Multi-Agent Dynamic Logics with Informational Test

  • Renate A. Schmidt
  • Dmitry Tishkovsky

Abstract

This paper investigates a family of logics for reasoning about the dynamic activities and informational attitudes of agents, namely the agents' beliefs and knowledge. The logics are based on a new formalisation and semantics of the test operator of propositional dynamic logic and a representation of actions which distinguishes abstract actions from concrete actions. The new test operator, called informational test, can be used to formalise the beliefs and knowledge of particular agents as dynamic modalities. This approach is consistent with the formalisation of the agents' beliefs and knowledge as K(D)45 and S5 modalities. Properties concerning informativeness, truthfulness and preservation of beliefs are proved for a derivative of the informational test operator. It is shown that common belief and common knowledge can be expressed in the considered logics. This means, the logics are more expressive than propositional dynamic logic with an extra modality for belief or knowledge. The logics remain decidable and belong to 2EXPTIME. Versions of the considered logics express natural additional properties of beliefs or knowledge and interaction of beliefs or knowledge with actions. It is shown that a simulation of PDL can be constructed in one of these extensions.

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References

  1. [1]
    P. Blackburn, M. de Rijke, and Y. Venema, Modal Logic (Cambridge Univ. Press, 2001).Google Scholar
  2. [2]
    P.R. Cohen and H.J. Levesque, Teamwork, Noûs 25(4) (1991) 487–512.Google Scholar
  3. [3]
    R. Fagin, J.Y. Halpern, Y. Moses and M.Y. Vardi, Reasoning about Knowledge (MIT Press, 1995).Google Scholar
  4. [4]
    M.J. Fischer and R.E. Ladner, Propositional dynamic logic of regular programs, J. Comput. Syst. Sci. 18(2) (1979) 194–211.Google Scholar
  5. [5]
    [5] D. Gabbay, A. Kurucz, F.Wolter and M. Zakharyaschev, Many-dimensional modal logics: Theory and applications, Manuscript, http://www.dcs.kcl.ac.uk/staff/mz/GKWZ/gkwz.html.Google Scholar
  6. [6]
    [6] D. Gabbay and V. Shehtman, Products of modal logics, Part 1, Logic J. IGPL 6(1) 73–146.Google Scholar
  7. [7]
    J.Y. Halpern and Y. Moses, A guide to completeness and complexity for modal logics of knowledge and belief, Artif. Intell. 54 (1992) 319–379.Google Scholar
  8. [8]
    J.Y. Halpern and M.Y. Vardi, The complexity of reasoning about knowledge and time. I. Lower bounds, J. Comput. System Sci. 38 (1989) 195–237.Google Scholar
  9. [9]
    D. Harel, D. Kozen and J. Tiuryn, Dynamic Logic (MIT Press, 2000).Google Scholar
  10. [10]
    A. Herzig, Personal communication (2002).Google Scholar
  11. [11]
    A. Herzig, J. Lang, D. Longin and T. Polacsek, A logic for planning under partial observability, in: Proc. AAAI'2000 (AAAI Press/MIT Press, 2000) pp. 768–773.Google Scholar
  12. [12]
    A. Herzig, J. Lang and T. Polacsek, A modal logic for epistemic tests, in: Proc. ECAI'2000 (IOS Press, 2000) pp. 553–557.Google Scholar
  13. [13]
    A. Herzig and D. Longin, Belief dynamics in cooperative dialogues, J. Semantics 17(2) (2000) 91–118.Google Scholar
  14. [14]
    N.R. Jennings and M. Wooldridge, Applications of agent technology, in: Agent Technology: Foundations, Applications, and Markets (Springer, 1998).Google Scholar
  15. [15]
    S.C. Kleene, Introduction to Metamathematics (North-Holland, 1952).Google Scholar
  16. [16]
    M. Kracht, Highway to the danger zone, J. Logic Comput. 5(1) (1995) 93–109.Google Scholar
  17. [17]
    A.R. Lomiscio, R. van der Meyden and M. Ryan, Knowledge in multi-agent systems: Initial configurations and broadcast, ACM Trans. Comput. Logic 1(2) (2000) 247–284.Google Scholar
  18. [18]
    R. Maddux, The equational theory of CA 3 is undecidable, J. Symb. Logic 45 (1980) 311–315.Google Scholar
  19. [19]
    M. Marx, Complexity of products of modal logics, J. Logic Comput. 9(2) (1999) 197–214.Google Scholar
  20. [20]
    J.-J.C. Meyer, W. van der Hoek and B. van Linder, A logical approach to the dynamics of commitments, Artif. Intell. 113(1-2) (1999) 1–40.Google Scholar
  21. [21]
    R.C. Moore, A formal theory of knowledge and action, in: Formal Theories of the Commonsense World, eds. J.R. Hobbs and R.C. Moore (Ablex, 1985) pp. 319–358.Google Scholar
  22. [22]
    A.S. Rao, Decision procedures for propositional linear-time belief-desire-intention logics, in: Proc. ATAL'95, Lecture Notes in Artificial Intelligence, Vol. 1037 (Springer, 1995) pp. 102–118.Google Scholar
  23. [23]
    A.S. Rao and M.P. Georgeff, Modeling rational agents within a BDI-architecture, in: Proc. KR'91 (Morgan Kaufmann, 1991) pp. 473–484.Google Scholar
  24. [24]
    R.A. Schmidt and D. Tishkovsky, Multi-agent logic of dynamic belief and knowledge, in: Proc. JELIA'2002, Lecture Notes in Artificial Intelligence, Vol. 2424 (Springer, 2002) pp. 38–49.Google Scholar
  25. [25]
    R.A. Schmidt and D. Tishkovsky, On axiomatic products of PDL and S5: Substitution, tests and knowledge, Bull. Section of Logic 31(1) (2002) 27–36.Google Scholar
  26. [26]
    R.A. Schmidt and D. Tishkovsky, Combining dynamic logic with doxastic modal logics, in: Advances in Modal Logic, Vol. 4 (King's College Publ., 2002) pp. 371–392.Google Scholar
  27. [27]
    W. van der Hoek, Logical foundations of agent-based computing, in: Multi-Agent Systems and Applications, Lecture Notes in Artificial Intelligence, Vol. 2086 (Springer, 2001) pp. 50–73.Google Scholar
  28. [28]
    B. van Linder, W. van der Hoek and J.-J. Meyer, Tests as epistemic updates, in: Proc. ECAI'94 (Wiley, 1994) pp. 331–335.Google Scholar
  29. [29]
    B. van Linder, W. van der Hoek and J.-J.C. Meyer, Formalizing abilities and opportunities of agents, Fundamenta Informaticae 34(1-2) (1998) 53–101.Google Scholar
  30. [30]
    M. Wooldridge, Agent-based computing, Interoperable Comm. Networks 1(1) (1998) 71–97.Google Scholar
  31. [31]
    M. Wooldridge and N.R. Jennings, Intelligent agents: Theory and practice, Knowledge Engineering Review 10(2) (1995) 115–152.Google Scholar
  32. [32]
    M. Zakharyaschev, F. Wolter and A. Chagrov, Advanced modal logic, in: Handbook of Philosophical Logic, Vol. 3, eds. D.M. Gabbay and F. Guenthner, 2nd edn (Kluwer, 2001) pp. 83–266.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Renate A. Schmidt
    • 1
  • Dmitry Tishkovsky
    • 1
  1. 1.Department of Computer ScienceUniversity of ManchesterUK

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