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An overview of temporal and modal logic programming

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Temporal Logic (ICTL 1994)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 827))

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Abstract

This paper presents an overview of the development of the field of temporal and modal logic programming. We review temporal and modal logic programming languages under three headings: (1) languages based on interval logic, (2) languages based on temporal logic, and (3) languages based on (multi)modal logics. The overview includes most of the major results developed, and points out some of the similarities, and the differences, between languages and systems based on diverse temporal and modal logics. The paper concludes with a brief summary and discussion.

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References

  1. M. Abadi. The power of temporal proofs. Theoretical Computer Science, 65(1989):35–83, 1989.

    Article  Google Scholar 

  2. M. Abadi and Z. Manna. Nonclausal temporal deduction. In R. Parikh, editor, Proc. of Conference on Logics of Programs, volume 193 of LNCS, pages 1–15. Springer-Verlag, 1985.

    Google Scholar 

  3. M. Abadi and Z. Manna. Temporal logic programming. In Proceedings of the 1987 Symposium on Logic Programming, pages 4–16, San Fransisco, Calif, 1987. IEEE Computer Society Press.

    Google Scholar 

  4. M. Abadi and Z. Manna. Temporal logic programming. Journal of Symbolic Computation, 8:277–295, 1989.

    Google Scholar 

  5. Hassan Ait-Kaci. The WAM: A (Real) Tutorial. Paris Research Laboratory, Digital Equipment Corporation, Paris, France, 1990.

    Google Scholar 

  6. Seiki Akama. A proposal of modal logic programming (extended abstract). In Proc. of the 6th Canadian Conference on Artificial Intelligence, pages 99–102, École Polytechnique de Montréal, Montréal, Québec, Canada, May 1986. Presses de l'Université du Québec.

    Google Scholar 

  7. Seiki Akama. A meta-logical foundation of modal logic programming. 1-20-1, Higashi-Yurigaoka, Asao-ku, Kawasaki-shi, 215, Japan, December 1989.

    Google Scholar 

  8. J. F. Allen. Maintaining knowledge about temporal intervals. Communications of the ACM, 26:832–843, November 1983.

    Article  Google Scholar 

  9. T. Aoyagi, M. Fujita, and T. Moto-oka. Temporal logic programming language Tokio. In E. Wada, editor, Logic Programming'85, volume 221 of LNCS, pages 138–147. Springer-Verlag, 1986.

    Google Scholar 

  10. E. A. Ashcroft, A. A. Faustini, and B. Huey. Eduction: A model of parallel computation and the programming language Lucid. In Proc. of Phoenix Conference on Computers and Communications, pages 9–15. IEEE Computer Society Press, 1985.

    Google Scholar 

  11. E. A. Ashcroft and W. W. Wadge. Lucid — a formal system for writing and proving programs. SIAM Journal on Computing, 5:336–54, September 1976.

    Article  Google Scholar 

  12. Y. Aufray and P. Enjalbert. Modal theorem proving: an equational viewpoint. To appear in Journal of Logic and Computation, 1992.

    Google Scholar 

  13. Philippe Balbiani, Luis Fariñas del Cerro, and Andreas Herzig. Declarative semantics for modal logic programs. In Proceedings of the 1988 International Conference on Fifth Generation Computer Systems, pages 507–514. ICOT, 1988.

    Google Scholar 

  14. Philippe Balbiani, Andreas Herzig, and Mamede Lima-Marques. TIM: The Toulouse inference machine for non-classical logic programming. In PDK'91: International Workshop on Processing Declarative Knowledge, volume 567 of LNAI, pages 365–382. Springer-Verlag, 1991.

    Google Scholar 

  15. Philippe Balbiani, Andreas Herzig, and Mamede Lima-Marques. Implementing Prolog extensions: a parallel inference machine. In Proc. of the 1992 International Conference on Fifth Generation Computer Systems, pages 833–842. ICOT, 1992.

