Deciding Refinement Relation in Belief-Intention Databases

  • Zhanhao XiaoEmail author
  • Andreas Herzig
  • Laurent Perrussel
  • Dongmo Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10640)


Bratman’s Belief-Desire-Intention (BDI) theory is seminal in the literature on BDI agents. His BDI theory is taken into account to extend Shoham’s database perspective on beliefs and intentions. In the extended framework, an intentions is considered as a high-level action, which cannot be executed directly, with a duration. They have to be progressively refined until executable basic actions are obtained. Higher- and lower-level actions are linked by the means-end relation, alias instrumentality relation. In this paper, we investigate the complexity of the decision problems for satisfiability, consequence, refinement and instrumentality in the database. Moreover, we translate these problems into the satisfiability and validity problems in propositional linear temporal logic (\(\mathsf {PLTL}\)). With such translations, we can utilize the efficient automated theorem provers for \(\mathsf {PLTL}\) to solve the problem of deciding the refinement relation between an intention and an intention set, as well as the instrumentality relation.



The work was supported by Chinese Scholarship Council and the project ANR-11-LABX-0040-CIMI within ANR-11-IDEX-0002-02.


  1. 1.
    Babiak, T., Křetínský, M., Řehák, V., Strejček, J.: LTL to Büchi automata translation: fast and more deterministic. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 95–109. Springer, Heidelberg (2012). CrossRefGoogle Scholar
  2. 2.
    Baral, C., Gelfond, M.: Reasoning about intended actions. In: Proceedings of the 20th National Conference on Artificial Intelligence (AAAI), Menlo Park, CA, vol. 20, pp. 689–694. AAAI Press, MIT Press, Cambridge 1999 (2005)Google Scholar
  3. 3.
    Biere, A., Cimatti, A., Clarke, E.M., Fujita, M., Zhu, Y.: Symbolic model checking using SAT procedures instead of BDDs. In: Proceedings of the 36th annual ACM/IEEE Design Automation Conference, pp. 317–320. ACM (1999)Google Scholar
  4. 4.
    Bratman, M.E.: Intention, Plans, and Practical Reason. Harvard University Press, Cambridge (1987). (reedited 1999 with CSLI Publications)Google Scholar
  5. 5.
    Bratman, M.E., Israel, D.J., Pollack, M.E.: Plans and resource-bounded practical reasoning. J. Comput. Intell. 4, 349–355 (1988)CrossRefGoogle Scholar
  6. 6.
    Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic model checking: \(10^{20}\) states and beyond. Inf. Comput. 98(2), 142–170 (1992)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Bylander, T.: The computational complexity of propositional STRIPS planning. Artif. Intell. 69(1), 165–204 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Cohen, P.R., Levesque, H.J.: Intention is choice with commitment. J. Artif. Intell. 42(2), 213–261 (1990)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Duret-Lutz, A., Poitrenaud, D.: Spot: an extensible model checking library using transition-based generalized büchi automata. In: Proceedings of the IEEE Computer Society’s 12th Annual International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunications Systems (MASCOTS 2004), pp. 76–83. IEEE (2004)Google Scholar
  10. 10.
    Emerson, E.A.: Temporal and modal logic. Handb. Theor. Comput. Sci. Volume B: Formal Models Sematics (B) 995(1072), 5 (1990)zbMATHGoogle Scholar
  11. 11.
    Herzig, A., Lorini, E., Perrussel, L., Xiao, Z.: BDI logics for BDI architectures: old problems, new perspectives. KI - Künstliche Intelligenz 31(1), 73–83 (2017)CrossRefGoogle Scholar
  12. 12.
    Herzig, A., Perrussel, L., Xiao, Z.: On hierarchical task networks. In: Michael, L., Kakas, A. (eds.) JELIA 2016. LNCS (LNAI), vol. 10021, pp. 551–557. Springer, Cham (2016). CrossRefGoogle Scholar
  13. 13.
    Herzig, A., Perrussel, L., Xiao, Z., Zhang, D.: Refinement of intentions. In: Michael, L., Kakas, A. (eds.) JELIA 2016. LNCS (LNAI), vol. 10021, pp. 558–563. Springer, Cham (2016). CrossRefGoogle Scholar
  14. 14.
    Sardina, S., de Silva, L., Padgham, L.: Hierarchical planning in BDI agent programming languages: a formal approach. In: Proceedings of the 5th International Conference on Autonomous Agents and Multiagent Systems (AAMAS), pp. 1001–1008 (2006)Google Scholar
  15. 15.
    Shilov, N.V.: Designing tableau-like axiomatization for propositional linear temporal logic at home of arthur prior. Bull. Novosibirsk Comput. Cent. Ser.: Comput. Sci. 23, 113–136 (2005)zbMATHGoogle Scholar
  16. 16.
    Shoham, Y.: Logical theories of intention and the database perspective. J. Philos. Logic 38(6), 633–647 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Wolper, P.: The tableau method for temporal logic: an overview. Logique et Analyse 28(110–111), 119–136 (1985)zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Zhanhao Xiao
    • 1
    • 2
    Email author
  • Andreas Herzig
    • 1
    • 3
  • Laurent Perrussel
    • 1
  • Dongmo Zhang
    • 2
  1. 1.IRITUniversity of ToulouseToulouseFrance
  2. 2.SCEMWestern Sydney UniversityPenrithAustralia
  3. 3.IRITCNRSToulouseFrance

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