davis, and H.-J. Schek, editors, International Conference on Very Large Data Bases, pp. 566–577, 1990.

    Google Scholar 

  29. J.M.V. de Castilho, M.A. Casanova, and A.L. Furtado. A Temporal Framework for Database Specifications. In International Conference on Very Large Data Bases, pp. 280–291, 1982.

    Google Scholar 

  30. E.A. Emerson. Temporal and Modal Logic. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B, chapter 16, pp. 995–1072. Elsevier/MIT Press, 1990.

    Google Scholar 

  31. D.M. Gabbay, I. Hodkinson, and M. Reynolds. Temporal Logic: Mathematical Foundations and Computational Aspects. Oxford University Press, 1994.

    Google Scholar 

  32. M. Gertz and U. Lipeck. Deriving Optimized Integrity Monitoring Triggers from Dynamic Integrity Constraints. Data and Knowledge Engineering, 20(2):163–193, 1996.

    Article  MATH  Google Scholar 

  33. K. Hülsmann and G. Saake. Theoretical Foundations of Handling Large Substitution Sets in Temporal Integrity Monitoring. Acta Informatica, 28(4), 1991.

    Google Scholar 

  34. N. Immerman and D. Kozen. Definability with Bounded Number of Bound Variables. Information and Computation, 83(2):121–139, November 1989.

    Article  MathSciNet  MATH  Google Scholar 

  35. ISO. Database Language SQL. ISO/IEC 9075:1992, International Organization for Standardization, 1992.

    Google Scholar 

  36. J. Jaffar and J. Lassez. Constraint Logic Programming. In ACM Symposium on Principles of Programming Languages, pp. 111–119, 1987.

    Google Scholar 

  37. C.S. Jensen, M.D. Soo, and R.T. Snodgrass. Unifying Temporal Data Models via a Conceptual Model. Information Systems, 19(7):513–547, 1994.

    Article  Google Scholar 

  38. J.A.W. Kamp. Tense Logic and the Theory of Linear Order. PhD thesis, University of California, Los Angeles, 1968.

    Google Scholar 

  39. J.A.W. Kamp. Formal Properties of ‘now’. Theoria, 37:227–273, 1971.

    Article  MathSciNet  MATH  Google Scholar 

  40. P.C. Kanellakis, G.M. Kuper, and P.Z. Revesz. Constraint Query Languages. Journal of Computer and System Sciences, 51(1):26–52, August 1995.

    Article  MathSciNet  Google Scholar 

  41. R. Koymans. Specifying Message Passing and Time-Critical Systems with Temporal Logic. PhD thesis, Technische Universiteit Eindhoven, 1989.

    Google Scholar 

  42. F. Kabanza, J. Stevenne, and P. Wolper. Handling Infinite Temporal Data. Journal of Computer and System Sciences, 51(1):3–17, August 1995.

    Article  MathSciNet  MATH  Google Scholar 

  43. C.H. Kung. On Verification of Database Temporal Constraints. In ACM SIGMOD International Conference on Management of Data, pp. 169–179, Austin, Texas, 1985.

    Google Scholar 

  44. U. Lipeck. Transformation of Dynamic Integrity Constraints into Transaction Specifications. Theoretical Computer Science, 76(1):115–142, 1990.

    Article  MathSciNet  MATH  Google Scholar 

  45. N.A. Lorentzos. The Interval-Extended Relational Model and Its Application to Valid-time Databases. In Tansel et al. [TCG+93], pp. 67–91.

    Google Scholar 

  46. U.W. Lipeck and G. Saake. Monitoring Dynamic Integrity Constraints Based on Temporal Logic. Information Systems, 12(3):255–269, 1987.

    Article  MATH  Google Scholar 

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

    Google Scholar 

  48. A. Pnueli. Applications of Temporal Logic to the Specification and Verification of Reactive Systems: a Survey of Current Trends. In Current Trends in Concurrency, pp. 510–584. Springer-Verlag, LNCS 224, 1986.

    Google Scholar 

  49. R.T. Snodgrass and I. Ahn. Temporal Databases. IEEE Computer, 19(9), 1986.

    Google Scholar 

  50. R.T. Snodgrass, I. Ahn, G. Ariav, D. Batory, J. Clifford, C.E. Dyreson, R. Elmasri, F. Grandi, C.S. Jensen, W. Kafer, N. Kline, K. Kulkarni, T.Y.C. Leung, N. Lorentzos, J.F. Roddick, A. Segev, M.D. Soo, and S.A. Sripada. TSQL2 Language Specification. SIGMOD Record, 23(1):65–86, March 1994.