    Google Scholar 

  16. M. Baudinet. On the semantics of temporal logic programming. Technical Report STAN-CS-88-1203, Computer Science Department, Stanford University, Stanford, Calif, June 1988.

    Google Scholar 

  17. M. Baudinet. Temporal logic programming is complete and expressive. In Conference Record of the Sixteenth ACM Symposium on Principles of Programming Languages, pages 267–280, Austin, Texas, January 1989. The Association for Computing Machinery.

    Google Scholar 

  18. M. Baudinet. A simple proof of the completeness of temporal logic programming. In L. Fariñas del Cerro and M. Penttonen, editors, Intensional Logics for Programming, pages 51–83. Oxford University Press, 1992.

    Google Scholar 

  19. M. Baudinet, J. Chomicki, and P. Wolper. Temporal deductive databases. In A. Tansel and et al, editors, Temporal Databases: Theory, Design, and Implementation. Benjamin/Cummings Publishing Company, Redwood City, CA, 1993.

    Google Scholar 

  20. Marianne Baudinet. Proving termination properties of Prolog programs: a semantic approach. Journal of Logic Programming, 14(1 & 2):1–30, October 1992.

    Article  Google Scholar 

  21. Pierre Bieber, Luis Fariñas del Cerro, and Andreas Herzig. MOLOG: A Modal Prolog. In E. Lusk and R. Overbeek, editors, Proceedings of the 9th International Conference on Automated Deduction, pages 762–763. Springer-Verlag, 1988.

    Google Scholar 

  22. H. A. Blair, A. L. Brown, and V. S. Subrahmanian. Monotone logic programming. In L. Fariñas del Cerro and M. Penttonen, editors, Intensional Logics for Programming, pages 1–22. Oxford University Press, 1992.

    Google Scholar 

  23. H. A. Blair and V. S. Subrahmanian. Paraconsistent logic programming. Theoretical Computer Science, 68:135–154, 1989.

    Article  Google Scholar 

  24. H.A. Blair et al. A logic programming semantics scheme, Part I. Technical Report LPRG-TR-88-8, Logic Programming Research Group, Syracuse University, 1988.

    Google Scholar 

  25. Christoph Brzoska. Temporal logic programming and its relation to constraint logic programming. In V. Saraswat and K. Ueda, editors, Proceedings of the 1991 International Logic Programming Symposium, pages 661–677, San Diego, Calif, October 28–31 1991.

    Google Scholar 

  26. Christoph Brzoska. Temporal logic programming with metric and past operators. Universität Karlsruhe, P.O.Box 6980, D-7500 Karlsruhe, Germany, January 1992.

    Google Scholar 

  27. R. Bull and K. Segerberg. Basic modal logic. In D. M. Gabbay and F. Guethner, editors, Handbook of Philosophical Logic, Vol. II, pages 1–88. D. Reidel Publishing Company, 1984.

    Google Scholar 

  28. J. P. Burgess. Basic tense logic. In D. M. Gabbay and F. Guethner, editors, Handbook of Philosophical Logic, Vol. II, pages 89–134. D. Reidel Publishing Company, 1984.

    Google Scholar 

  29. B. F. Chellas. Modal Logic: An Introduction. Cambridge University Press, 1980.

    Google Scholar 

  30. Cheng-Chia Chen and I-Peng Lin. The computational complexity of satisfiability of temporal Horn formulas in propositional linear-time logic. Information Processing Letters, 45:131–136, March 1993.

    Article  MathSciNet  Google Scholar 

  31. Jan Chomicki and Tomasz Imieliński. Temporal deductive databases and infinite objects. In Proceedings of the Seventh ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, pages 61–73. The Association for Computing Machinery, 1988.

    Google Scholar 

  32. Eugène Chouraqui. Formal expression of time in a knowledge base. In P. Smets, A. Mamdani, D. Dubois, and H. Prade, editors, Non-Standard Logics for Automated Reasoning, pages 81–103. Academic Press, 1988.

