Artificial Intelligence Review

, Volume 17, Issue 1, pp 1–20 | Cite as

Combinations of Modal Logics

  • Brandon Bennett
  • Clare Dixon
  • Michael Fisher
  • Ullrich Hustadt
  • Enrico Franconi
  • Ian Horrocks
  • Maarten de Rijke
Article

Abstract

There is increasing use of combinations of modal logics in bothfoundational and applied research areas. This article provides anintroduction to both the principles of such combinations and to thevariety of techniques that have been developed for them. In addition,the article outlines many key research problems yet to be tackledwithin this callenging area of work.

knowledge representation logical reasoning modal logics 

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References

  1. Aiello, M., C. Areces & M. de Rijke (1999). Spatial Reasoning for Image Retrieval. In Proceedings of the International Workshop on Description Logics (DL'99). Sweden: Linköpings Universitet, 23–27.Google Scholar
  2. Areces, C., H. de Nivelle & M. de Rijke (1999). Prefixed Resolution: A Resolution Method forModal and Description Logics. In Proceedings of the 16th International Conference on Automated Deduction (CADE-16), volume 1632 in Lecture Notes in Artificial Intelligence. Springer, 187–201.Google Scholar
  3. Areces, C. and M. de Rijke (2000). Description and/or Hybrid Logics. In Proceedings of AiML-2000 Workshop, 1-14.Google Scholar
  4. Artale, A. and E. Franconi (1998). A Temporal Description Logic for Reasoning about Actions and Plans. Journal of Artificial Intelligence Research 9: 463–506.Google Scholar
  5. Artale, A. and E. Franconi (1999). Representing a Robotic Domain using Temporal Description Logics. Journal of Artificial Intelligence for Engineering Design, Analysis and Manufacturing (AIEDAM) 2(13): 105–117.Google Scholar
  6. Artale, A. and E. Franconi (1999). Temporal Entity-Relationship Modeling with Description Logics. In Proceedings of the 18th International Conference on Conceptual Modeling (ER'99), volume 1728 in Lecture Notes in Computer Science. Springer, 81–95.Google Scholar
  7. Artale, A. and E. Franconi (to appear). A Survey of Temporal Extensions of Description Logics. Annals of Mathematics and Artificial Intelligence (AMAI). Kluwer Academic Publishers.Google Scholar
  8. Artale, A. and E. Franconi (forthcoming). Temporal Description Logics. In Handbook of Time and Temporal Reasoning in Artificial Intelligence.Google Scholar
  9. Auffray, Y. and P. Enjalbert (1992). Modal Theorem Proving: An Equational Viewpoint. Journal of Logic and Computation, 2(3): 247–297.Google Scholar
  10. Bachmair, L. and H. Ganzinger (to appear). A Theory of Resolution. In J.A. Robinson and A. Voronkov (eds.), Handbook of Automated Reasoning. MIT Press.Google Scholar
  11. Baker, P. G., A. Brass, S. Bechhofer, C. Goble, N. Paton and R. Stevens (1998). Tambis: Transparent Access to Multiple Bioinformatics Information Sources: An Overview. In Proceedings of the 6th International Conference on Intelligent Systems for Molecular Biology (ISMB'98).Google Scholar
  12. Beckert, B. and D. Gabbay (1998). Fibring Semantic Tableaux. In Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX'98), volume 1397 in Lecture Notes in Artificial Intelligence, Springer, 77–92.Google Scholar
  13. Bennett, B. (1996). Modal logics for qualitative spatial reasoning. Bulletin of the Interest Group in Pure and Applied Logic (IGPL) 4(1): 23–45. ftp://ftp.mpi-sb.mpg.de/pub/ igpl/Journal/V4-1/index.html.Google Scholar
  14. Bennett, B. (1997). Logical Representations for Automated Reasoning about Spatial Relationships. PhD thesis, School of Computer Studies, The University of Leeds. Abstract and postscript at http://www.scs.leeds.ac.uk/brandon/thesis.html.Google Scholar
  15. Blackburn, P., M. de Rijke and Y. Venema (2001). Modal Logic. Cambridge University Press (See http://www.mlbook.org.)Google Scholar
  16. Bolotov, A. and M. Fisher (1999). A Resolution Method for CTL Branching-Time Temporal Logic. Journal of Theoretical and Experimental Artificial Intelligence 11: 77–93.Google Scholar
  17. Calvanese, D., G. De Giacomo and M. Lenzerini (1998). On the decidability of query containment under constraints. In Proceedings of the 17th ACM SIGACT SIGMOD SIGART Symposium on Principles of Database Systems (PODS-98). ACM Press, 149-158.Google Scholar
