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ISRN Artificial Intelligence
Volume 2012 (2012), Article ID 616087, 19 pages
http://dx.doi.org/10.5402/2012/616087
Review Article

Reasoning with Time Intervals: A Logical and Computational Perspective

Department of Information and Communication Engineering, University of Murcia, 30100 Murcia, Spain

Received 25 June 2012; Accepted 19 July 2012

Academic Editors: K. W. Chau and S. Likothanassis

Copyright © 2012 Guido Sciavicco. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. Øhrstrøm and P. F. V. Hasle, Temporal Logic: From Ancient Ideas to Artificial Intelligence, Springer, 1995.
  2. J. Benthem, The Logic of Time: A Model-Theoretic Investigation into the Varieties of Temporal Ontology and Temporal Discourse, Kluwer Academic Publishers, 2nd edition, 1991.
  3. C. Hamblin, “Instants and intervals,” in The Study of Time (Volume 1), J. Fraser, F. Haber, and G. Mueller, Eds., pp. 324–331, Springer, 1972.
  4. P. Balbiani, V. Goranko, and G. Sciavicco, “Two sorted pointinterval temporal logic,” in Proceedings of the 7th Workshop on Methods for Modalities (M4M-7' 11), vol. 278 of Electronic Notes in Theoretical Computer Science, pp. 31–45, Springer, 2011.
  5. E. Grädel, “Why are modal logics so robustly decidable?” in Current Trends in Theoretical Computer Science, pp. 393–408, 2001.
  6. J. Y. Halpern and Y. Shoham, “A propositional modal logic of time intervals,” Journal of the ACM, vol. 38, no. 4, pp. 935–962, 1991. View at Scopus
  7. Y. Venema, “A modal logic for chopping intervals,” Journal of Logic and Computation, vol. 1, no. 4, pp. 453–476, 1991. View at Publisher · View at Google Scholar · View at Scopus
  8. B. Moszkowski, “Reasoning about digital circuits,” Tech. Rep. stan-cs-83-970, Department of Computer Science, Stanford University, Stanford, Calif, USA, 1983.
  9. R. Barua and Z. Chaochen, “Neighbourhood logics: NL and NL 2,” Tech. Rep. 120, UNU/IIST, Macau, China, 1997.
  10. R. Barua, S. Roy, and Z. Chaochen, “Completeness of neighbourhood logic,” Journal of Logic and Computation, vol. 10, no. 2, pp. 271–295, 2000. View at Scopus
  11. Z. Chaochen and M. R. Hansen, “An adequate first order interval logic,” in Proceedings of the International Symposium on Compositionality: the Significant Difference, W. de Roever, H. Langmark, and A. Pnueli, Eds., vol. 1536 of Lecture Notes in Computer Science, pp. 584–608, Springer, 1998.
  12. Z. Chaochen, C. A. R. Hoare, and A. P. Ravn, “A calculus of durations,” Information Processing Letters, vol. 40, no. 5, pp. 269–276, 1991. View at Publisher · View at Google Scholar · View at Scopus
  13. I. Hodkinson, A. Montanari, and G. Sciavicco, “Non-finite axiomatizability and undecidbility of interval temporal logics with C, D, and T,” in Proceedings of the 17th EACSL Annual Conference on Computer Science Logic (CSL' 08), vol. 5213 of Lecture Notes in Computer Science, pp. 308–322, 2008.
  14. E. C. Freuder and A. Mackworth, Eds., Constraint-Based Reasoning, MIT Press, 1994.
  15. R. T. Snodgrass, Ed., The TSQL2 Temporal Query Language, Kluwer, 1995.
  16. P. Terenziani and R. T. Snodgrass, “Reconciling point-based and interval-based semantics in temporal relational databases: a treatment of the telic/atelic distinction,” IEEE Transactions on Knowledge and Data Engineering, vol. 16, no. 5, pp. 540–551, 2004. View at Publisher · View at Google Scholar · View at Scopus
  17. C. Combi and P. Sala, “Temporal functional dependencies based on interval relations,” in Proceedings of the 18th International Symposium on Temporal Representation and Reasoning, pp. 23–30, 2011.