    Google Scholar 

  33. John G. Cleary and Vinit N. Kaushik. Updates in a temporal logic programming language. Technical report, Department of Computer Science, University of Calgary, Calgary, Alberta, Canada, 1991.

    Google Scholar 

  34. James Clifford and David S. Warren. Formal semantics for time in databases. ACM Transactions on Database Systems, 8(2):214–254, June 1983.

    Article  Google Scholar 

  35. W. Clocksin and C. Mellish. Programming in Prolog. Springer-Verlag, 1981.

    Google Scholar 

  36. Françoise Debart, Patrice Enjalbert, and Madeleine Lescot. Multimodal logic programming using equational and order-sorted logic. Theoretical Computer Science, 105(1992):141–166, 1992.

    Article  Google Scholar 

  37. L. Fariñas del Cerro and M. Penttonen. The complexity of the satisfiability of modal Horn clauses. Journal of Logic Programming, 4:1–10, March 1987.

    Article  Google Scholar 

  38. Luis Fariñas del Cerro. A simple deduction method for modal logic. Information Processing Letters, 14(2), 1982.

    Google Scholar 

  39. Luis Fariñas del Cerro. MOLOG: A system that extends PROLOG with modal logic. New Generation Computing, 4:35–50, 1986.

    Google Scholar 

  40. Luis Fariñas del Cerro and Andreas Herzig. Metaprogramming through intensional deduction: some examples. In Meta-Programming in Logic: Proc. of the Third International Workshop, META-92, Uppsala, Sweden, pages 11–25. Springer-Verlag, June 1992.

    Google Scholar 

  41. Luis Fariñas del Cerro and Martti Penttonen, editors. Intensional Logics for Programming. Oxford University Press, 1992. ISBN 019-853775-1.

    Google Scholar 

  42. A. A. Faustini and W. W. Wadge. An eductive interpreter for pLucid. Technical Report TR-006-86, Department of Computer Science and Engineering, Arizona State University, 1986.

    Google Scholar 

  43. Melvin Fitting. Logic programming on a topological bilattice. Fundamenta Informaticae, XI:209–18, 1988.

    Google Scholar 

  44. D. M. Gabbay. Modal and temporal logic programming. In A. Galton, editor, Temporal Logics and Their Applications, pages 197–237. Academic Press, 1987.

    Google Scholar 

  45. D. M. Gabbay. A temporal logic programming machine [modal and temporal logic programming, Part 2]. Department of Computing, Imperial College, November 1989.

    Google Scholar 

  46. D. M. Gabbay. Metalevel features in the object level: modal and temporal logic programming III. In L. Fariñas del Cerro and M. Penttonen, editors, Intensional Logics for Programming, pages 85–123. Oxford University Press, 1992.

    Google Scholar 

  47. Dov Gabbay and Peter McBrien. Temporal logic & historical databases. In Proceedings of the 17th Very Large Data Bases Conference, pages 423–430, Barcelona, Spain, September 1991. Morgan Kauffman, Los Altos, Calif.

    Google Scholar 

  48. A. Galton. Temporal logic and computer science: an overwiev. In A. Galton, editor, Temporal Logics and Their Applications, pages 1–52. Academic Press, 1987.

    Google Scholar 

  49. A. Galton, editor. Temporal Logics and Their Applications. Academic Press, 1987.

    Google Scholar 

  50. R. Gerth, M. Codish, Y. Lichtenstein, and E. Y. Shapiro. Fully abstract denotational semantics for Flat Concurrent Prolog. Technical Report CS88-03, Department of Applied Math. and Computer Science, The Weizmann Institute of Science, Rehovot, Israel, April 1988.

    Google Scholar 

  51. R. Goldblatt. Logics of Time and Computation. CSLI — Center for the Study of Language and Information, Stanford University, 1987. Lecture Notes no:7.

