Computing Argumentation in Polynomial Number of BDD Operations: A Preliminary Report

  • Yuqing Tang
  • Timothy J. Norman
  • Simon Parsons
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6614)


Many advances in argumentation theory have been made, but the exponential complexity of argumentation-based reasoning has made it impractical to apply argumentation theory. In this paper, we propose a binary decision diagram (BDD) approach to argumentation-based reasoning. In the approach, sets of arguments and defeats are encoded into BDDs so that an argumentation process can work on a set of arguments and defeats simultaneously in one BDD operation. As a result, the argumentation can be computed in polynomial number of BDD operations on the number of input sentences.


Multiagent System Argumentation Framework Binary Decision Diagram Polynomial Number Symbolic Model Check 
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.


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  1. 1.
    Amgoud, L., Cayrol, C.: Inferring from inconsistency in preference-based argumentation frameworks. Journal of Automated Reasoning 29(2), 125–169 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Amgoud, L., Cayrol, C.: A reasoning model based on the production of acceptable arguments. Annals of Mathematics and Artificial Intelligence 34(1-3), 197–215 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Berghammer, R., Fronk, A.: Exact computation of minimum feedback vertex sets with relational algebra. Fundam. Inf. 70(4), 301–316 (2005)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Bollig, B., Wegener, I.: Improving the variable ordering of OBDDs is NP-Complete. IEEE Transations on Computers 45(9), 993–1002 (1996)CrossRefzbMATHGoogle Scholar
  5. 5.
    Bryant, R.E.: Symbolic boolean manipulation with ordered binary-decision diagrams. ACM Computing Surveys 24(3), 293–318 (1992)CrossRefGoogle Scholar
  6. 6.
    Burch, J., Clarke, E., McMillan, K., Dill, D., Burch, L.H.J.R., Clarke, E.M., Mcmilla, K.L., Dill, D.L., Hwang, L.J.: Symbolic Model Checking: 1020 States and Beyond. In: Proceedings of the Fifth Annual IEEE Symposium on Logic in Computer Science, pp. 1–33. IEEE Computer Society Press, Washington, D.C (1990)Google Scholar
  7. 7.
    Burch, J.R., Clarke, E.M., Long, D.E.: Symbolic model checking with partitioned transition relations. In: Proceedings of International Conference on Very Large Scale Integration, pp. 49–58. North-Holland, Amsterdam (1991)Google Scholar
  8. 8.
    Cabodi, G., Camurati, P., Lavagno, L., Quer, S.: Disjunctive partitioning and partial iterative squaring: an effective approach for symbolic traversal of large circuits. In: DAC 1997: Proceedings of the 34th Annual Conference on Design Automation, pp. 728–733. ACM Press, New York (1997)Google Scholar
  9. 9.
    Chauhan, P., Clarke, E.M., Jha, S., Kukula, J., Shiple, T., Veith, H., Wang, D.: Non-linear quantification scheduling in image computation. In: ICCAD 2001: Proceedings of the 2001 IEEE/ACM International Conference on Computer-aided Design, pp. 293–298. IEEE Computer Society Press, Piscataway (2001)Google Scholar
  10. 10.
    Cimatti, A., Pistore, M., Roveri, M., Traverso, P.: Weak, strong, and strong cyclic planning via symbolic model checking. Artificial Intelligence 147(1-2), 35–84 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Coudert, O., Berthet, C., Madre, J.C.: Verification of synchronous sequential machines based on symbolic execution. In: Automatic Verification Methods for Finite State Systems, pp. 365–373 (1989)Google Scholar
  12. 12.
    Coudert, O., Madre, J.C.: The implicit set paradigm: a new approach to finite state system verification. Formal Methods in System Design 6(2), 133–145 (1995)CrossRefGoogle Scholar
  13. 13.
    Dimopoulos, Y., Nebel, B., Toni, F.: On the computational complexity of assumption-based argumentation for default reasoning. Artificial Intelligence 141, 57–78 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Drechsler, R., Drechsler, N., Günther, W.: Fast exact minimization of BDDs. In: DAC 1998: Proceedings of the 35th Annual Conference on Design Automation, pp. 200–205. ACM Press, New York (1998)Google Scholar
  15. 15.
    Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence 77(2), 321–358 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Dunne, P.E., Bench-capon, T.J.M.: Two party immediate response disputes: properties and efficiency. Artificial Intelligence 149, 2003 (2001)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Gordon, T., Karacapilidis, N.: The zeno argumentation framework. In: in Proceedings of the Sixth International Conference on AI and Law, pp. 10–18. ACM Press, New York (1997)Google Scholar
  18. 18.
