Tractable Reasoning about Group Beliefs

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8758)


In contemporary autonomous systems, like robotics, the need to apply group knowledge has been growing consistently with the increasing complexity of applications, especially those involving teamwork. However, classical notions of common knowledge and common belief, as well as their weaker versions, are too complex. Also, when modeling real-world situations, lack of knowledge and inconsistency of information naturally appear. Therefore, we propose a shift in perspective from reasoning in multi-modal logics to querying paraconsistent knowledge bases. This opens the possibility for exploring a new approach to group beliefs. To demonstrate expressiveness of our approach, examples of social procedures leading to complex belief structures are constructed via the use of epistemic profiles. To achieve tractability without compromising the expressiveness, as an implementation tool we choose 4QL, a four-valued rule-based query language. This permits both to tame inconsistency in individual and group beliefs and to execute the social procedures in polynomial time. Therefore, a marked improvement in efficiency has been achieved over systems such as (dynamic) epistemic logics with common knowledge and ATL, for which problems like model checking and satisfiability are PSPACE- or even EXPTIME-hard.


Cooperation reasoning for robotic agents formal models of agency knowledge representation tractability 


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  1. 1.
    de Amo, S., Pais, M.: A paraconsistent logic approach for querying inconsistent databases. International Journal of Approximate Reasoning 46, 366–386 (2007)CrossRefMathSciNetzbMATHGoogle Scholar
  2. 2.
    Balakirsky, S., et al.: Towards heterogeneous robot teams for disaster mitigation: Results and performance metrics from RoboCup Rescue. Journal of Field Robotics 24(11-12), 943–967 (2007)CrossRefGoogle Scholar
  3. 3.
    Baral, C., Gelfond, G., Son, T.C., Pontelli, E.: Using answer set programming to model multi-agent scenarios involving agents’ knowledge about other’s knowledge. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems, vol. 1, pp. 259–266. International Foundation for Autonomous Agents and Multiagent Systems (2010)Google Scholar
  4. 4.
    Bézieau, J.J., Carnielli, W., Gabbay, D. (eds.): Handbook of Paraconsistency. College Publications (2007)Google Scholar
  5. 5.
    Bordini, R., Dastani, M., Dix, J., El Fallah-Seghrouchni, A. (eds.): Multi-Agent Programming: Languages, Platforms and Applications. Springer (2009)Google Scholar
  6. 6.
    Brewka, G., Eiter, T.: Equilibria in heterogeneous nonmonotonic multi-context systems. In: Proc. of the 22nd AAAI Conf. on Artificial Intelligence, pp. 385–390. AAAI Press (2007)Google Scholar
  7. 7.
    Brewka, G., Eiter, T., Fink, M., Weinzierl, A.: Managed multi-context systems. In: Walsh, T. (ed.) Proc. of the 22nd International Joint Conference on Artificial Intelligence, IJCAI 2011, pp. 786–791. IJCAI/AAAI (2011)Google Scholar
  8. 8.
    Brewka, G., Eiter, T., Truszczynski, M.: Answer set programming at a glance. Commun. ACM 54(12), 92–103 (2011)CrossRefGoogle Scholar
  9. 9.
    Brewka, G.: Answer sets and qualitative decision making. Synthese 146(1-2), 171–187 (2005)CrossRefMathSciNetzbMATHGoogle Scholar
  10. 10.
    Casali, A., Godo, L., Sierra, C.: A language for the execution of graded BDI agents. Logic Journal of the IGPL 21(3), 332–354 (2013)CrossRefMathSciNetzbMATHGoogle Scholar
  11. 11.
    Chalkiadakis, G., Elkind, E., Wooldridge, M.: Computational Aspects of Cooperative Game Theory. Morgan & Claypool Publishers (2011)Google Scholar
  12. 12.
    Clark, H., Marshall, C.: Definite reference and mutual knowledge. In: Joshi, A., Webber, B., Sag, I. (eds.) Elements of Discourse Understanding, pp. 10–63. Cambridge University Press (1981)Google Scholar
  13. 13.
    Dignum, F., Dunin-Kęplicz, B., Verbrugge, R.: Creating collective intention through dialogue. Logic Journal of the IGPL 9, 145–158 (2001)CrossRefGoogle Scholar
  14. 14.