    Google Scholar 

  52. R. Hale. Temporal logic programming. In A. Galton, editor, Temporal Logics and Their Applications, pages 91–119. Academic Press, 1987.

    Google Scholar 

  53. C. Hewitt and Gul Agha. Guarded Horn clause languages: Are they deductive and logical? In Proceedings of the 1988 International Conference on Fifth Generation Computer Systems, pages 650–657. ICOT, 1988.

    Google Scholar 

  54. Tomas Hrycej. Temporal Prolog. In Proc. of the European Conference on Artificial Intelligence, pages 296–301, Munich, Germany, 1988.

    Google Scholar 

  55. Tomas Hrycej. A temporal extension of Prolog. Journal of Logic Programming, 15(1 & 2):113–145, January 1993.

    Article  Google Scholar 

  56. G. E. Hughes and M. J. Creswell. An Introduction to Modal Logic. Methuen and Co Ltd, London, 1968.

    Google Scholar 

  57. P. Jackson, H. Reichgelt, and F. van Harmelen, editors. Logic-Based Knowledge Representation. MIT Press, 1989.

    Google Scholar 

  58. J. Jaffar and J-L. Lassez. Constraint logic programming. In Conference Record of the Fourteenth ACM Symposium on Principles of Programming Languages, pages 111–119, Munich, Germany, 1987. ACM Press.

    Google Scholar 

  59. Max I. Kanovich. Linear logic as a logic of computations. In Proc. of the 7th Annual IEEE Symposium on Logic in Computer Science, pages 200–210, Santa Cruz, Calif, June 1992. IEEE Computer Society Press.

    Google Scholar 

  60. S. Kono, T. Aoyagi, M. Fujita, and H. Tanaka. Implementation of temporal logic programming language Tokio. In E. Wada, editor, Logic Programming'85, volume 221 of LNCS, pages 138–147. Springer-Verlag, 1986.

    Google Scholar 

  61. R. A. Kowalski. Predicate logic as programming language. In Proceedings of IFIP'74, pages 569–574, Amsterdam, 1974. North-Holland.

    Google Scholar 

  62. Valentinas Kriaučiukas. Non-classical models for logic programs. In PDK'91: International Workshop on Processing Declarative Knowledge, volume 567 of LNAI, pages 179–190. Springer-Verlag, 1991.

    Google Scholar 

  63. Fred Kroger. Temporal Logic of Programs. Springer-Verlag, Berlin Heidelberg, 1987.

    Google Scholar 

  64. J. W. Lloyd. Foundations of Logic Programming. Springer-Verlag, 1984.

    Google Scholar 

  65. Z. Manna and A. Pnueli. Verification of concurrent programs: the temporal framework. In Boyer and Moore, editors, Correctness Problem in Computer Science, pages 215–273. Academic Press, 1981.

    Google Scholar 

  66. Fujita Masahiro et al. Using the temporal logic programming language Tokio for algorithm description and automatic CMOS gate array synthesis. In E. Wada, editor, Logic Programming'85, volume 221 of LNCS, pages 246–255. Springer-Verlag, 1986.

    Google Scholar 

  67. W. H. Mitchell. Intensional Horn clause logic as a programming language — it's use and implementation. Master's thesis, Department of Computer Science and Engineering, Arizona State University, Tempe, Arizona, 1988.

    Google Scholar 

  68. W. H. Mitchell and A. A. Faustini. The intensional logic language InTense. In Proceedings of the 1989 International Symposium on Lucid and Intensional Programming, Arizona State University, May 8 1989.

    Google Scholar 

  69. R. Montague. Formal Philosophy, Selected Papers of Richard Montague. Yale University Press, 1974. edited by Richmond Thomason.

    Google Scholar 

  70. B. Moszkowski. Executing Temporal Logic Programs. Cambridge University Press, 1986.

    Google Scholar 

  71. Hans Jürgen Ohlbach. A resolution calculus for modal logics. In E. Lusk and R. Overbeek, editors, Proceedings of the 9th International Conference on Automated Deduction, pages 500–516. Springer-Verlag, 1988.

