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Monodic Fragments of First-Order Temporal Logics: 2000–2001 A.D.

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Logic for Programming, Artificial Intelligence, and Reasoning (LPAR 2001)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2250))

Abstract

The aim of this paper is to summarize and analyze some results obtained in 2000–2001 about decidable and undecidable fragments of various first-order temporal logics, give some applications in the field of knowledge representation and reasoning, and attract the attention of the ‘temporal community’ to a number of interesting open problems.

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References

  1. M. Abadi. The power of temporal proofs. In Proc. Symp. on Logic in Computer Science, pages 176–186, Ithaca, 1979.

    Google Scholar 

  2. S. Abiteboul, L. Herr, and J. van den Bussche. Temporal connectives versus explicit timestamps in temporal query languages. In J. Clifford and A. Tuzhilin, editors, Recent Advances in Temporal Databases, pages 43–57. Springer, 1995.

    Google Scholar 

  3. S. Abiteboul, L. Herr, and J. van den Bussche. Temporal versus first-order logic in query temporal databases. In ACM Symposium on Principles of Database Systems, pages 49–57, Montreal, Canada, 1996.

    Google Scholar 

  4. H. Andréka, I. Németi, and I. Sain. Completeness problems in verification of programs and program schemes. In Mathematical Foundations of Computer Science 1979, Lecture Notes in Computer Science. Springer-Verlag, 1979.

    Google Scholar 

  5. H. Andréka, J. van Benthem, and I. Németi. Modal languages and bounded fragments of predicate logic. Journal of Philosophical Logic, 27:217–274, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Artale and E. Franconi. A computational account for a description logic of time and action. In Proceedings of the fourth Conference on Principles of Knowledge Representation and Reasoning, pages 3–14, Montreal, Canada, 1994. Morgan Kaufmann.

    Google Scholar 

  7. A. Artale and E. Franconi. Temporal description logics. In Handbook of Time and Temporal Reasoning in Arti.cial Intelligence. MIT Press, 2001. To appear.

    Google Scholar 

  8. A. Artale, E. Franconi, M. Mosurovic, F. Wolter, and M. Zakharyaschev. The DLRUS temporal description logic. In D. McGuinness, P. Patel-Schneider, C. Goble and R. Möller, editors, Proceedings of the 2001Description Logic Workshop (DL-2001), Stanford, pages 96–105, 2001.

    Google Scholar 

  9. F. Baader and A. Laux. Terminological logics with modal operators. In Proceedings of the 14th International Joint Conference on Artificial Intelligence, pages 808–814, Montreal, Canada, 1995. Morgan Kaufmann.

    Google Scholar 

  10. F. Baader and H.J. Ohlbach. A multi-dimensional terminological knowledge representation language. Journal of Applied Non-Classical Logic, 5:153–197, 1995.

    MATH  MathSciNet  Google Scholar 

  11. B. Bennett, A. Cohn, and A. Isli. A logical approach to incorporating qualitative spatial reasoning into GIS. In Proceedings the International Conference on Spatial Information Theory (COSIT), pages 503–504, 1997.

    Google Scholar 

  12. J. van Benthem. Dynamic bits and pieces. Technical Report LP-97-01, ILLC, University of Amsterdam, 1997.

    Google Scholar 

  13. E. Börger, E. Grädel, and Yu. Gurevich. The Classical Decision Problem. Perspectives in Mathematical Logic. Springer, 1997.

    Google Scholar 

  14. R. Brachman and J. Schmolze. An overview of the KL-ONE knowledge representation system. Cognitive Science, 9:171–216, 1985.

    Article  Google Scholar 

  15. J. Büchi. On a decision method in restricted second order arithmetic. In Logic, Methodology, and Philosophy of Science: Proc. 1960 Intern. Congress, pages 1–11. Stanford University Press, 1962.

    Google Scholar 

  16. J. Burgess. Logic and time. Journal of Symbolic Logic, 44:566–582, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  17. J. Burgess and Yu. Gurevich. The decision problem for linear temporal logic. Notre Dame J. Formal Logic, 26(2):115–128, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  18. D. Calvanese, G. De Giacomo, M. Lenzerini, and D. Nardi. Reasoning in expressive description logics. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, pages 1581–1634. Elsevier Science Publishers B.V., 2001.

    Google Scholar 

  19. D. Calvanese, M. Lenzerini, and D. Nardi. Unifying class-based representation formalisms. Journal of Arti.cial Intelligence Research, 11: 199–240, 1999

    MATH  MathSciNet  Google Scholar 

  20. J. Chomicki. Temporal query languages: a survey. In D. Gabbay and H.J. Ohlbach, editors, Temporal Logic, First International Conference, pages 506–534, Montreal, Canada, 1994. Springer-Verlag.