  18. Calvanese, D., G. De Giacomo, M. Lenzerini, D. Nardi and R. Rosati (1998). Description Logic Framework for Information Integration. In Proceedings of the 6th International Conference on the Principles of Knowledge Representation and Reasoning (KR-98). Morgan Kaufmann, 2-13.Google Scholar
  19. Chellas, B. (1980). Modal Logic: An Introduction. Cambridge University Press.Google Scholar
  20. De Giacomo, G. and F. Massacci (1996). Tableaux and Algorithms for Propositional Dynamic Logic with Converse. In Proceedings of the 13th International Conference on Automated Deduction (CADE-13), volume 1104 in Lecture Notes in Artificial Intelligence, Springer, 613–628.Google Scholar
  21. Dixon, C. and M. Fisher (2000). Clausal Resolution for Logics of Time and Knowledge with Synchrony and Perfect Recall. In Proceedings of ICTL 2000. Leipzig, Germany, October 2000.Google Scholar
  22. Dixon, C., M. Fisher and M. Wooldridge (1998). Resolution for Temporal Logics of Knowledge. Journal of Logic and Computation 8(3): 345–372.Google Scholar
  23. Dixon, C. (1996). Search Strategies for Resolution in Temporal Logics. In Proceedings of the 13th International Conference on Automated Deduction (CADE-13), volume 1104 of Lecture Notes in Artificial Intelligence. Springer, 672–687.Google Scholar
  24. Dixon, C. (1998). Temporal Resolution using a Breadth-First Search Algorithm. Annals of Mathematics and Artificial Intelligence 22: 87–115.Google Scholar
  25. Dixon, C. (1999). Removing Irrelevant Information in Temporal Resolution Proofs. Journal of Experimental and Theoretical Artificial Intelligence 11: 95–121.Google Scholar
  26. Fariñas del Cerro, L. and A. Herzig (1988). Quantified modal logic and unification theory. Technical Report LSI 293, University Paul Sabatier.Google Scholar
  27. Fermüller, C., A. Leitsch, U. Hustadt and T. Tammet (to appear). Resolution decision procedures. In J. A. Robinson and A. Voronkov (eds.), Handbook of Automated Reasoning. MIT Press.Google Scholar
  28. Finger, M. and D. M. Gabbay (1992). Adding a Temporal Dimension to a Logic System. Journal of Logic, Language, and Information 1: 203–234.Google Scholar
  29. Fisher, M., C. Dixon and M. Peim (2001). Clausal Temporal Resolution. ACM Transactions on Computational Logic 2(1).Google Scholar
  30. Fisher, M. (1991). A Resolution Method for Temporal Logic. In Proceedings of the 12th International Joint Conference on Artificial Intelligence (IJCAI'91). Morgan Kaufman, 99-104.Google Scholar
  31. Fisher, M. (1997). A Normal Form for Temporal Logic and its Application in Theorem-Proving and Execution. Journal of Logic and Computation 7(4): 429–456.Google Scholar
  32. Fisher, M. (1997). Implementing BDI-like Systems by Direct Execution. In Proceedings of the 15th International joint Conference on Artificial Intelligence (IJCAI'97). Morgan Kaufmann, 316-321.Google Scholar
  33. Fisher, M. and C. Ghidini (1999). Programming Resource-Bounded Deliberative Agents. In Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI'99). Morgan Kaufmann, 200-205.Google Scholar
  34. Fagin, R., J. Halpern, Y.Moses andM. Vardi (1996). Reasoning About Knowledge.MIT Press.Google Scholar
  35. Gabbay, D. M. (1999). Fibring Logics, Oxford Logic Guides 38. Oxford University Press.Google Scholar
  36. Ganzinger, H., U. Hustadt, C. Meyer and R. A. Schmidt (to appear). A Resolution-Based Decision Procedure for Extensions Of K4. In Advances in Modal Logic 2. CSLI Publications.Google Scholar
  37. Ganzinger, H., C. Meyer and M. Veanes (1999). The Two-Variable Guarded Fragment with Transitive Relations. In Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science (LICS'99). IEEE Computer Society Press, 24-34.Google Scholar
  38. Halpern, J. Y. and M. Y. Vardi (1986). The Complexity of Reasoning about Knowledge and Time: Extended Abstract. In Proceedings of the 18th Annual ACM Symposium on Theory of Computing. ACM Press, 304-315.Google Scholar
  39. Halpern, J. Y. and M. Y. Vardi (1988). Reasoning about Knowledge and Time in Asynchronous Systems. In Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing. ACM Press, 53-65.Google Scholar
