Numeric Kernel for Reasoning about Plans Involving Numeric Fluents

  • Enrico Scala
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8249)


The paper proposes the notion of numeric kernel as a means for reasoning about plans involving numeric state variables, i.e. numeric fluents. A numeric kernel identifies the sufficient and necessary conditions that allow to directly - without any search and any propagation - assess whether a plan is valid in a specific world state. The notion generalizes the propositional kernels defined for the STRIPS language, to support domains involving numeric information as well. A regression method to build such kernels is reported, and its correctness is theoretically proved. To evaluate the numeric kernels contribution, we report two possible repair strategies that can be employed as a direct application of the numeric kernel properties. Results show the promise of the approach both from the computational point of view and in terms of plan quality.


World State Plan Execution Repair Strategy Intelligence Research Numeric Action 
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.
    Hoffmann, J.: The metric-ff planning system: Translating “ignoring delete lists” to numeric state variables. Journal of Artificial Intelligence Research 20, 291–341 (2003)zbMATHGoogle Scholar
  2. 2.
    Gerevini, A., Saetti, I., Serina, A.: An approach to efficient planning with numerical fluents and multi-criteria plan quality. Artificial Intelligence 172(8-9), 899–944 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Coles, A.J., Coles, A., Fox, M., Long, D.: Colin: Planning with continuous linear numeric change. Journal of Artificial Intelligence Research 44, 1–96 (2012)zbMATHGoogle Scholar
  4. 4.
    Fox, M., Long, D.: Pddl2.1: An extension to pddl for expressing temporal planning domains. Journal of Artificial Intelligence Research 20, 61–124 (2003)zbMATHGoogle Scholar
  5. 5.
    Coles, A.J., Coles, A.I., Fox, M., Long, D.: Forward-chaining partial-order planning. In: Proc. of International Conference on Automated Planning and Scheduling, ICAPS 2010 (2010)Google Scholar
  6. 6.
    Conrad, P.R., Williams, B.C.: Drake: An efficient executive for temporal plans with choice. Journal of Artificial Intelligence Research 42, 607–659 (2011)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Dechter, R., Meiri, I., Pearl, J.: Temporal constraint networks. Artificial Intelligence 49(1-3), 61–95 (1991)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Kvarnström, J., Heintz, F., Doherty, P.: A temporal logic-based planning and execution monitoring system. In: Proc. of International Conference on Automated Planning and Scheduling (ICAPS 2008), pp. 198–205 (2008)Google Scholar
  9. 9.
    Policella, N., Cesta, A., Oddi, A., Smith, S.: Solve-and-robustify. Journal of Scheduling 12, 299–314 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Stergiou, K., Koubarakis, M.: Backtracking algorithms for disjunctions of temporal constraints. Artificial Intelligence 120(1), 81–117 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Fikes, R., Hart, P.E., Nilsson, N.J.: Learning and executing generalized robot plans. Artificial Intelligence 3(1-3), 251–288 (1972)CrossRefGoogle Scholar
  12. 12.
    Fritz, C., McIlraith, S.A.: Monitoring plan optimality during execution. In: Proc. of International Conference on Automated Planning and Scheduling (ICAPS 2007), pp. 144–151 (2007)Google Scholar
  13. 13.
    Garrido, A., Guzman, C., Onaindia, E.: Anytime plan-adaptation for continuous planning. In: Proc. of P&S Special Interest Group Workshop, PLANSIG 2010 (2010)Google Scholar
  14. 14.
    Brenner, M., Nebel, B.: Continual planning and acting in dynamic multiagent environments. Journal of Autonomous Agents and Multiagent Systems 19(3), 297–331 (2009)CrossRefGoogle Scholar
  15. 15.
    Chen, Y., Wah, B.W., Hsu, C.-W.: Temporal planning using subgoal partitioning and resolution in sgplan. Journal of Artificial Intelligence Research 26, 369 (2006)Google Scholar
  16. 16.
    Scala, E.: Reconfiguration and Replanning for robust Execution of Plans Involving Continous and Consumable Resources. Phd thesis in computer science, Department of Computer Science - Universita’ di Torino (2013)Google Scholar
  17. 17.
    Nebel, B., Koehler, J.: Plan reuse versus plan generation: A theoretical and empirical analysis. Artificial Intelligence 76(1-2), 427–454 (1995)CrossRefGoogle Scholar
  18. 18.
    Gerevini, A., Saetti, A., Serina, I.: Case-based planning for problems with real-valued fluents: Kernel functions for effective plan retrieval. In: Proc. of European Conference on AI (ECAI 2012), pp. 348–353 (2012)Google Scholar
  19. 19.
    van der Krogt, R., de Weerdt, M.: Plan repair as an extension of planning. In: Proc. of International Conference on Automated Planning and Scheduling (ICAPS 2005), pp. 161–170 (2005)Google Scholar
  20. 20.
    Fox, M., Gerevini, A., Long, D., Serina, I.: Plan stability: Replanning versus plan repair. In: Proc. of International Conference on Automated Planning and Scheduling (ICAPS 2006), pp. 212–221 (2006)Google Scholar
  21. 21.
    Gerevini, A.E., Roubíčková, A., Saetti, A., Serina, I.: On the plan-library maintenance problem in a case-based planner. In: Delany, S.J., Ontañón, S. (eds.) ICCBR 2013. LNCS, vol. 7969, pp. 119–133. Springer, Heidelberg (2013)CrossRefGoogle Scholar

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© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Enrico Scala
    • 1
  1. 1.Dipartimento di InformaticaUniversita’ di TorinoTorinoItaly

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