Towards a Paraconsistent Approach to Actions in Distributed Information-Rich Environments

  • Łukasz Białek
  • Barbara Dunin-Kęplicz
  • Andrzej Szałas
Part of the Studies in Computational Intelligence book series (SCI, volume 737)


The paper introduces ActLog, a rule-based language capable of specifying actions paraconsistently. ActLog is an extension of 4QL\(^{\!\text{ Bel }}\), a rule-based language for reasoning with paraconsistent and paracomplete belief bases and belief structures. Actions considered in the paper act on belief bases rather than states represented as sets of ground literals. Each belief base stores multiple world representations which can be though of as a representation of possible states. In this context ActLog’s action may be then seen as a method of transforming one belief base into another. In contrast to other approaches, ActLog permits to execute actions even if the underlying belief base state is partial or inconsistent. Finally, the framework introduced in this paper is tractable.


Action languages Paraconsistent reasoning Paracomplete reasoning Belief structures 



This research has been supported by the Polish National Science Centre grant 2015/19/B/ST6/02589.


  1. 1.
    Bertossi, L., Hunter, A., Schaub, T.: Introduction to inconsistency tolerance. Bertossi et al. [2], pp. 1–14Google Scholar
  2. 2.
    Bertossi, L., Hunter, A., Schaub, T. (eds.): Inconsistency Tolerance, LNCS, vol. 3300. Springer (2005)Google Scholar
  3. 3.
    Białek Ł., Dunin-Kęplicz, B., Szałas, A.: Rule-based reasoning with belief structures. In: Kryszkiewicz, M., Appice, A., Ślęzak, D., Rybiński, H., Skowron, A., Raś, Z. (eds.) Foundations of Intelligent Systems, Proceedings of ISMIS Conference. LNAI, vol. 10352, pp. 229–239. Springer (2017)Google Scholar
  4. 4.
    Doherty, P., Szałas, A.: Stability, supportedness, minimality and Kleene answer set programs. In: Eiter, T., Strass, H., Truszczyński, M., Woltran, S. (eds.) Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation, LNCS, vol. 9060, pp. 125–140. Springer International Publishing (2015)Google Scholar
  5. 5.
    Dunin-Kęplicz, B., Szałas, A.: Epistemic profiles and belief structures. In: Proceedings KES-AMSTA 2012: Agents and Multi-agent Systems: Technologies and Applications. LNCS, vol. 7327, pp. 360–369. Springer (2012)Google Scholar
  6. 6.
    Dunin-Kęplicz, B., Szałas, A.: Taming complex beliefs. Trans. Comput. Collect. Intel. XI LNCS 8065, 1–21 (2013)Google Scholar
  7. 7.
    Dunin-Kęplicz, B., Szałas, A.: Indeterministic belief structures. In: Jezic, G., Kusek, M., Lovrek, I., J. Howlett, Lakhmi, J. (eds.) Agent and Multi-Agent Systems: Technologies and Applications: Proceedings 8th International Conference KES-AMSTA, pp. 57–66. Springer (2014)Google Scholar
  8. 8.
    Dunin-Kęplicz, B., Verbrugge, R.: Teamwork in Multi-Agent Systems. A Formal Approach. Wiley (2010)Google Scholar
  9. 9.
    Dunin-Kęplicz, B., Verbrugge, R., Ślizak, M.: Teamlog in action: a case study in teamwork. Comput. Sci. Inf. Syst. 7(3), 569–595 (2010)Google Scholar
  10. 10.
    Eiter, T., Faber, W., Leone, N., Pfeifer, G., Polleres, A.: Planning under incomplete knowledge. In: Lloyd, J., Dahl, V., Furbach, U., Kerber, M., Lau, K.K., Palamidessi, C., Pereira, L., Sagiv, Y., Stuckey, P. (eds.) Proceedings Computational Logic: 1st International Conference, pp. 807–821. Springer (2000)Google Scholar
  11. 11.
    Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning About Knowledge. The MIT Press (2003)Google Scholar
  12. 12.
    Ferraris, P., Lifschitz, V.: On the minimality of stable models. In: Balduccini, M., Son, T. (eds.) Logic Programming, Knowledge Representation, and Nonmonotonic Reasoning. LNCS, vol. 6565, pp. 64–73. Springer (2011)Google Scholar
  13. 13.
    Fikes, R.E., Nilsson, N.J.: Strips: a new approach to the application of theorem proving to problem solving. In: Proceedings of the 2nd International Joint Conference on Artificial Intelligence, pp. 608–620. IJCAI’71, Morgan Kaufmann Publishers Inc. (1971)Google Scholar
  14. 14.
    Hewitt, C.: Formalizing common sense for scalable inconsistency-robust information integration using direct logic reasoning and the actor model. arXiv:0812.4852 (2008)
  15. 15.
    Hewitt, C., Woods, J. (eds.): Inconsistency Robustness. College Publications (2015)Google Scholar
  16. 16.
    Małuszyński, J., Szałas, A.: Living with inconsistency and taming nonmonotonicity. In: de Moor, O., Gottlob, G., Furche, T., Sellers, A. (eds.) Datalog 2.0. LNCS, vol. 6702, pp. 384–398. Springer (2011)Google Scholar
  17. 17.
    Małuszyński, J., Szałas, A.: Logical foundations and complexity of 4QL, a query language with unrestricted negation. J. Appl. Non-Classical Logics 21(2), 211–232 (2011)Google Scholar
  18. 18.
    Małuszyński, J., Szałas, A.: Partiality and inconsistency in agents’ belief bases. In: Barbucha, D., Le, M., Howlett, R., Jain, L. (eds.) KES-AMSTA. Frontiers in Artificial Intelligence and Applications, vol. 252, pp. 3–17. IOS Press (2013)Google Scholar
  19. 19.
    Mueller, E.: Commonsense Reasoning. Morgan Kaufmann (2006)Google Scholar
  20. 20.
    Sakama, C., Inoue, K.: An alternative approach to the semantics of disjunctive logic programs and deductive databases. J. Autom. Reason. 13(1), 145–172 (1994)Google Scholar
  21. 21.
    Shieber, S.M.: Solving problems in an uncertain world. Bachelor’s Thesis, Harvard College (1981)Google Scholar
  22. 22.
    Soininen, T., Niemelä, I.: Developing a declarative rule language for applications in product configuration. In: Gupta, G. (ed.) Proceedings PADL’99. LNCS, vol. 1551, pp. 305–319. Springer (1999)Google Scholar
  23. 23.
    Szałas, A.: How an agent might think. Logic J. IGPL 21(3), 515–535 (2013)Google Scholar
  24. 24.
    Thrun, S., Burgard, W., Fox, D.: Probabilistic Robotics (Intelligent Robotics and Autonomous Agents). The MIT Press (2005)Google Scholar
  25. 25.
    Zadeh, L.: Fuzzy sets. Inf. Control 8, 333–353 (1965)Google Scholar

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© Springer International Publishing AG 2018

Authors and Affiliations

  • Łukasz Białek
    • 1
  • Barbara Dunin-Kęplicz
    • 1
  • Andrzej Szałas
    • 1
    • 2
  1. 1.Institute of Informatics, University of WarsawWarsawPoland
  2. 2.Department of Computer and Information ScienceLinköping UniversityLinköpingSweden

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