    Chapter  Google Scholar 

  21. J. Chomicki and D. Niwinski. On the feasibility of checking temporal integrity constraints. Journal of Computer and Systems Sciences, 51:523–535, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  22. A. Degtyarev, M. Fisher, and A. Lisitsa. Equality and monodic first-order temporal logic. Studia Logica, 2001. (To appear.)

    Google Scholar 

  23. A. Degtyarev and M. Fisher. Towards First-Order Temporal Resolution. In F. Baader, G. Brewka and T. Eiter, editors, KI 2001: Advances in Artificial Intelligence, volume 2174 of LNCS, pages 18–32. Springer, 2001.

    Chapter  Google Scholar 

  24. M. Egenhofer and R. Franzosa. Point-set topological spatial relations. International Journal of Geographical Information Systems, 5:161–174, 1991.

    Article  Google Scholar 

  25. M. Egenhofer and D. Mark. Naive geography. In A. Frank and W. Kuhn, editors, Spatial Information Theory: a theoretical basis for GIS, volume 988 of Lecture Notes in Computer Science, pages 1–16. Springer-Verlag, Berlin, 1995.

    Google Scholar 

  26. E. Emerson. Temporal and modal logic. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 996–1076, 1990.

    Google Scholar 

  27. R. Fagin, J. Halpern, Y. Moses, and M. Vardi. Reasoning about Knowledge. MIT Press, 1995.

    Google Scholar 

  28. D. Gabbay, I. Hodkinson, and M. Reynolds. Temporal Logic: Mathematical Foundations and Computational Aspects, Volume 1. Oxford University Press, 1994.

    Google Scholar 

  29. D. Gabbay, A. Kurucz, F. Wolter, and M. Zakharyaschev. Many-Dimensional Modal Logics: Theory and Applications. Elsevier, 2002.

    Google Scholar 

  30. D. Gabbay, M. Reynolds, and M. Finger. Temporal Logic: Mathematical Foundations and Computational Aspects, Volume 2. Oxford University Press, 2000.

    Google Scholar 

  31. J. Garson. Quantification in modal logic. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, volume 2, pages 249–307. Kluwer Academic Publishers, 1984.

    Google Scholar 

  32. C. Günsel and M. Wittmann. Towards an implementation of the temporal description logic T LALC. In D. McGuinness, P. Patel-Schneider, C. Goble and R. Möller, editors, Proceedings of the 2001Description Logic Workshop (DL-2001), Stanford, pages 162–169, 2001.

    Google Scholar 

  33. E. Grädel. Decision procedures for guarded logics. In Automated Deduction— CADE-16, Proceedings of the 16th International Conference on Automated Deduction, volume 1632 of LNCS, pages 31–51. Springer, 1999.

    Google Scholar 

  34. R. Hirsch, I. Hodkinson, and A. Kurucz. On modal logics between K × K × K and S5 × S5 × S5. Journal of Symbolic Logic, 2001. (In press.)

    Google Scholar 

  35. I. Hodkinson, F. Wolter, and M. Zakharyaschev. Decidable fragments of first-order temporal logics. Annals of Pure and Applied Logic, 106:85–134, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  36. I. Hodkinson, A. Kurucz, F. Wolter, and M. Zakharyaschev. Decidable and undecidable fragments of first-order logics of branching time. Manuscript, 2001.

    Google Scholar 

  37. I. Hodkinson. Monodic packed fragment with equality is decidable. Studia Logica, 2001. (To appear.)

    Google Scholar 

  38. H. Kamp. Tense Logic and the Theory of Linear Order. Ph.D. Thesis, University of California, Los Angeles, 1968.

    Google Scholar 

  39. H. Kamp. Formal properties of ‘now’. Theoria, 37:237–273, 1971.

    MathSciNet  Google Scholar 

  40. C. Lutz, H. Sturm, F. Wolter, and M. Zakharyaschev. Tableaux for temporal description logic with constant domains. In Proceedings of the 1st International Joint Conference on Automated Reasoning, IJCAR 2001, pages 121–136, LNAI 2083. Springer-Verlag, 2001.

    Google Scholar 

  41. R. Maddux. The equational theory of CA3 is undecidable. Journal of Symbolic Logic, 45:311–316, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  42. Z. Manna and A. Pnueli. The temporal logic of reactive and concurrent systems. Springer-Verlag, 1992.

    Google Scholar 

  43. Z. Manna and A. Pnueli. Temporal Veri.cation of Reactive Systems: Safety. Springer-Verlag, 1995.

    Google Scholar 

  44. S. Merz. Decidability and incompleteness results for first-order temporal logics of linear time. Journal of Applied Non-classical Logic, 2, 1992.

