Modal Logics for Brane Calculus

  • Marino Miculan
  • Giorgio Bacci
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4210)


The Brane Calculus is a calculus of mobile processes, intended to model the transport machinery of a cell system. In this paper, we introduce the Brane Logic, a modal logic for expressing formally properties about systems in Brane Calculus. Similarly to previous logics for mobile ambients, Brane Logic has specific spatial and temporal modalities. Moreover, since in Brane Calculus the activity resides on membrane surfaces and not inside membranes, we need to add a specific logic (akin Hennessy-Milner’s) for reasoning about membrane activity.

We present also a proof system for deriving valid sequents in Brane Logic. Finally, we present a model checker for a decidable fragment of this logic.


Model Checker Modal Logic Label Transition System Semliki Forest Virus Satisfaction Relation 
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., Bray, D., Lewis, J., Raff, M., Roberts, K., Watson, J.D.: Molecular biology of the cell, 2nd edn., Garland (1989)Google Scholar
  2. 2.
    Caires, L.: Behavioral and spatial observations in a logic for the pi-calculus. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 72–89. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  3. 3.
    Cardelli, L.: Brane calculi. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 257–278. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Cardelli, L.: Abstract machines of systems biology. T. Comp. Sys. Biology 3737, 145–168 (2005)Google Scholar
  5. 5.
    Cardelli, L., Gordon, A.D.: Anytime, anywhere: Modal logics for mobile ambients. In: Proc. POPL, pp. 365–377 (2000)Google Scholar
  6. 6.
    Charatonik, W., Dal-Zilio, S., Gordon, A.D., Mukhopadhyay, S., Talbot, J.-M.: Model checking mobile ambients. Theor. Comput. Sci. 308(1-3), 277–331 (2003)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Danos, V., Pradalier, S.: Projective brane calculus. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 134–148. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. J. ACM 32(1), 137–161 (1985)MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Hughes, G.E., Cresswell, M.J.: A companion to Modal Logic. Methuen, London (1984)MATHGoogle Scholar
  10. 10.
    Mardare, R., Priami, C.: A decidable extension of hennessy-milner logic with spatial operators. Technical Report DIT-06-009, Dipartimento di Informatica e Telecomunicazioni, University of Trento (2006)Google Scholar
  11. 11.
    Miculan, M., Bacci, G.: Modal logics for brane calculus. Technical Report UDMI/08/2006/RR, Dept. of Mathematics and Computer Science, Univ. of Udine (2006),
  12. 12.
    Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)MATHGoogle Scholar
  13. 13.
    Regev, A., Silverman, W., Shapiro, E.Y.: Representation and simulation of biochemical processes using the pi-calculus process algebra. In: Pacific Symposium on Biocomputing, pp. 459–470 (2001)Google Scholar
  14. 14.
    Reynolds, J.C.: Separation logic: A logic for shared mutable data structures. In: LICS, pp. 55–74. IEEE Computer Society Press, Los Alamitos (2002)Google Scholar
  15. 15.
    Sangiorgi, D.: Extensionality and intensionality of the ambient logics. In: Proc. POPL, pp. 4–13 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Marino Miculan
    • 1
  • Giorgio Bacci
    • 1
  1. 1.Dept. of Mathematics and Computer ScienceUniversity of UdineItaly

Personalised recommendations