Partial Knowledge in Membrane Systems: A Logical Approach

  • Matteo Cavaliere
  • Radu Mardare
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4361)


We propose a logic for specifying and proving properties of membrane systems. The main idea is to approach a membrane system by using the “point of view” of an external observer. Observers (as epistemic agents) accumulate their knowledge from the partial information they collect by observing subparts of the system and by applying logical reasoning to this information. We provide a formal framework to combine and interpret distributed knowledge in order to recover the complete knowledge about a membrane system. The proposed logic can be used to model biological situations where information concerning parts of the biological system is missing or incomplete.


Membrane System Partial Information Axiomatic System Epistemic Logic Dynamic Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., Walter, P.: Molecular Biology of the Cell, 4th edn. Garland Publishing, Inc. (2002)Google Scholar
  2. 2.
    Caires, L., Cardelli, L.: A Spatial Logic for Concurrency (Part I). Information and Computation 186(2) (2003)Google Scholar
  3. 3.
    Caires, L., Cardelli, L.: A Spatial Logic for Concurrency (Part II). In: Brim, L., Jančar, P., Křetínský, M., Kucera, A. (eds.) CONCUR 2002. LNCS, vol. 2421, p. 209. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Caires, L., Lozes, É.: Elimination of Quantifiers and Decidability in Spatial Logics for Concurrency. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 240–257. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  5. 5.
    Cardelli, L., Gordon, A.D.: Anytime, Anywhere: Modal Logics for Mobile Ambients. In: Proceedings of the 27th ACM Symposium on Principles of Programming Languages (2000)Google Scholar
  6. 6.
    Cardelli, L., Gordon, A.D.: Ambient Logic. Mathematical Structures in Computer Science (to appear)Google Scholar
  7. 7.
    Cavaliere, M., Leupold, P.: Evolution and Observation: A New Way to Look at Membrane Systems. In: Martín-Vide, C., Mauri, G., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2003. LNCS, vol. 2933, pp. 70–87. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Dassow, J., Păun, G.: Regulated Rewriting in Formal Language Theory. Springer, Berlin (1989)Google Scholar
  9. 9.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (1995)MATHGoogle Scholar
  10. 10.
    Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)MATHGoogle Scholar
  11. 11.
    Hennessy, M., Milner, R.: Algebraic Laws for Nondeterminism and Concurrency. Journal of ACM 32(1) (1985)Google Scholar
  12. 12.
    Mardare, R.: Logical Analysis of Complex Systems: Dynamic Epistemic Spatial Logics. PhD Thesis, DIT, University of Trento, Italy (2006), Available from:
  13. 13.
    Mardare, R., Priami, C.: Decidable Extensions of Hennessy-Milner Logic. In: Najm, E., Pradat-Peyre, J.-F., Donzeau-Gouge, V.V. (eds.) FORTE 2006. LNCS, vol. 4229, pp. 196–211. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. 14.
    Mardare, R., Priami, C.: Model Checking Dynamic Epistemic Spatial Logics.Technical Report DIT-06-009, Informatica e Telecomunicationi, University of Trento (2006)Google Scholar
  15. 15.
    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
  16. 16.
    Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)MATHGoogle Scholar
  17. 17.
    Rozenberg, G., Salomaa, A. (eds.): Handbook of Formal Languages. Springer, Berlin (1997)MATHGoogle Scholar
  18. 18.
    The P Systems Web Page:

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Matteo Cavaliere
    • 1
  • Radu Mardare
    • 2
  1. 1.Centre for Computational and Systems BiologyMicrosoft Research – University of TrentoTrentoItaly
  2. 2.D.I.TUniversity of TrentoTrentoItaly

Personalised recommendations