    Grumberg, O., Livne, S., Markovitch, S.: Learning to order BDD variables in verification. Journal of Artificial Intelligence Research (JAIR) 18, 83–116 (2003)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Hojati, R., Krishnan, S.C., Brayton, R.K.: Early quantification and partitioned transition relations. In: ICCD 1996: Proceedings of the 1996 International Conference on Computer Design, VLSI in Computers and Processors, pp. 12–19. IEEE Computer Society Press, Washington, DC, USA (1996)Google Scholar
  20. 20.
    Jain, J., Adams, W., Fujita, M.: Sampling schemes for computing OBDD variable orderings. In: ICCAD 1998: Proceedings of the 1998 IEEE/ACM International Conference on Computer-aided Design, pp. 631–638. ACM Press, New York (1998)Google Scholar
  21. 21.
    Jensen, R.M., Bryant, R.E., Veloso, M.M.: An efficient BDD-based A* algorithm. In: Proceedings of AIPS 2002 Workshop on Planning via Model Checking (2002)Google Scholar
  22. 22.
    Jensen, R.M., Bryant, R.E., Veloso, M.M.: SetA*: An efficient BDD-based heuristic search algorithm. In: Proceedings of 18th National Conference on Artificial Intelligence (AAAI 2002), pp. 668–673 (2002)Google Scholar
  23. 23.
    Jensen, R.M., Veloso, M.M., Bryant, R.E.: State-set branching: Leveraging BDDs for heuristic search. Artificial Intelligence 172(2-3), 103–139 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Jhala, R., Majumdar, R.: Software model checking. ACM Comput. Surv. 41(4), 1–54 (2009)CrossRefGoogle Scholar
  25. 25.
    Kakas, A.C., Toni, F.: Computing argumentation in logic programming. Journal of Logic and Computation 9, 515–562 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Karacapilidis, N., Papadias, D.: Computer supported argumentation and collaborative decision making: The hermes system. Information Systems 26, 259–277 (2001)CrossRefzbMATHGoogle Scholar
  27. 27.
    Katzav, J., Reed, C.: On argumentation schemes and the natural classification of arguments. Argumentation 18(2) (2004)Google Scholar
  28. 28.
    Meinel, C., Theobald, T.: Algorithms and Data Structures in VLSI Design. Springer-Verlag New York, Inc, Secaucus (1998)CrossRefzbMATHGoogle Scholar
  29. 29.
    Moon, I.-H., Kukula, J.H., Ravi, K., Somenzi, F.: To split or to conjoin: the question in image computation. In: DAC 2000: Proceedings of the 37th Conference on Design Automation, pp. 23–28. ACM Press, New York (2000)Google Scholar
  30. 30.
    Panda, S., Somenzi, F., Plessier, B.F.: Symmetry detection and dynamic variable ordering of decision diagrams. In: ICCAD 1994: Proceedings of the 1994 IEEE/ACM International Conference on Computer-aided Design, pp. 628–631. IEEE Computer Society Press, Los Alamitos (1994)Google Scholar
  31. 31.
    Pearl, J.: Heuristics: intelligent search strategies for computer problem solving. Addison-Wesley Longman Publishing Co., Inc., Boston (1984)Google Scholar
  32. 32.
    Prakken, H.: Coherence and flexibility in dialogue games for argumentation. Journal of Logic and Computation 15(6), 1009–1040 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Rahwan, I., Ramchurn, S.D., Jennings, N.R., Mcburney, P., Parsons, S., Sonenberg, L.: Argumentation-based negotiation. The Knowledge Engineering Review 18(4), 343–375 (2003)CrossRefGoogle Scholar
  34. 34.
    Tang, Y., Norman, T.J., Parsons, S.: A model for integrating dialogue and the execution of joint plans. In: Proceedings of the Eigth International Joint Conference on Autonomous Agents and Multiagent Systems, Budapest, Hungary, May 10-15 (2009)Google Scholar
  35. 35.
    Tang, Y., Norman, T.J., Parsons, S.: Towards the implementation of a system for planning team activities. In: Proceedings of the Second Annual Conference of the ITA. University of Maryland University College, Maryland (2009)Google Scholar
  36. 36.
    Tang, Y., Parsons, S.: Argumentation-based dialogues for deliberation. In: Proceedings of the Fourth International Joint Conference on Autonomous Agents and Multiagent Systems, pp. 552–559. ACM Press, New York (2005)CrossRefGoogle Scholar
  37. 37.
    Tang, Y., Parsons, S.: Using argumentation-based dialogues for distributed plan management. In: Proceedings of the AAAI Spring Symposium on Distributed Plan and Schedule Management, Stanford (2006)Google Scholar
  38. 38.
    Tang, Y., Parsons, S.: A dialogue mechanism for public argumentation using conversation policies. In: Proceedings of the Seventh International Joint Conference on Autonomous Agents and Multiagent Systems, Estoril, Portugal, May 12-16, pp. 445–452 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yuqing Tang
    • 1
  • Timothy J. Norman
    • 2
  • Simon Parsons
    • 1
    • 3
  1. 1.Dept. of Computer Science, Graduate CenterCity University of New YorkNew YorkUSA
  2. 2.Dept of Computing ScienceThe University of AberdeenAberdeenUK
  3. 3.Dept of Computer & Information ScienceBrooklyn College, City University of New YorkBrooklynUSA

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