    Ditmarsch, H.P.v., Ruan, J., Verbrugge, L.C.: Model checking sum and product. In: Zhang, S., Jarvis, R.A. (eds.) AI 2005. LNCS (LNAI), vol. 3809, pp. 790–795. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    van Ditmarsch, H.P., Ruan, J., Verbrugge, R.: Sum and product in dynamic epistemic logic. Journal of Logic and Computation 18(4), 563–588 (2008)CrossRefMathSciNetzbMATHGoogle Scholar
  16. 16.
    van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic, vol. 337. Springer (2007)Google Scholar
  17. 17.
    Doherty, P., Heintz, F., Kvarnström, J.: High-level mission specification and planning for collaborative unmanned aircraft systems using delegation. Unmanned Systems 1(1), 75–119 (2013)CrossRefGoogle Scholar
  18. 18.
    Dunin-Kęplicz, B., Strachocka, A., Szałas, A., Verbrugge, R.: A paraconsistent approach to speech acts. In: Proc. Workshop on Argumentation in Multi-Agent Systems, pp. 59–78. IFAAMAS (2012)Google Scholar
  19. 19.
    Dunin-Kęplicz, B., Szałas, A.: Epistemic profiles and belief structures. In: Jezic, G., Kusek, M., Nguyen, N.-T., Howlett, R.J., Jain, L.C. (eds.) KES-AMSTA 2012. LNCS, vol. 7327, pp. 360–369. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  20. 20.
    Dunin-Kęplicz, B., Szałas, A.: Paraconsistent distributed belief fusion. In: Fortino, G., Badica, C., Malgeri, M., Unland, R. (eds.) Intelligent Distributed Computing VI. SCI, vol. 446, pp. 56–69. Springer, Heidelberg (2013)Google Scholar
  21. 21.
    Dunin-Kęplicz, B., Szałas, A.: Taming complex beliefs. In: Nguyen, N.T. (ed.) Transactions on CCI XI. LNCS, vol. 8065, pp. 1–21. Springer, Heidelberg (2013)Google Scholar
  22. 22.
    Dunin-Kęplicz, B., Szałas, A.: Indeterministic belief structures. In: Jezic, G., Kusek, M., Lovrek, I., Howlett, R. J., Jain, L.C. (eds.) Agent and Multi-Agent Systems: Technologies and Applications. AISC, vol. 296, pp. 57–66. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  23. 23.
    Dunin-Kęplicz, B., Verbrugge, R.: Teamwork in Multi-Agent Systems: A Formal Approach. Wiley (2010)Google Scholar
  24. 24.
    Dunin-Kęplicz, B., Verbrugge, R., Slizak, M.: TEAMLOG in action: A case study in teamwork. Comput. Sci. Inf. Syst. 7(3), 569–595 (2010)CrossRefGoogle Scholar
  25. 25.
    Dunin-Kęplicz, B., Strachocka, A.: Perceiving rules under incomplete and inconsistent information. In: Leite, J., Son, T.C., Torroni, P., van der Torre, L., Woltran, S. (eds.) CLIMA XIV 2013. LNCS (LNAI), vol. 8143, pp. 256–272. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  26. 26.
    Eiter, T., Fink, M., Schüller, P.: Approximations for explanations of inconsistency in partially known multi-context systems. In: Delgrande, J.P., Faber, W. (eds.) LPNMR 2011. LNCS (LNAI), vol. 6645, pp. 107–119. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  27. 27.
    Etzioni, O., Golden, K., Weld, D.: Sound and efficient closed-world reasoning for planning. Artificial Intelligence 89, 113–148 (1997)CrossRefMathSciNetzbMATHGoogle Scholar
  28. 28.
    Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning About Knowledge. MIT Press (1995)Google Scholar
  29. 29.
    Gabbay, D., Hunter, A.: Making inconsistency respectable: A logical framework for inconsistency in reasoning. In: Jorrand, P., Kelemen, J. (eds.) FAIR 1991. LNCS, vol. 535, pp. 19–32. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  30. 30.
    Gelfond, M., Kahl, Y.: Knowledge Representation, Reasoning, and the Design of Intelligent Agents - The Answer-Set Programming Approach. Cambridge University Press (2014)Google Scholar
  31. 31.
    Giunchiglia, F., Serafini, L.: Multilanguage hierarchical logics, or: How we can do without modal logics. Artificial Intelligence 65(1), 29–70 (1994)CrossRefMathSciNetzbMATHGoogle Scholar
  32. 32.
    Giunchiglia, F., Serafini, L., Giunchiglia, E., Frixione, M.: Non-omniscient belief as context-based reasoning. In: IJCAI, vol. 93, pp. 9206–9203 (1993)Google Scholar
  33. 33.
    Harrenstein, P., van der Hoek, W., Meyer, J.J., Witteveen, C.: Boolean games. In: van Benthem, J. (ed.) Proc. of the 8th Conference on Theoretical Aspects of Rationality and Knowledge, pp. 287–298. Morgan Kaufmann Publishers Inc. (2001)Google Scholar
  34. 34.
    van der Hoek, W., Lomuscio, A., Wooldridge, M.: On the complexity of practical ATL model checking. In: Proc. of the 5th AAMAS, pp. 201–208. ACM (2006)Google Scholar
  35. 35.
