Decidable Extensions of Hennessy-Milner Logic

  • Radu Mardare
  • Corrado Priami
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4229)


We propose a new class of logics for specifying and model-checking properties of distributed systems – Dynamic Epistemic Spatial Logics. They have been designed as extensions of Hennessy-Milner logic with spatial operators (inspired by Cardelli-Gordon-Caires spatial logic) and epistemic operators (inspired by dynamic-epistemic logics). Our logics focus on observers, agents placed in different locations of the system having access to some subsystems. Treating them as epistemic agents, we develop completely axiomatized and decidable logics that express the information flow between them in a dynamic and distributed environment. The knowledge of an epistemic agent, is understood as the information, locally available to our observer, about the overall-global system.


Model Check Parallel Operator Process Semantic Axiomatic System Epistemic Logic 


  1. 1.
    Bergstra, J.A.: Handbook of Process Algebra. Elsevier Science Inc., New York (2001)MATHGoogle Scholar
  2. 2.
    Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. JACM 32(1), 137–161 (1985)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Stirling, C.: Modal and temporal properties of processes. Springer, New York (2001)CrossRefMATHGoogle Scholar
  4. 4.
    Milner, R., Parrow, J., Walker, D.: Modal logics for mobile processes. Theoretical Computer Science 114, 149–171 (1993)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Dam, M.: Proof systems for π-calculus. In: de Queiroz, (ed.) Logic for Concurrency and Synchronisation, Studies in Logic and Computation. Oxford University Press, Oxford (to appear)Google Scholar
  6. 6.
    Dam, M.: Model checking mobile processes. Information and Computation 129(1), 35–51 (1996)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Caires, L., Cardelli, L.: A spatial logic for concurrency (part i). Information and Computation 186/2, 194–235 (2003)CrossRefMATHGoogle Scholar
  8. 8.
    Cardelli, L., Gordon, A.D.: Ambient logic. Mathematical Structures in Computer Science (to appear, 2003)Google Scholar
  9. 9.
    Cardelli, L., Gordon, A.D.: Anytime, anywhere: Modal logics for mobile ambients, 365–377 (2000)Google Scholar
  10. 10.
    Cardelli, L., Gordon, A.D.: Mobile ambients. In: Nivat, M. (ed.) FOSSACS 1998. LNCS, vol. 1378, p. 140. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  11. 11.
    Caires, L., Lozes, É.: Elimination of quantifiers and undecidability in spatial logics for concurrency. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 240–257. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Charatonik, W., Talbot, J.-M.: The decidability of model checking mobile ambients. In: Fribourg, L. (ed.) CSL 2001 and EACSL 2001. LNCS, vol. 2142, pp. 339–354. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  13. 13.
    Charatonik, W., Gordon, A.D., Talbot, J.-M.: Finite-control mobile ambients. In: Le Métayer, D. (ed.) ESOP 2002. LNCS, vol. 2305, pp. 295–313. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  14. 14.
    Milner, R.: A Calculus of Communicating Systems. Springer, New York (1982)MATHGoogle Scholar
  15. 15.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (1995)MATHGoogle Scholar
  16. 16.
    Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)MATHGoogle Scholar
  17. 17.
    Baltag, A., Moss, L.S.: Logics for epistemic programs. In: Symons, J., Hintikka, J. (eds.) Synthese: Knowledge, Rationality and Action, vol. 139 (2), pp. 165–224. Springer, Heidelberg (2004)Google Scholar
  18. 18.
    Gerbrandy, J., Groeneveld, W.: Reasoning about information change. Journal of Logic, Language and Information 6, 146–169 (1997)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    van Benthem, J.F.A.K.: Games in dynamic epistemic logic. Bulletin of Economic Research 53(4), 219–248 (2001)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Syverson, P.F., Cervesato, I.: The logic of authentication protocols. In: Focardi, R., Gorrieri, R. (eds.) FOSAD 2000. LNCS, vol. 2171, p. 63. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  21. 21.
    Mardare, R., Priami, C.: Dynamic epistemic spatial logics. Technical Report, 03/2006, Microsoft Research Center for Computational and Systems Biology, Trento, Italy (2006)Google Scholar
  22. 22.
    Mardare, R., Priami, C.: A decidable extension of hennessy-milner logic with spatial operators. Technical Report DIT-06-009, Informatica e Telecomunicationi, University of Trento (2006)Google Scholar
  23. 23.
    Mardare, R.: Logical analysis of complex systems: Dynamic epistemic spatial logics. PhD. thesis, DIT, University of Trento, Italy (March 2006),
  24. 24.
    Calcagno, C., Cardelli, L., Gordon, A.D.: Deciding validity in a spatial logic for trees, 62–73 (2003)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2006

Authors and Affiliations

  • Radu Mardare
    • 1
  • Corrado Priami
    • 1
    • 2
  1. 1.University of TrentoItaly
  2. 2.Microsoft Research – University of TrentoCenter for Computational and Systems BiologyTrentoItaly

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