  40. Halpern, J. Y. and M. Y. Vardi (1988). The Complexity of Reasoning about Knowledge and Time: Synchronous Systems. Technical Report RJ 6097, IBM Almaden Research Center.Google Scholar
  41. Halpern, J. Y. and M. Y. Vardi (1989). The Complexity of Reasoning about Knowledge and Time. I Lower Bounds. Journal of Computer and System Sciences 38: 195–237.Google Scholar
  42. Halpern, J. Y., R. van der Meyden and M. Vardi (submitted). Complete axiomatizations for reasoning about knowledge and time.Google Scholar
  43. Halpern, J. Y. and Y. Shoham (1991). A Propositional Modal Logic of Time Intervals. Journal of ACM 38(4): 935–962.Google Scholar
  44. Hemaspaandra, E. (1994). Complexity Transfer for Modal Logic. In Proceedings of the 9th Annual IEEE Symposium on Logic in Computer Science (LICS'94). IEEE Computer Society Press, 164-175.Google Scholar
  45. Horrocks, I. (1998). The FaCT system. In Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX'98), volume 1397 in Lecture Notes in Artificial Intelligence. Springer, 307–312.Google Scholar
  46. Horrocks, I. (1998). Using an Expressive Description Logic: Fact or Fiction? In Proceedings of the 6th International Conference on Principles of Knowledge Representation and Reasoning (KR'98). Morgan Kaufmann, 636-647.Google Scholar
  47. Horrocks, I. (1999). FaCT and iFaCT. In, P. Lambrix, A. Borgida, M. Lenzerini, R. Möller and P. Patel-Schneider (eds.), Proceedings of International Description Logics Workshop (DL'99). Linköpings Universitet, Sweden, July 1999, 133–135. (See http://sunsite.informatik.rwth-aachen.de/Publications/CEUR-WS/Vol-22/)Google Scholar
  48. Horrocks, I. and U. Sattler (1999). A Description Logic with Transitive and Inverse Roles and Role Hierarchies. Journal of Logic and Computation 9(3): 385–410.Google Scholar
  49. Hustadt, U., C. Dixon, R. A. Schmidt and M. Fisher (2000). Normal Forms and Proofs in Combined Modal and Temporal Logics. In Proceedings of the Third International Workshop on Frontiers of Combining Systems (FroCoS'2000), volume 1794 in Lecture Notes in Artificial Intelligence. Springer, 73–87.Google Scholar
  50. Hustadt, U. and R. A. Schmidt (2000). Issues of Decidability for Description Logics in the Framework of Resolution. In Automated Deduction in Classical and Non-Classical Logics: Selected Papers, volume 1761 in Lecture Notes in Artificial Intelligence. Springer.Google Scholar
  51. Hustadt, U. and R. A. Schmidt (2000). Using Resolution for Testing Modal Satisfiability and Building Models. To appear in the SAT 2000 Special Issue of Journal of Automated Reasoning.Google Scholar
  52. Hustadt, U. (1999). Resolution-Based Decision Procedures for Subclasses of First-Order Logic. PhD thesis, Universität des Saarlandes, Saarbrücken, Germany.Google Scholar
  53. Hustadt, U. and R. A. Schmidt (1999). Maslov's Class K Revisited. In Proceedings of the 16th International Conference on Automated Deduction (CADE-16), volume 1632 in Lecture Notes in Artificial Intelligence. Springer, 172–186.Google Scholar
  54. Hustadt, U. and R. A. Schmidt (1999). On the Relation of Resolution and Tableaux Proof Systems for Description Logics. In Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI'99). Morgan Kaufmann, 110-115.Google Scholar
  55. Kurtonina, N. and M. de Rijke (in preparation). Hybrid Logics and Linguistic Inference.Google Scholar
  56. Kracht, M. (1995). Highway to the Danger Zone. Journal of Logic and Computation 5(1): 93–109.Google Scholar
  57. Kracht, M. and F. Wolter (1997). Simulation and Transfer Results in Modal Logic. Studia Logica 59: 149–177.Google Scholar
  58. van Linder, B., W. van der Hoek and J. J. Ch. Meyer (1996). Formalising Motivational Attitudes of Agents: On Preferences, Goals and Commitments. In Intelligent Agents II, volume 1037 in Lecture Notes in Artificial Intelligence. Springer, 17–32.Google Scholar
  59. Mints, G. (1990). Gentzen-Type Systems and Resolution Rules, Part I: Propositional Logic. In Proceedings of the International Conference on Computer Logic, volume 417 in Lecture Notes in Computer Science. Springer, 198–231.Google Scholar
  60. Moore, R. C. (1990). A Formal Theory of Knowledge and Action. In Readings in Planning. Morgan-Kaufmann.Google Scholar
  61. Nonnengart, A. (1995). A Resolution-Based Calculus For Temporal Logics. PhD thesis, Universität des Saarlandes, Saarbrücken, Germany.Google Scholar