  18. J. Augusto and C. Nugent, “The use of temporal reasoning and management of complex events in smart home,” in Proceedings of the 16th European Conference on Artificial Intelligence (ECAI' 04), pp. 778–782, 2004.
  19. A. Hommersom, P. Lucas, and M. Balser, “Meta-level verification of the quality of medical guidelines using interactive theorem proving,” in Proceedings of the 9th European Conference on Logics in Artificial Intelligence (JELIA '04), pp. 654–666, September 2004. View at Scopus
  20. G. Sciavicco, J. Juarez, and M. Campos, “Quality checking of medical guidelines using interval temporal logics: a casestudy,” in Proceedings of the 3rd International Work-Conference on the Interplay Between Natural and Artificial Computation, vol. 5602 of Lecture Notes in Computer Science, pp. 158–167, Springer, 2009.
  21. W. Bibel, “Let’s plan it deductively,” in Proceedings of the 15th International Joint Conference on Artificial Intelligence (IJCAI' 97), pp. 1549–1562, 1997.
  22. H. Kautz and B. Selman, “Planning as satisfiability,” in Proceedings of the 10th European Conference on Artificial Intelligence (ECAI' 92), pp. 359–363, 1992.
  23. M. C. Mayer, C. Limongelli, A. Orlandini, and V. Poggioni, “Linear temporal logic as an executable semantics for planning languages,” Journal of Logic, Language and Information, vol. 16, no. 1, pp. 63–89, 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. D. E. Smith, “The case for durative actions: a commentary on pddl2.1,” Journal of Artificial Intelligence Research, vol. 20, pp. 149–154, 2003. View at Scopus
  25. G. Fainekos, H. Kress-Gazit, and G. Pappas, “Temporal logic motion planning for mobile robots,” in Proceedings of the IEEE International Conference on Robotics and Automation (ICRA' 05), pp. 2020–2025, IEEE Computer Society Press, April 2005. View at Publisher · View at Google Scholar · View at Scopus
  26. M. Otto, “Two variable first-order logic over ordered domains,” Journal of Symbolic Logic, vol. 66, no. 2, pp. 685–702, 2001. View at Scopus
  27. D. Bresolin, V. Goranko, A. Montanari, and G. Sciavicco, “Propositional interval neighborhood logics: expressiveness, decidability, and undecidable extensions,” Annals of Pure and Applied Logic, vol. 161, no. 3, pp. 289–304, 2009. View at Publisher · View at Google Scholar · View at Scopus
  28. D. Bresolin, D. Della Monica, A. Montanari, and G. Sciavicco, “The light side of interval temporal logics: the Bernays-Schoenfinkel’s fragment of CDT,” in Proceedings of the 18th International Symposium on Temporal Representation and Reasoning (TIME' 11), pp. 123–130, 2011.
  29. J. F. Allen, “Maintaining knowledge about temporal intervals,” Communications of the ACM, vol. 26, no. 11, pp. 832–843, 1983. View at Publisher · View at Google Scholar · View at Scopus
  30. J. F. Allen and P. J. Hayes, “A common-sense theory of time,” in Proceedings of the 9th International Joint Conference on Artificial Intelligence (IJCAI' 85), pp. 528–531, 1985.
  31. P. Ladkin, “Models of axioms for time intervals,” in Proceedings of the 6th National Conference on Artificial Intelligence, pp. 234–239, Morgan Kaufmann, 1987.
  32. Y. Venema, “Expressiveness and completeness of an interval tense logic,” Notre Dame Journal of Formal Logic, vol. 31, no. 4, pp. 529–547, 1990.
  33. V. Goranko, A. Montanari, and G. Sciavicco, “Propositional interval neighborhood temporal logics,” Journal of Universal Computer Science, vol. 9, no. 9, pp. 1137–1167, 2003. View at Scopus
  34. C. J. Coetzee, Representation theorems for classes of interval structures [M.S. thesis], Department of Mathematics, University of Johannesburg, 2009.
