A Formal Language for Electronic Contracts

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4468)


In this paper we propose a formal language for writing electronic contracts, based on the deontic notions of obligation, permission, and prohibition. We take an ought-to-do approach, where deontic operators are applied to actions instead of state-of-affairs. We propose an extension of the μ-calculus in order to capture the intuitive meaning of the deontic notions and to express concurrent actions. We provide a translation of the contract language into the logic, the semantics of which faithfully captures the meaning of obligation, permission and prohibition. We also show how our language captures most of the intuitive desirable properties of electronic contracts, as well as how it avoids most of the classical paradoxes of deontic logic. We finally show its applicability on a contract example.


Model Check Atomic Action Deontic Logic Concurrent Action Intuitive Meaning 
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.


  1. 1.
    Aagedal, J.: Quality of Service Support in Development of Distributed Systems. PhD thesis, Dept. of Informatics, Faculty of Mathematics and Natural Sciences, University of Oslo (2001)Google Scholar
  2. 2.
    Beugnard, A., Jézéquel, J.M., Plouzeau, N.: Making components contract aware. IEEE 32, 38–45 (1999)Google Scholar
  3. 3.
    Biere, A.: mu-cke - efficient mu-calculus model checking. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 468–471. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  4. 4.
    Broersen, J.: Action negation and alternative reductions for dynamic deontic logics. J. Applied Logic 2, 153–168 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Broersen, J., Wieringa, R., Meyer, J.J.C.: A fixed-point characterization of a deontic logic of regular action. Fundam. Inf. 48, 107–128 (2001)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Daskalopulu, A.: Model Checking Contractual Protocols. In: Breuker, L.R., Leenes, R., Winkels, R. (eds.) Legal Knowledge and Information Systems, JURIX 2000. Frontiers in Artificial Intelligence and Applications, vol. 48, pp. 35–47. IOS Press, Amsterdam (2000)Google Scholar
  7. 7.
    Daskalopulu, A., Maibaum, T.S.E.: Towards Electronic Contract Performance. In: Legal Information Systems Applications. 12th International Conference and Workshop on Database and Expert Systems Applications, pp. 771–777. IEEE Computer Society Press, Los Alamitos (2001)Google Scholar
  8. 8.
    Davulcu, H., Kifer, M., Ramakrishnan, I.V.: CTR-S: A Logic for Specifying Contracts in Semantic Web Services. In: WWW04. pp. 144–153 (2004)Google Scholar
  9. 9.
    Fischer, M.J., Ladner, R.E.: Propositional modal logic of programs. In: STOC’77, pp. 286–294. ACM Press, New York (1977)Google Scholar
  10. 10.
    Girard, J.Y.: Linear logic. Theor. Compu. Sci. 50, 1–102 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Governatori, G.: Representing business contracts in RuleML. International Journal of Cooperative Information Systems 14, 181–216 (2005)CrossRefGoogle Scholar
  12. 12.
    Governatori, G., Rotolo, A.: Logic of violations: A gentzen system for reasoning with contrary-to-duty obligations. Australian Journal of Logic 4, 193–215 (2006)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Kozen, D.: Results on the propositional mu-calculus. Theor. Comput. Sci. 27, 333–354 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Kozen, D.: Kleene algebra with tests. ACM Transactions on Programming Languages and Systems (TOPLAS’97) 19, 427–443 (1997)CrossRefzbMATHGoogle Scholar
  15. 15.
    Kozen, D., Parikh, R.: A decision procedure for the propositional μ-calculus. In: Clarke, E., Kozen, D. (eds.) Logics of Programs. LNCS, vol. 164, pp. 313–325. Springer, Heidelberg (1984)CrossRefGoogle Scholar
  16. 16.
    Kozen, D.: On kleene algebras and closed semirings. In: Rovan, B. (ed.) Mathematical Foundations of Computer Science 1990. LNCS, vol. 452, pp. 26–47. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  17. 17.
    Mally, E.: Grundgesetze des Sollens. Elemente fer Logik des Willens. Leuschner & Lubensky, Graz (1926)Google Scholar
  18. 18.
    Mateescu, R., Sighireanu, M.: Efficient on-the-fly model-checking for regular alternation-free μ-calculus. Sci. Comp. Program. 46(3), 255–281 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    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, 109–136 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    McNamara, P.: Deontic logic. In: Gabbay, D.M., Woods, J. (eds.) Handbook of the History of Logic, vol. 7, pp. 197–289. North-Holland Publishing, Amsterdam (2006)Google Scholar
  21. 21.
    Molina-Jimenez, C., Shrivastava, S., Solaiman, E., Warne, J.: Run-time Monitoring and Enforcement of Electronic Contracts. Electronic Commerce Research and Applications 3, 108–125 (2004)CrossRefGoogle Scholar
  22. 22.
    Paschke, A., Dietrich, J., Kuhla, K.: A Logic Based SLA Management Framework. In: Gil, Y., Motta, E., Benjamins, V.R., Musen, M.A. (eds.) ISWC 2005. LNCS, vol. 3729, Springer, Heidelberg (2005)Google Scholar
  23. 23.
    Pnueli, A.: Temporal logic of programs. In: FOCS’77, pp. 46–57. IEEE, Los Alamitos (1977)Google Scholar
  24. 24.
    Prakken, H., Sergot, M.: Contrary-to-duty obligations. Studia Logica 57, 91–115 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Pratt, V.R.: Semantical considerations on floyd-hoare logic. In: FOCS’76, pp. 109–121. IEEE, Los Alamitos (1976)Google Scholar
  26. 26.
    Pratt, V.R.: A practical decision method for propositional dynamic logic: Preliminary report. In: STOC’78, pp. 326–337. ACM Press, New York (1978)Google Scholar
  27. 27.
    Pratt, V.R.: Dynamic algebras and the nature of induction. In: STOC’80, pp. 22–28. ACM Press, New York (1980)Google Scholar
  28. 28.
    Prisacariu, C., Schneider, G.: Towards a formal definition of electronic contracts. Technical report 348, Department of Informatics, University of Oslo (2007)Google Scholar
  29. 29.
    Song, I., Governatori, G.: Nested rules in defeasible logic. In: Adi, A., Stoutenburg, S., Tabet, S. (eds.) RuleML 2005. LNCS, vol. 3791, pp. 204–208. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  30. 30.
    Tosic, V.: On Comprehensive Contractual Descriptions of Web Services. In: IEEE International Conference on e-Technology, e-Commerce, and e-Service, pp. 444–449. IEEE, Los Alamitos (2005)CrossRefGoogle Scholar
  31. 31.
    Walukiewicz, I.: A Complete Deductive System for the μ-Calculus. PhD thesis, Warsaw University (1993)Google Scholar
  32. 32.
    Walukiewicz, I.: Completeness of Kozen’s axiomatisation of the propositional μ-calculus. In: LICS’95, pp. 14–24. IEEE, Los Alamitos (1995)Google Scholar
  33. 33.
    Wright, G.H.V.: Deontic logic. Mind 60, 1–15 (1951)CrossRefGoogle Scholar
  34. 34.
    Wright, G.H.V.: Deontic logic: A personal view. Ratio Juris 12, 26–38 (1999)CrossRefGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2007

Authors and Affiliations

  1. 1.Dept. of Informatics – Univ. of Oslo, P.O. Box 1080 Blindern, N-0316 OsloNorway

Personalised recommendations