    Article  Google Scholar 

  51. R.T. Snodgrass, M.H. Böhlen, C.S. Jensen, and A. Steiner. Adding Valid Time to SQL/Temporal. ISO/IEC JTC1/SC21/WG3 DBL MAD-146r2 21/11/96, (change proposal), International Organization for Standardization, 1996.

    Google Scholar 

  52. R.T. Snodgrass, C.S. Jensen, and M.H. Böhlen. Evaluating and Enhancing the Completeness of TSQL2. Technical Report TR 95-5, Computer Science Department, University of Arizona, 1995.

    Google Scholar 

  53. R. Snodgrass. The Temporal Query Language TQuel. ACM Transactions on Database Systems, 12(2):247–298, June 1987.

    Article  Google Scholar 

  54. R.T. Snodgrass. An Overview of TQuel. In Tansel et al. [TCG+93], pp. 141–182.

    Google Scholar 

  55. R.T. Snodgrass, editor. The TSQL2 Temporal Query Language. Kluwer Academic Publishers, 1995.

    Google Scholar 

  56. J. Stavi. Functional Completeness over Rationals. Unpublished manuscript, Bar-Ilan University, Israel, 1979.

    Google Scholar 

  57. A.P. Sistla and O. Wolfson. Temporal Triggers in Active Databases. IEEE Transactions on Knowledge and Data Engineering, 7(3):471–486, 1995.

    Article  Google Scholar 

  58. A. Tuzhilin and J. Clifford. A Temporal Relational Algebra as a Basis for Temporal Relational Completeness. In D. McLeod, R. Sacks-Davis, and H.-J. Schek, editors, International Conference on Very Large Data Bases, pp. 13–23, 1990.

    Google Scholar 

  59. A. Tansel, J. Clifford, S. Gadia, S. Jajodia, A. Segev, and R.T. Snodgrass, editors. Temporal Databases: Theory, Design, and Implementation. Benjamin/Cummings, 1993.

    Google Scholar 

  60. D. Toman, J. Chomicki, and D.S. Rogers. Datalog with Integer Periodicity Constraints. In M. Bruynooghe, editor, International Logic Programming Symposium, pp. 189–203. MIT Press, 1994. Full version to appear in Journal of Logic Programming.

    Google Scholar 

  61. D. Toman and D. Niwinski. First-Order Queries over Temporal Databases Inexpressible in Temporal Logic. In International Conference on Extending Database Technology, pp. 307–324, Avignon, France, 1996. Springer-Verlag, LNCS 1057.

    Google Scholar 

  62. D. Toman. Point vs. Interval-based Query Languages for Temporal Databases. In ACM Symposium on Principles of Database Systems, pp. 58–67, Montréal, Canada, June 1996.

    Google Scholar 

  63. D. Toman. Point-based Temporal Extensions of SQL. In International Conference on Deductive and Object-Oriented Databases, 1997.

    Google Scholar 

  64. J.D. Ullman. Principles of Database and Knowledge-Base Systems, volume 2. Computer Science Press, 1989.

    Google Scholar 

  65. M.Y. Vardi. A Temporal Fixpoint Calculus. In ACM Symposium on Principles of Programming Languages, pp. 250–259, 1988.

    Google Scholar 

  66. J.F.A.K. van Benthem. The Logic of Time. D. Reidel, 1983.

    Google Scholar 

  67. J. Widom and S. Ceri, editors. Active Database Systems. Morgan Kaufmann, 1996.

    Google Scholar 

  68. P. Wolper. Temporal Logic Can Be More Expressive. Information and Control, 56:72–99, 1983.

    Article  MathSciNet  MATH  Google Scholar 

  69. P. Wolper. On the Relation of Programs and Computations to Models of Temporal Logic. In B. Banieqbal, B. Barringer, and A. Pnueli, editors, Temporal Logic in Specification, pp. 75–123. Springer-Verlag, LNCS 398, 1989.

    Google Scholar 

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Chomicki, J., Toman, D. (1998). Temporal Logic in Information Systems. In: Chomicki, J., Saake, G. (eds) Logics for Databases and Information Systems. The Springer International Series in Engineering and Computer Science, vol 436. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5643-5_3

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  • DOI: https://doi.org/10.1007/978-1-4615-5643-5_3

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