Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Several theorem provers for \(\mathsf {PLTL}\) can be found on
http://users.cecs.anu.edu.au/~rpg/PLTLProvers/ (accessed on 2 Sep. 2017).
- 2.
For the database, time points are encoded in a binary way while they are considered as decimal in the size of the resulted \(\mathsf {PLTL}\) formula. Therefore, the size of the resulted formula is not polynomial with respect to the size of the database.
References
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). https://doi.org/10.1007/978-3-642-28756-5_8
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)
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)
Bratman, M.E.: Intention, Plans, and Practical Reason. Harvard University Press, Cambridge (1987). (reedited 1999 with CSLI Publications)
Bratman, M.E., Israel, D.J., Pollack, M.E.: Plans and resource-bounded practical reasoning. J. Comput. Intell. 4, 349–355 (1988)
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)
Bylander, T.: The computational complexity of propositional STRIPS planning. Artif. Intell. 69(1), 165–204 (1994)
Cohen, P.R., Levesque, H.J.: Intention is choice with commitment. J. Artif. Intell. 42(2), 213–261 (1990)
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)
Emerson, E.A.: Temporal and modal logic. Handb. Theor. Comput. Sci. Volume B: Formal Models Sematics (B) 995(1072), 5 (1990)
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)
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). https://doi.org/10.1007/978-3-319-48758-8_38
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). https://doi.org/10.1007/978-3-319-48758-8_39
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)
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)
Shoham, Y.: Logical theories of intention and the database perspective. J. Philos. Logic 38(6), 633–647 (2009)
Wolper, P.: The tableau method for temporal logic: an overview. Logique et Analyse 28(110–111), 119–136 (1985)
Acknowledgments.
The work was supported by Chinese Scholarship Council and the project ANR-11-LABX-0040-CIMI within ANR-11-IDEX-0002-02.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Xiao, Z., Herzig, A., Perrussel, L., Zhang, D. (2017). Deciding Refinement Relation in Belief-Intention Databases. In: Esposito, F., Basili, R., Ferilli, S., Lisi, F. (eds) AI*IA 2017 Advances in Artificial Intelligence. AI*IA 2017. Lecture Notes in Computer Science(), vol 10640. Springer, Cham. https://doi.org/10.1007/978-3-319-70169-1_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-70169-1_14
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-70168-4
Online ISBN: 978-3-319-70169-1
eBook Packages: Computer ScienceComputer Science (R0)