    Google Scholar 

  72. M. A. Orgun. On temporal deductive databases. Technical Report 93-140C, Department of Computing, Macquarie University, Sydney, NSW 2109, Australia, December 1993.

    Google Scholar 

  73. M. A. Orgun and W. Du. Multi-dimensional logic programming. In Proceedings of ICCI'94: The Sixth International Conference on Computing and Information, Trent University, Peterborough, Ontario, Canada, May 26–28 1994. To appear.

    Google Scholar 

  74. M. A. Orgun and W. W. Wadge. Chronolog: A temporal logic programming language and its formal semantics. Department of Computer Science, University of Victoria, Victoria, B.C., Canada, January 1988.

    Google Scholar 

  75. M. A. Orgun and W. W. Wadge. A theoretical basis for intensional logic programming. In Proceedings of the 1988 International Symposium on Lucid and Intensional Programming, pages 33–49, Sidney, B.C., Canada, April 7–8 1988.

    Google Scholar 

  76. M. A. Orgun and W. W. Wadge. Theory and practice of temporal logic programming. In L. Fariñas del Cerro and M. Penttonen, editors, Intensional Logics for Programming, pages 23–50. Oxford University Press, 1992.

    Google Scholar 

  77. M. A. Orgun and W. W. Wadge. Towards a unified theory of intensional logic programming. Journal of Logic Programming, 13(4):413–440, August 1992.

    Article  Google Scholar 

  78. M. A. Orgun and W. W. Wadge. Chronolog admits a complete proof procedure. In Proceedings of the Sixth International Symposium on Lucid and Intensional Programming, pages 120–135, Université Laval, Québec City, Québec, Canada, April 26–27 1993.

    Google Scholar 

  79. M. A. Orgun and W. W. Wadge. Extending temporal logic programming with choice predicates non-determinism. To appear in Journal of Logic and Computation, 1994.

    Google Scholar 

  80. M. A. Orgun, W. W. Wadge, and W. Du. Chronolog(Z): Linear-time logic programming. In Proceedings of ICCI'93: The Fifth International Conference on Computing and Information, Laurentian University, Sudbury, Ontario, Canada, May 27–29 1993. IEEE Computer Society Press.

    Google Scholar 

  81. R. Ramanujam. Semantics of distributed logic programs. Theoretical Computer Science, 68:203–220, 1989.

    Article  Google Scholar 

  82. N. Rescher and A. Urquhart. Temporal Logic. Springer-Verlag, 1971.

    Google Scholar 

  83. D. W. Rolston. Chronolog: A pure tense-logic-based infinite-object programming language. Department of Computer Science and Engineering, Arizona State University, Tempe, Arizona, August 1986.

    Google Scholar 

  84. D. W. Rolston. Toward a tense-logic-based mitigation of the frame problem. In F. M. Brown, editor, Proceedings of the 1987 Workshop on the Frame Problem in AI, Lawrence, Kansas, April 1987. Morgan Kaufmann, Los Altos, Calif.

    Google Scholar 

  85. D. W. Rolston. Parallel Logic Programming Using an Intensional Model of Computation. PhD thesis, Department of Computer Science and Engineering, Arizona State University, Tempe, Arizona, 1992.

    Google Scholar 

  86. F. Sadri. Three approaches to temporal reasoning. In A. Galton, editor, Temporal Logics and Their Applications, pages 121–168. Academic Press, 1987.

    Google Scholar 

  87. Y. Sakakibara. Programming in modal logic: An extension of PROLOG based on modal logic. In E. Wada, editor, Logic Programming'86, volume 264 of LNCS, pages 81–91. Springer-Verlag, 1987.

    Google Scholar 

  88. Takahashi Sakuragawa. Temporal Prolog. In Proc. of RIMS Conference on Software Science and Engineering. Springer-Verlag, 1987.