  35. W. Conradie and G. Sciavicco, “On the expressive power of first order logic extended with allens relations in the strict case,” in Proceedings of the 14th Conferencia Asociacin Espaola para la Inteligencia Artificial (CAEPIA' 11), vol. 7023 of Lecture Notes in Computer Science, pp. 173–182, Springer, 2011.
  36. P. Blackburn, M. de Rijke, and Y. Venema, Modal Logic, Cambridge University Press, 2002.
  37. J. Halpern and Y. Shoham, “A propositional modal logic of time intervals,” in Proceedings of the 2nd IEEE Symposium on Logic in Computer Science, pp. 279–292, 1986.
  38. D. Della Monica, V. Goranko, A. Montanari, and G. Sciavicco, “Expressiveness of the interval logics of allen’s relations on the class of all linear orders: complete classification,” in Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI' 11), pp. 845–850, 2011.
  39. D. Bresolin, D. D. Monica, A. Montanari, P. Sala, and G. Sciavicco, “Interval temporal logics over finite linear orders: the complete picture,” in Proceedings of the 20th European Conference on Artificial Intelligence (ECAI' 12), 2012.
  40. D. Bresolin, D. D. Monica, V. Goranko, A. Montanari, and G. Sciavicco, “The dark side of interval temporal logic: sharpening the undecidability border,” in Proceedings of the 18th International Symposium on Temporal Representation and Reasoning (TIME' 11), pp. 131–138, 2011. View at Publisher · View at Google Scholar · View at Scopus
  41. J. Marcinkowski and J. Michaliszyn, “The ultimate undecidability result for the Halpern-Shoham logic,” in Proceedings of the 26th Symposium on Logic in Computer Science (LICS' 11), pp. 377–386, 2011.
  42. D. Bresolin, D. Della Monica, V. Goranko, A. Montanari, and G. Sciavicco, “Decidable and undecidable fragments of Halpern and Shoham's interval temporal logic: towards a complete classification,” in Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning (LPAR' 08), vol. 5330 of Lecture Notes in Computer Science, pp. 590–604, Springer, 2008.
  43. V. Goranko, A. Montanari, and G. Sciavicco, “A road map of interval temporal logics and duration calculi,” Journal of Applied Non-Classical Logics, vol. 14, no. 1-2, pp. 9–54, 2004.
  44. D. Bresolin, A. Montanari, and G. Sciavicco, “An optimal decision procedure for right propositional neighborhood logic,” Journal of Automated Reasoning, vol. 38, no. 1–3, pp. 173–199, 2007. View at Publisher · View at Google Scholar · View at Scopus
  45. D. Bresolin, P. Sala, and G. Sciavicco, “On begins, meets, and before,” International Journal on Foundations of Computer Science, vol. 23, no. 3, pp. 559–583, 2012.
  46. A. Montanari, G. Puppis, P. Sala, and G. Sciavicco, “Decidability of the interval temporal logic abb over the natural numbers,” in Proceedings of the Symposium on Theoretical Aspects of Computer Science (STACS' 10), pp. 597–608, 2010.
  47. A. Kurucz, F. Wolter, M. Zakharyaschev, and D. M. Gabbay, Many-Dimensional Modal Logics: Theory and Applications, vol. 148 of Studies in Logic and the Foundations of Mathematics, Elsevier, 2003.
  48. A. Montanari, G. Puppis, and P. Sala, “Maximal decidable fragments of Halpern and Shoham’s modal logic of intervals,” in Proceedings of the 37th International Colloquium on Automata, Languages, and Programming—Part II (ICALP-2' 10), vol. 6199 of Lecture Notes in Computer Science, pp. 345–356, Springer, July 2010.
  49. P. Sala, Decidability of interval temporal logics [Ph.D. thesis], University of Udine, 2010.
  50. P. Schnoebelen, “Verifying lossy channel systems has nonprimitive recursive complexity,” Information Processing Letters, vol. 83, no. 5, pp. 251–261, 2002. View at Publisher · View at Google Scholar · View at Scopus
  51. D. Bresolin, D. D. Monica, A. Montanari, P. Sala, and G. Sciavicco, “Interval temporal logics over strongly discrete linear orders: the complete picture,” Submitted, 2012.
