\(\mathcal{CL}\): An Action-Based Logic for Reasoning about Contracts

  • Cristian Prisacariu
  • Gerardo Schneider
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5514)

Abstract

This paper presents a new version of the \(\mathcal{CL}\) contract specification language. \(\mathcal{CL}\) combines deontic logic with propositional dynamic logic but it applies the modalities exclusively over structured actions. \(\mathcal{CL}\) features synchronous actions, conflict relation, and an action negation operation. The \(\mathcal{CL}\) version that we present here is more expressive and has a cleaner semantics than its predecessor. We give a direct semantics for \(\mathcal{CL}\) in terms of normative structures. We show that \(\mathcal{CL}\) respects several desired properties from legal contracts and is decidable. We relate this semantics with a trace semantics of \(\mathcal{CL}\) which we used for run-time monitoring contracts.

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References

  1. 1.
    Owe, O., Schneider, G., Steffen, M.: Components, objects, and contracts. In: SAVCBS 2007, pp. 91–94. ACM Digital Library, Dubrovnik (2007)Google Scholar
  2. 2.
    van der Torre, L.: Contextual deontic logic: Normative agents, violations and independence. Ann. Math. Artif. Intell. 37(1-2), 33–63 (2003)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    von Wright, G.H.: Deontic logic. Mind 60, 1–15 (1951)CrossRefGoogle Scholar
  4. 4.
    Fischer, M.J., Ladner, R.E.: Propositional modal logic of programs. In: STOC 1977, pp. 286–294. ACM Press, New York (1977)Google Scholar
  5. 5.
    Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)MATHGoogle Scholar
  6. 6.
    von Wright, G.H.: An Essay in Deontic Logic and the General Theory of Action. North Holland Publishing Co., Amsterdam (1968)MATHGoogle Scholar
  7. 7.
    Segerberg, K.: A deontic logic of action. Studia Logica 41(2), 269–282 (1982)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Meyer, J.J.C.: A different approach to deontic logic: Deontic logic viewed as a variant of dynamic logic. Notre Dame Journal of Formal Logic 29(1), 109–136 (1988)MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Broersen, J., Wieringa, R., Meyer, J.J.C.: A fixed-point characterization of a deontic logic of regular action. Fundam. Inf. 48(2-3), 107–128 (2001)MathSciNetMATHGoogle Scholar
  10. 10.
    Milner, R.: Calculi for synchrony and asynchrony. TCS 25, 267–310 (1983)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Berry, G.: The foundations of Esterel. In: Proof, language, and interaction: essays in honour of Robin Milner, pp. 425–454. MIT Press, Cambridge (2000)Google Scholar
  12. 12.
    Prisacariu, C., Schneider, G.: A formal language for electronic contracts. In: Bonsangue, M.M., Johnsen, E.B. (eds.) FMOODS 2007. LNCS, vol. 4468, pp. 174–189. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Kyas, M., Prisacariu, C., Schneider, G.: Run-time monitoring of electronic contracts. In: Cha, S(S.), Choi, J.-Y., Kim, M., Lee, I., Viswanathan, M. (eds.) ATVA 2008. LNCS, vol. 5311, pp. 397–407. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  14. 14.
    Van der Meyden, R.: Dynamic logic of permission, the. In: LICS 1990, pp. 72–78. IEEE Computer Society Press, Los Alamitos (1990)Google Scholar
  15. 15.
    Castro, P.F., Maibaum, T.: A complete and compact propositional deontic logic. In: Jones, C.B., Liu, Z., Woodcock, J. (eds.) ICTAC 2007. LNCS, vol. 4711, pp. 109–123. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  16. 16.
    Harel, D.: Recurring dominoes: Making the highly undecidable highly understandable. In: Karpinski, M. (ed.) FCT 1983. LNCS, vol. 158, pp. 177–194. Springer, Heidelberg (1983)CrossRefGoogle Scholar
  17. 17.
    Peleg, D.: Concurrent dynamic logic. In: STOC 1985, pp. 232–239. ACM Press, New York (1985)Google Scholar
  18. 18.
    Prakken, H., Sergot, M.: Dyadic deontic logic and contrary-to-duty obligation. In: Defeasible Deontic Logic, pp. 223–262. Kluwer Academic Publishers, Dordrecht (1997)CrossRefGoogle Scholar
  19. 19.
    Prisacariu, C.: Extending Kleene Algebra with Synchrony – technicalities. Technical Report 376, Univ. Oslo (2008)Google Scholar
  20. 20.
    Ben-Ari, M., Halpern, J.Y., Pnueli, A.: Finite models for deterministic propositional dynamic logic. In: Even, S., Kariv, O. (eds.) ICALP 1981. LNCS, vol. 115, pp. 249–263. Springer, Heidelberg (1981)CrossRefGoogle Scholar
  21. 21.
    Harel, D., Sherman, R.: Propositional dynamic logic of flowcharts. In: Karpinski, M. (ed.) FCT 1983. LNCS, vol. 158, pp. 195–206. Springer, Heidelberg (1983)CrossRefGoogle Scholar
  22. 22.
    Prisacariu, C., Schneider, G.: CL: A Logic for Reasoning about Legal Contracts –Semantics. Technical Report 371, Univ. Oslo (2008)Google Scholar
  23. 23.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press, Cambridge (2001)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Cristian Prisacariu
    • 1
  • Gerardo Schneider
    • 1
  1. 1.Department of InformaticsUniversity of OsloOsloNorway

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