    Google Scholar 

  89. P. Schroeder-Heister, editor. International Workshop on Extensions of Logic Programming, volume 475 of LNAI. Springer-Verlag, 1991.

    Google Scholar 

  90. D. Scott. Advice on modal logic. In K. Lambert, editor, Philosophical Problems in Logic, pages 143–173. D.Reidel Publishing Company, 1970.

    Google Scholar 

  91. E. Shapiro. The family of concurrent logic programming languages. In Friedrich L. Bauer, editor, Logic, Algebra, and Computation, pages 359–485. Springer-Verlag, Berlin Heidelberg, 1991.

    Google Scholar 

  92. Yoav Shoham. Reasoning About Change. MIT Press, 1988.

    Google Scholar 

  93. P. Smets, A. Mamdani, D. Dubois, and H. Prade, editors. Non-Standard Logics for Automated Reasoning. Academic Press, 1988.

    Google Scholar 

  94. A. Szalas. Concerning the semantic consequence relation in first-order temporal logic. Theoretical Computer Science, 47:329–334, 1986.

    Article  Google Scholar 

  95. Alexander Tuzhilin and James Clifford. A temporal relational algebra as a basis for temporal relational completeness. In D. McLeod, R. Sacks-Davis, and H. Schek, editors, Proceedings of the 16th International Conference on Very Large Data Bases, pages 13–23, Brisbane, Australia, August 13–16 1990. Morgan Kaufmann Publishers Inc., Los Altos, Calif.

    Google Scholar 

  96. M.H. van Emden and R.A. Kowalski. The semantics of predicate logic as a programming language. Journal of the Association for Computing Machinery, 23:733–42, 1976.

    Google Scholar 

  97. M.H. van Emden and M.A. Nait Abdallah. Top-down semantics of fair computations of logic programs. Technical Report CS-84-27, Department of Computer Science, University of Waterloo, October 1984.

    Google Scholar 

  98. M. Y. Vardi. A temporal fixpoint calculus. In Conference Record of the Sixteenth ACM Symposium on Principles of Programming Languages, pages 250–259, San Diego, Calif, January 1988. ACM Press.

    Google Scholar 

  99. W. W. Wadge. Tense logic programming: a respectable alternative. Department of Computer Science, University of Victoria, Victoria, B.C., Canada, 1985.

    Google Scholar 

  100. W. W. Wadge. Tense logic programming: a respectable alternative. In Proceedings of the 1988 International Symposium on Lucid and Intensional Programming, pages 26–32, Sidney, B.C., Canada, April 7–8 1988.

    Google Scholar 

  101. W. W. Wadge and E. A. Ashcroft. Lucid, the Dataflow Programming Language. Academic Press, 1985.

    Google Scholar 

  102. David H. D. Warren. An abstract Prolog instruction set. Technical report, SRI International, Menlo Park, Calif, October 1983.

    Google Scholar 

  103. R. Wojcicki. Theory of Logical Calculi. Kluwer Academic Publishers, 1988.

    Google Scholar 

  104. K. Zhang and M. A. Orgun. Parallel execution of temporal logic programs using dataflow computation. In Proceedings of ICCI'94: The Sixth International Conference on Computing and Information, Trent University, Peterborough, Ontario, Canada, May 26–28 1994. To appear.

    Google Scholar 

  105. Kang Zhang and R. Thomas. DIALOG — A dataflow model for parallel execution of logic programs. Future Generation Computer Systems, 6(4):373–388, September 1991.

    Google Scholar 

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Dov M. Gabbay Hans Jürgen Ohlbach

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Orgun, M.A., Ma, W. (1994). An overview of temporal and modal logic programming. In: Gabbay, D.M., Ohlbach, H.J. (eds) Temporal Logic. ICTL 1994. Lecture Notes in Computer Science, vol 827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014004

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