  52. S. Demri and R. Lazić, “LTL with the freeze quantifier and register automata,” in Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science (LICS' 06), IEEE Computer Society, pp. 17–26, August 2006. View at Publisher · View at Google Scholar · View at Scopus
  53. P. Bouyer, N. Markey, J. Ouaknine, P. Schnoebelen, and J. Worrell, “On termination for faulty channel machines,” in Proceedings of the 29th Symposium on Theoretical Aspects of Computer Science (STACS' 08), pp. 121–132, February 2008. View at Scopus
  54. D. Bresolin, A. Montanari, P. Sala, and G. Sciavicco, “Optimal tableau systems for propositional neighborhood logic over all, dense, and discrete linear orders,” in Proceedings of the 20th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX' 11), vol. 6793 of Lecture Notes in Computer Science, pp. 73–87, Springer, 2011.
  55. D. Bresolin, A. Montanari, P. Sala, and G. Sciavicco, “What’s decidable about Halpern and Shoham's interval logic? the maximal fragment ABBL,” in Proceedings of the 26th Symposium on Logic in Computer Science (LICS' 11), pp. 387–396, 2011.
  56. A. Montanari, G. Puppis, and P. Sala, “A decidable spatial logic with cone-shape cardinal directions (extended version of [51]), Research Report 3,” Dipartimento di Matematica ed Informatica, Universit`a di Udine, 2010.
  57. A. Montanari, I. Pratt-Hartmann, and P. Sala, “Decidability of the logics of the reflexive sub-interval and super-interval relations over finite linear orders,” in Proceedings of the 17th International Symposium on Temporal Representation and Reasoning (TIME '10), pp. 27–34, September 2010. View at Publisher · View at Google Scholar · View at Scopus
  58. J. Marcinkowski, J. Michaliszyn, and E. Kieronski, “B and D are enough to make the halpern-shoham logic undecidable,” in Proceedings of the 37th International Colloquium on Automata, Languages, and Programming—Part II (ICALP-2' 10), vol. 6199 of Lecture Notes in Computer Science, pp. 357–368, Springer, July 2010.
  59. E. A. Emerson, “Temporal and modal logic,” in Handbook of Theoretical Computer Science, Volume B: Formal Models and Semantics, J. van Leeuwen, Ed., pp. 995–1072, MIT Press, 1990.
  60. L. Aksoy and E. Gunes, “An evolutionary local search algorithm for the satisfiability problem,” in Proceedings of the 14th Turkish Conference on Artificial Intelligence and Neural Networks, pp. 185–193, Springer, 2006.
  61. H. Ellerweg, A study of evolutionary algorithms for the satisfiability problem [Ph.D. thesis], University of Paderborn, 2004.
  62. J. Gottlieb, E. Marchiori, and C. Rossi, “Evolutionary algorithms for the satisfiability problem,” Evolutionary Computation, vol. 10, no. 1, pp. 35–50, 2002. View at Scopus
  63. H. Jin-Kao, F. Lardeux, and F. Saubion, “Evolutionary computing for the satisfiability problem,” in Proceedings of the 3rd European Workshop on Evolutionary Computation in Combinatorial Optimization, vol. 2611 of Lecture Notes in Computer Science, pp. 258–268, Springer, 2003.
  64. P. Van Emde Boas, “The convenience of tilings,” in Complexity, Logic and Recursion Theory, vol. 187 of Lecture Notes in Pure and Applied Mathematics, pp. 331–363, Marcel Dekker, 1997.
  65. K. Lodaya, R. Parikh, R. Ramanujam, and P. S. Thiagarajan, “A logical study of distributed transition systems,” Information and Computation, vol. 119, no. 1, pp. 91–118, 1995. View at Publisher · View at Google Scholar · View at Scopus