  62. Ohlbach, H. J. (1991). Semantics-Based Translation Methods for Modal Logics. Journal of Logic and Computation 1(5): 691–746.Google Scholar
  63. Ohlbach, H. J., A. Nonnengart, M. de Rijke and D. M. Gabbay (to appear). Encoding two-valued non-classical logics in classical logic. In J. A. Robinson and A. Voronkov (eds.), Handbook of Automated Reasoning. MIT Press.Google Scholar
  64. Ohlbach, H. J. and R. A. Schmidt (1997). Functional Translation and Second-Order Frame Properties of Modal Logics. Journal of Logic and Computation 7(5): 581–603.Google Scholar
  65. Patel-Schneider, P. F. (1998). DLP system Description. In Collected Papers from the International Description Logics Workshop (DL'98). CEUR, 87-89.Google Scholar
  66. Rao, A. S. and M. P. Georgeff (1991). Modeling Agents within a BDI-Architecture. In Proceedings of the 2nd International Conference on Principles of Knowledge Representation and Reasoning. Morgan Kaufmann, 473-484.Google Scholar
  67. Rao, A. S. (1996). Decision Procedures for Propositional Linear-Time Belief-Desire-Intention Logics. In Intelligent Agents II, volume 1037 in Lecture Notes in Artificial Intelligence. Springer, 33–48.Google Scholar
  68. Rector, A., S. Bechhofer, C. A. Goble, I. Horrocks, W. A. Nowlan and W. D. Solomon (1997). The GRAIL Concept Modelling Language forMedical Terminology. Artificial Intelligence in Medicine 9: 139–171.Google Scholar
  69. Renz, J. and B. Nebel (1997). On the Complexity of Qualitative Spatial Reasoning: AMaximal Tractable Fragment of the Region Connection Calculus. In Proceedings of the 15th International Joint Conference on Artificial Intelligence (IJCAI'97). Morgan Kaufmann, 522-527.Google Scholar
  70. Sattler, U. (1996). A Concept Language Extended with Different Kinds of Transitive Roles. In 20. Deutsche Jahrestagung für Künstliche Intelligenz, volume 1137 in Lecture Notes in Artificial Intelligence. Springer, 333–345.Google Scholar
  71. Schild, K. (1991). A Correspondence Theory for Terminological Logics. In Proceedings of the 12th International Joint Conference on Artificial Intelligence (IJCAI'91). Morgan Kaufmann, 466-471.Google Scholar
  72. Schmidt, R. A. (1997). Optimised Modal Translation and Resolution. PhD thesis, Universität des Saarlandes, Saarbrücken, Germany.Google Scholar
  73. Schmidt, R. A. (1999). Decidability by Resolution for Propositional Modal Logics. Journal of Automated Reasoning 22(4): 379–396.Google Scholar
  74. Schild, K. D. (1993). Combining Terminological Logics with Tense Logic. In Proceedings of the 6th Portuguese Conference on Artificial Intelligence (EPIA'93). Springer, 105-120.Google Scholar
  75. van Benthem, J. (1976). Modal Correspondence Theory. PhD Thesis, Mathematisch Instituut & Instituut voor Grondslagenonderzoek, University of Amsterdam, The Netherlands.Google Scholar
  76. van der Hoek, W., B. van Linder and J.J. Ch. Meyer (1997). An Integrated Modal Approach to Rational Agents. Technical Report UU-CS-1997-06, Department of Computer Science, Utrecht University, The Netherlands.Google Scholar
  77. Wolter, F. and M. Zakharyaschev. Modal Description Logic: Modalizing Roless. Fundamenta Informaticae 39: 411-438.Google Scholar
  78. Wolter, F. and M. Zakharyaschev (2000). Temporalizing Description Logics. In Proceedings of the Second International Workshop on Frontiers of Combining Systems (FroCoS'98). Research Studies Press, 391-401.Google Scholar
  79. Wolter, F., M. Zakharyaschev and M. Mosurovic (2001). Temporal Description Logics: a Point-based Approach. In Italian Association for Artificial Intelligence "AI*IA" Notizie" journal.Google Scholar
  80. Wooldridge, M., C. Dixon, and M. Fisher (1998). A Tableau-Based Proof Method for Temporal Logics of Knowledge and Belief. Journal of Applied Non-Classical Logics 8(3): 225–258.Google Scholar
  81. Wooldridge, M. and N. R. Jennings (1995). Intelligent Agents: Theory and Practice. The Knowledge Engineering Review 10(2): 115–152.Google Scholar

Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Brandon Bennett
  • Clare Dixon
  • Michael Fisher
  • Ullrich Hustadt
  • Enrico Franconi
  • Ian Horrocks
  • Maarten de Rijke

There are no affiliations available

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