    Google Scholar 

  45. A. Pnueli. Applications of temporal logic to the specification and verification of reacrive systems, a survey of current trends. In Current Trends in Concurrency, Lecture Notes in Computer Science, pages 510–584. Springer-Verlag, 1986.

    Chapter  Google Scholar 

  46. M. Rabin. Decidability of second order theories and automata on infinite trees. Trans. Amer. Math. Soc., 141:1–35, 1969.

    Article  MATH  MathSciNet  Google Scholar 

  47. D. Randell, Z. Cui, and A. Cohn. A spatial logic based on regions and connection. In Proceedings of the 3rd International Conference on Knowledge Representation and Reasoning, pages 165–176. Morgan Kaufmann, 1992.

    Google Scholar 

  48. M. Reynolds. Axiomatizing first-order temporal logic: Until and Since over linear time. Studia Logica, 57:279–302, 1996.

    Article  MATH  MathSciNet  Google Scholar 

  49. K. Schild. Combining terminological logics with tense logic. In Proceedings of the 6th Portuguese Conference on Artificial Intelligence, pages 105–120, Porto, 1993.

    Google Scholar 

  50. A. Sernadas. Temporal aspect of logical procedure definition. Information Systems, 5:167–187, 1980.

    Article  MATH  Google Scholar 

  51. C. Stirling. Modal and temporal logics. In D. Gabbay, S. Abramsky, and T. Maibaum, editors, Handbook of Logic in Computer Science, volume 2, pages 478–551. Clarendon Press, Oxford, 1992.

    Google Scholar 

  52. H. Sturm and F. Wolter. A tableau calculus for temporal description logic: the expanding domain case. Journal of Logic and Computation, 2001. (In press.)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  54. A. Szalas and L. Holenderski. Incompleteness of first-order temporal logic with until. Theoretical Computer Science, 57:317–325, 1988.

    Article  MathSciNet  MATH  Google Scholar 

  55. P. Wolper. The tableau method for temporal logic: an overview. Logique et Analyse, 28:119–152, 1985.

    MathSciNet  MATH  Google Scholar 

  56. F. Wolter and M. Zakharyaschev. Satisfiability problem in description logics with modal operators. In A.G. Cohn, L. Schubert, and S.C. Shapiro, editors, Proceedings of the sixth Conference on Principles of Knowledge Representation and Reasoning, KR’98, Trento, Italy, pages 512–523, Montreal, Canada, 1998. Morgan Kaufmann.

    Google Scholar 

  57. F. Wolter and M. Zakharyaschev. Modal description logics: modalizing roles. Fundamenta Informaticae, 39:411–438, 1999.

    MATH  MathSciNet  Google Scholar 

  58. F. Wolter and M. Zakharyaschev. Spatial reasoning in RCC-8 with Boolean region terms. In W. Horn, editor, Proceedings of the fourteenth European Conference on Artificial Intelligence, ECAI 2000, Berlin, Germany, pages 244–248. IOS Press, 2000.

    Google Scholar 

  59. F. Wolter and M. Zakharyaschev. Spatio-temporal representation and reasoning based on RCC-8. In Proceedings of the seventh Conference on Principles of Knowledge Representation and Reasoning, KR2000, Breckenridge, USA, pages 3–14, Montreal, Canada, 2000. Morgan Kaufmann.

    Google Scholar 

  60. F. Wolter and M. Zakharyaschev. Temporalizing description logics. In D. Gabbay and M. de Rijke, editors, Frontiers of Combining Systems II, pages 379–401. Studies Press/Wiley, 2000.

    Google Scholar 

  61. F. Wolter and M. Zakharyaschev. Decidable fragments of first-order modal logics. Journal of Symbolic Logic, 2001. (In press).

    Google Scholar 

  62. F. Wolter and M. Zakharyaschev. Qualitative spatio-temporal representation and reasoning: a computational perspective. In G. Lakemeyer and B. Nebel, editors, Exploring Artificial Intelligence in the New Millenium, Morgan Kaufmann, 2001.

    Google Scholar 

  63. F. Wolter and M. Zakharyaschev. Axiomatizing the monodic fragment of first-order temporal logic. Annals of Pure and Applied Logic, 2001. (In press).

    Google Scholar 

  64. A. Zanardo. Branching-time logic with quantification over branches: the point of view of modal logic. Journal of Symbolic Logic, 61:1–39, 1996.

    Article  MATH  MathSciNet  Google Scholar 

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Hodkinson, I., Wolter, F., Zakharyaschev, M. (2001). Monodic Fragments of First-Order Temporal Logics: 2000–2001 A.D.. In: Nieuwenhuis, R., Voronkov, A. (eds) Logic for Programming, Artificial Intelligence, and Reasoning. LPAR 2001. Lecture Notes in Computer Science(), vol 2250. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45653-8_1

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  • DOI: https://doi.org/10.1007/3-540-45653-8_1

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