Namespace Logic: A Logic for a Reflective Higher-Order Calculus

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3705)


In [19] it was observed that a theory like the π-calculus, dependent on a theory of names, can be closed, through a mechanism of quoting, so that (quoted) processes provide the necessary notion of names. Here we expand on this theme by examining a construction for a Hennessy-Milner logic corresponding to an asynchronous message-passing calculus built on a notion of quoting.

Like standard Hennessy-Milner logics, the logic exhibits formulae corresponding to sets of processes, but a new class of formulae, corresponding to sets of names, also emerges. This feature provides for a number of interesting possible applications from security to data manipulation. Specifically, we illustrate formulae for controlling process response on ranges of names reminiscent of a (static) constraint on port access in a firewall configuration. Likewise, we exhibit formulae in a names-as-data paradigm corresponding to validation for fragment of XML Schema.


Mobile Process Communication Rule Lift Operator Spatial Logic Structural Congruence 
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.
    Abadi, M., Blanchet, B.: Analyzing security protocols with secrecy types and logic programs. In: POPL, pp. 33–44 (2002)Google Scholar
  2. 2.
    Abadi, M., Blanchet, B.: Secrecy types for asymmetric communication. Theor. Comput. Sci. 3(298), 387–415 (2003)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Abadi, M., Gordon, A.D.: A calculus for cryptographic protocols: The spi calculus. In: ACM Conference on Computer and Communications Security, pp. 36–47 (1997)Google Scholar
  4. 4.
    Barendregt, H.P.: The Lambda Calculus – Its Syntax and Semantics. Studies in Logic and the Foundations of Mathematics, vol. 103. North-Holland, Amsterdam (1984)zbMATHGoogle Scholar
  5. 5.
    Caires, L.: Behavioral and spatial observations in a logic for the p-calculus. In: Walukiewicz, I. (ed.) FOSSACS 2004. LNCS, vol. 2987, pp. 72–89. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  6. 6.
    Caires, L., Cardelli, L.: A spatial logic for concurrency (part i). Inf. Comput. 186(2), 194–235 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Caires, L., Cardelli, L.: A spatial logic for concurrency - ii. Theor. Comput. Sci. 322(3), 517–565 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Conway, J.H.: On Numbers and Games. Academic Press, London (1976)zbMATHGoogle Scholar
  9. 9.
    Cowan, J., Tobin, R.: Xml information set. W3C (2004)Google Scholar
  10. 10.
    des Rivieres, J., Smith, B.C.: The implementation of procedurally reflective languages. In: ACM Symposium on Lisp and Functional Programming, pp. 331–347 (1984)Google Scholar
  11. 11.
    Fontana, W.: private conversation (2004)Google Scholar
  12. 12.
    Gabbay, M.J.: The π-calculus in FM. In: Kamareddine, F. (ed.) Thirty-five years of Automath. Kluwer Academic Publishers, Dordrecht (2003)Google Scholar
  13. 13.
    Gabbay, M., Cheney, J.: A sequent calculus for nominal logic. In: LICS, pp. 139–148 (2004)Google Scholar
  14. 14.
    Gordon, A.D., Jeffrey, A.: Typing correspondence assertions for communication protocols. Theor. Comput. Sci. 1-3(300), 379–409 (2003)CrossRefMathSciNetGoogle Scholar
  15. 15.
    Hermida, C., Power, J.: Fibrational control structures. In: CONCUR, pp. 117–129 (1995)Google Scholar
  16. 16.
    Krivine, J.-L.: The curry-howard correspondence in set theory. In: Abadi, M. (ed.) Proceedings of the Fifteenth Annual IEEE Symp. on Logic in Computer Science, LICS 2000, June 2000. IEEE Computer Society Press, Los Alamitos (2000)Google Scholar
  17. 17.
    Microsoft Corporation. Microsoft biztalk server,
  18. 18.
    Carbone, M., Maffeis, S.: On the expressive power of polyadic synchronisation in pi-calculus. Nordic Journal of Computing 10(2), 70–98 (2003)zbMATHMathSciNetGoogle Scholar
  19. 19.
    Meredith, L.G., Radestock, M.: A reflective higher-order calculus. In: Viroli, M. (ed.) ETAPS 2005 Satellites. Springer, Heidelberg (2005)Google Scholar
  20. 20.
    Milner, R.: The polyadic π-calculus: A tutorial. In: Logic and Algebra of Specification. Springer, Heidelberg (1993)Google Scholar
  21. 21.
    Milner, R.: Strong normalisation in higher-order action calculi. In: Ito, T., Abadi, M. (eds.) TACS 1997. LNCS, vol. 1281, pp. 1–19. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  22. 22.
    Pavlovic, D.: Categorical logic of names and abstraction in action calculus. Math. Structures in Comp. Sci. 7, 619–637 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Sangiorgi, D., Walker, D.: The π-Calculus: A Theory of Mobile Processes. Cambridge University Press, Cambridge (2001)Google Scholar
  24. 24.
    Thompson, H.S., Beech, D., Maloney, M., Mendelsohn, N.: Xml schema part i: Structures, 2nd edn. W3C (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.CTO, Djinnisys CorporationSeattleUSA
  2. 2.CTO, LShift, Ltd.LondonUK

Personalised recommendations