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Computational Complexity of Propositional Linear Temporal Logics Based on Qualitative Spatial or Temporal Reasoning

  • Philippe Balbiani
  • Jean-François Condotta 
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2309)

Abstract

We consider the language obtained by mixing the model of the regions and the propositional linear temporal logic. In particular, we propose alternative languages where the model of the regions is replaced by different forms of qualitative spatial or temporal reasoning. In these languages, qualitative formulas describe the movement and the relative positions of spatial or temporal entities in some spatial or temporal universe. This paper addresses the issue of the formal proof that for all forms of qualitative spatial and temporal reasoning such that consistent atomic constraint satisfaction problems are globally consistent, determining of any given qualitative formula whether it is satisfiable or not is PSPACE-complete.

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References

  1. 1.
    Allen, J.: Maintaining knowledge about temporal intervals. Communications of the Association for Computing Machinery 26 (1983) 832–843.zbMATHGoogle Scholar
  2. 2.
    Balbiani, P., Condotta, J.-F.: Spatial reasoning about points in a multidimensional setting. Applied Intelligence, to appear.Google Scholar
  3. 3.
    Balbiani, P., Condotta, J.-F., Fariñas del Cerro, L.: A model for reasoning about bidimensional temporal relations. In Cohn, A., Schubert, L., Shapiro, S. (Eds.): Proceedings of the Sixth International Conference on Principles of Knowledge Representation and Reasoning. Morgan Kaufmann (1998) 124–130.Google Scholar
  4. 4.
    Balbiani, P., Osmani, O.: A model for reasoning about topologic relations between cyclic intervals. In Cohn, A., Giunchiglia, F., Selman, B. (Eds.): Proceedings of the Seventh International Conference on Principles of Knowledge Representation and Reasoning. Morgan Kaufmann (2000) 378–385.Google Scholar
  5. 5.
    Bennett, B.: Determining consistency of topological relations. Constraints 3 (1998)213–225.zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Bennett, B., Cohn, A., Wolter, F., Zakharyaschev, M.: Multi-dimensional modal logic as a framework for spatio-temporal reasoning. Applied Intelligence, to appear.Google Scholar
  7. 7.
    Cristani, M.: The complexity of reasoning about spatial congruence. Journal of Artificial Intelligence Research 11 (1999) 361–390.zbMATHMathSciNetGoogle Scholar
  8. 8.
    Freuder, E.: Synthesizing constraint expressions. Communications of the Association for Computing Machinery 21 (1978) 958–966.zbMATHMathSciNetGoogle Scholar
  9. 9.
    Gerevini, A., Renz, J.: Combining topological and qualitative size constraints for spatial reasoning. In Maher, M., Puget, J.-F. (Eds.): Proceedings of the Fourth International Conference on Principles and Practice of Constraint Programming. Springer-Verlag, Lecture Notes in Computer Science 1520 (1998) 220–234.Google Scholar
  10. 10.
    Isli, A., Cohn, A.: A new approach to cyclic ordering of 2D orientations using ternary relation algebras. Artificial Intelligence 122 (2000) 137–187.zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Ligozat, G.: On generalized interval calculi. In Dean, T., McKeown, K. (Eds.): Proceedings of the Ninth National Conference on Artificial Intelligence AAAI Press (1991) 234–240.Google Scholar
  12. 12.
    Ligozat, G.: Reasoning about cardinal directions. Journal of Visual Languages and Computing 9 (1998) 23–44.CrossRefGoogle Scholar
  13. 13.
    Moratz, R., Renz, J., Wolter, D.: Qualitative spatial reasoning about line segments. In Horn, W. (Ed.): Proceedings of the Fourteenth European Conference on Artificial Intelligence. Wiley (2000) 234–238.Google Scholar
  14. 14.
    Nebel, B.: Computational properties of qualitative spatial reasoning: first results. In Wachsmuth, I., Rollinger, C.-R., Brauer, W. (Eds.): Proceedings of the Nineteenth German Conference on Artificial Intelligence. Springer-Verlag, Lecture Notes in Artificial Intelligence 981 (1995) 233–244.Google Scholar
  15. 15.
    Randell, D., Cui, Z., Cohn, A.: A spatial logic based on regions and connection. In Nebel, B., Rich, C., Swartout, W. (Eds.): Proceedings of the Third International Conference on Principles of Knowledge Representation and Reasoning. Morgan Kaufman (1992) 165–176.Google Scholar
  16. 16.
    Renz, J., Nebel, B.: On the complexity of qualitative spatial reasoning: a maximal tractable fragment of the region connection calculus. Artificial Intelligence 108 (1999) 69–123.zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Savitch, W.: Relationships between nondeterministic and deterministic tape complexities. Journal of Computer and System Sciences 4 (1970) 177–192.zbMATHMathSciNetGoogle Scholar
  18. 18.
    Sistla, A., Clarke, E.: The complexity of propositional linear temporal logics. Journal of the Association for Computing Machinery 32 (1985) 733–749.zbMATHMathSciNetGoogle Scholar
  19. 19.
    Vilain, M., Kautz, H.: Constraint propagation algorithms for temporal reasoning. In Kehler, T., Rosenschein, S., Filman, R., Patel-Schneider, P. (Eds.): Proceedings of the Fifth National Conference on Artificial Intelligence. American Association for Artificial Intelligence (1986) 377–382.Google Scholar
  20. 20.
    Wolter, F., Zakharyaschev, M.: Spatio-temporal representation and reasoning based on RCC-8. In Cohn, A., Giunchiglia, F., Selman, B. (eds.): Proceedings of the Seventh International Conference on Principles of Knowledge Representation and Reasoning. Morgan Kaufmann (2000) 3–14.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Philippe Balbiani
    • 1
  • Jean-François Condotta 
    • 2
  1. 1.Institut de recherche en informatique de ToulouseToulouse CEDEX 4France
  2. 2.Laboratoire d’informatique pour la mécanique et les sciences de l’ingénieurOrsay CEDEXFrance

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