    van der Hoek, W., Wooldridge, M.: On the logic of cooperation and propositional control. Artificial Intelligence 164(1-2), 81–119 (2005)CrossRefMathSciNetzbMATHGoogle Scholar
  36. 36.
    Lakemeyer, G., Lespérance, Y.: Efficient reasoning in multiagent epistemic logics. In: De Raedt, L., Bessière, C., Dubois, D., Doherty, P., Frasconi, P., Heintz, F., Lucas, P. (eds.) Proc. of ECAI 2012 - 20th European Conference on Artificial Intelligence. Frontiers in Artificial Intelligence and Applications, vol. 242, pp. 498–503. IOS Press (2012)Google Scholar
  37. 37.
    Landén, D., Heintz, F., Doherty, P.: Complex task allocation in mixed-initiative delegation: A UAV case study. In: Desai, N., Liu, A., Winikoff, M. (eds.) PRIMA 2010. LNCS, vol. 7057, pp. 288–303. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  38. 38.
    Levesque, H.J.: A logic of implicit and explicit belief. In: Proceedings of the Fourth National Conference on Artificial Intelligence (AAAI 1984), pp. 198–202 (1984)Google Scholar
  39. 39.
    Liu, F.: Diversity of agents. In: Agotnes, T., Alechina, N. (eds.) Proc. of the ESSLLI Workshop on Resource-bounded Agents, pp. 88–98 (2006)Google Scholar
  40. 40.
    Małuszyński, J., Szałas, A.: Living with inconsistency and taming nonmonotonicity. In: de Moor, O., Gottlob, G., Furche, T., Sellers, A. (eds.) Datalog 2010. LNCS, vol. 6702, pp. 384–398. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  41. 41.
    Małuszyński, J., Szałas, A.: Logical foundations and complexity of 4QL, a query language with unrestricted negation. Journal of Applied Non-Classical Logics 21(2), 211–232 (2011)CrossRefMathSciNetGoogle Scholar
  42. 42.
    Małuszyński, J., Szałas, A.: Partiality and inconsistency in agents’ belief bases. In: Barbucha, D., et al. (eds.) Proc. KES-AMSTA. Frontiers of Artificial Intelligence and Applications, vol. 252, pp. 3–17. IOS Press (2011)Google Scholar
  43. 43.
    Mares, E.: A paraconsistent theory of belief revision. Erkenntnis 56, 229–246 (2002)CrossRefMathSciNetzbMATHGoogle Scholar
  44. 44.
    Meyer, J.J.C., van der Hoek, W.: Epistemic Logic for Computer Science and Artificial Intelligence. Cambridge University Press (1995)Google Scholar
  45. 45.
    Moore, R.: Possible-world semantics for autoepistemic logic. In: Proc. 1st Nonmonotonic Reasoning Workshop, pp. 344–354 (1984)Google Scholar
  46. 46.
    Nguyen, L.A.: On modal deductive databases. In: Eder, J., Haav, H.-M., Kalja, A., Penjam, J. (eds.) ADBIS 2005. LNCS, vol. 3631, pp. 43–57. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  47. 47.
    Nourbakhsh, I., Sycara, K., Koes, M., Yong, M., Lewis, M., Burion, S.: Human-robot teaming for search and rescue. IEEE Pervasive Computing 4(1), 72–79 (2005)CrossRefGoogle Scholar
  48. 48.
    Nurmi, H.: Voting Procedures under Uncertainty. Springer (2002)Google Scholar
  49. 49.
    Nute, D.: Defeasible logic. In: Handbook of Logic in Artificial Intelligence and Logic Programming, pp. 353–395. Oxford University Press (1994)Google Scholar
  50. 50.
    Priest, G.: Paraconsistent belief revision. Theoria 67, 214–228 (2001)CrossRefMathSciNetGoogle Scholar
  51. 51.
    Reiter, R.: A logic for default reasoning. Artificial Intelligence Journal 13, 81–132 (1980)CrossRefMathSciNetzbMATHGoogle Scholar
  52. 52.
    Sim, K.: Epistemic logic and logical omniscience: A survey. International Journal of Intelligent Systems 12, 57–81 (1997)CrossRefzbMATHGoogle Scholar
  53. 53.
    Szałas, A.: How an agent might think. Logic Journal of the IGPL 21(3), 515–535 (2013)CrossRefMathSciNetzbMATHGoogle Scholar
  54. 54.
    Vitória, A., Małuszyński, J., Szałas, A.: Modeling and reasoning with paraconsistent rough sets. Fundamenta Informaticae 97(4), 405–438 (2009)MathSciNetzbMATHGoogle Scholar
  55. 55.
    Walther, D., Lutz, C., Wolter, F., Wooldridge, M.: ATL satisfiability is indeed EXPTIME-complete. Journal of Logic and Computation 16(6), 765–787 (2006)CrossRefMathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institute of InformaticsWarsaw UniversityPoland
  2. 2.Dept. of Computer and Information ScienceLinköping UniversitySweden
  3. 3.Institute of Artificial IntelligenceUniversity of GroningenThe Netherlands

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