Functional Strips: A More Flexible Language for Planning and Problem Solving
Effective planning requires good modeling languages and good algorithms. The Strips language has shaped most of the work in planning since the early 70′s due to its effective solution of the frame problem and its support for divide-and-conquer strategies. In recent years, however, planning strategies not based on divide-and-conquer and work on theories of actions suggest that alternative languages can make modeling and planning easier. With this goal in mind, we have developed Functional Strips, a language that adds first-class function symbols to Strips providing additional flexibility in the codification of planning problems. This extension is orthogonal and complementary to extensions accommodated in other languages such as conditional effects, quantification, negation, etc. Function symbols, unlike relational symbols, can be nested so objects need not be referred to by their explicit names and as a result more efficient encodings can be provided. For example, a problem like the 8-puzzle can be codified in terms of four actions with no arguments; Hanoi, can be codified with a number of ground actions independent of the number of disks; resources and constraints can be easily represented, etc.
Functional Strips is both an action and a planning language in the sense that actions are understood declaratively in terms of a state-based semantics and operationally in terms of efficient updates on state representations. In this paper, we present the language, the semantics and a number of examples, and discuss possible uses in planning and problem solving.
KeywordsAction languages Strips planning modeling problem solving
Unable to display preview. Download preview PDF.
- Anderson, C., Smith, D., and Weld, D. (1998). Conditional effects in Graphplan. In Simmons, R., Veloso, M., and Smith, S., editors, Proceedings of the Fourth International Conference on AI Planning Systems (AIPS-98), pages 44–53. AAAI Press.Google Scholar
- Blum, A. and Furst, M. (1995). Fast planning through planning graph analysis. In Mellish, C., editor, Proceedings of IJCAI-95, pages 1636–1642. Morgan Kaufmann.Google Scholar
- Bonet, B. and Geffner, H. (1998). High-level planning and control with incomplete information using POMDPs. In Giacomo, G. D., editor, Proceedings AAAI Fall Symp. on Cognitive Robotics, pages 52–60. AAAI Press.Google Scholar
- Bonet, B. and Geffner, H. (1999). Planning as heuristic search: New results. In Proceedings of ECP-99, pages 359–371. Springer.Google Scholar
- Bonet, B. and Geffner, H. (2000). Planning with incomplete information as heuristic search in belief space. In Chien, S., Kambhampati, S., and Knoblock, C., editors, Proc. of the Fifth International Conference on AI Planning and Scheduling (AIPS-2000), pages 52–61. AAAI Press.Google Scholar
- Bonet, B., Loerincs, G., and Geffner, H. (1997). A robust and fast action selection mechanism for planning. In Proceedings of AAAI-97, pages 714–719. MIT Press.Google Scholar
- El-Kholy, A. and Richards, B. (1996). Temporal and resource reasoning in planning: the parcPLAN approach. In Wahlster, W., editor, Proc. ECAI-96, pages 614–618. Wiley.Google Scholar
- Fox, M. and Long, D. (1999). The detection and exploitation of symmetry in planning domains. In Dean, T., editor, Proc. IJCAI-99, pages 956–961. Morgan Kaufmann.Google Scholar
- Gazen, B. and Knoblock, C. (1997). Combining the expressiveness of UCPOP with the efficiency of Graphplan. In Steel, S. and Alami, R., editors, Recent Advances in AI Planning. Proc. 4th European Conf. on Planning (ECP-97). Lect. Notes in AI 1348, pages 221–233. Springer.Google Scholar
- Jonsson, P. and Bäckstrom, C. (1994). Tractable planning with state variables by exploiting structural restrictions. In Proc. AAAI-94, pages 998–1003. AAAI Press/MIT Press.Google Scholar
- Kautz, H. and Selman, B. (1996). Pushing the envelope: Planning, propositional logic, and stochastic search. In Proceedings of AAAI-96, pages 1194–1201. AAAI Press/MIT Press.Google Scholar
- Kautz, H. and Selman, B. (1999). Unifying SAT-based and Graph-based planning. In Dean, T., editor, Proceedings IJCAI-99, pages 318–327. Morgan Kaufmann.Google Scholar
- Koehler, J. (1998). Planning under resource constraints. In Proc. of the 13th European Conference on AI (ECAI-98), pages 489–493. Wiley.Google Scholar
- Koehler, J., Nebel, B., Hoffman, J., and Dimopoulos, Y. (1997). Extending planning graphs to an ADL subset. In Steel, S. and Alami, R., editors, Recent Advances in AI Planning. Proc. 4th European Conf. on Planning (ECP-97). Lect. Notes in AI 1348, pages 273–285. Springer.Google Scholar
- Korf, R. (1998). Finding optimal solutions to Rubik’s cube using pattern databases. In Proceedings of AAAI-98, pages 1202–1207. AAAI Press MIT Press.Google Scholar
- Laborie, P. and Ghallab, M. (1995). Planning with sharable resources constraints. In Mellish, C., editor, Proc. IJCAI-95, pages 1643–1649. Morgan Kaufmann.Google Scholar
- Lifschitz, V. (1986). On the semantics of STRIPS. In Georgeff, M. and Lansky, A., editors, Proc. Reasoning about Actions and Plans, pages 1–9. Morgan Kaufmann.Google Scholar
- Long, D. and Fox, M. (1999). The efficient implementation of the plan-graph. JAIR, 10:85–115.Google Scholar
- Marriot, K. and Stuckey, P. (1999). Programming with Constraints. MIT Press.Google Scholar
- McCain, N. and Turner, H. (1998). Fast satisfiability planning with causal theories. In T. Cohn, L. S. and Shapiro, S., editors, Proceedings of the Sixth Int. Conference on Principles of Knowledge Representation and Reasoning (KR-98), pages 121–130. Morgan Kaufmann.Google Scholar
- McDermott, D. (1998a). AIPS-98 Planning Competition Results. At http://ftp.es.yale.edu/pub/mcdermott/aipscomp-results.html.
- McDermott, D. (1998b). PDDL — the planning domain definition language. Available at http://ftp.cs.yale.edu/pub/mcdermott.
- Nebel, B. (1998). On the compilability and expressive power of propositional planning formalisms. Technical Report 101, Freiburg University. At http://www.informatik.uni-freiburg.de/nebel.
- Newell, A. and Simon, H. (1972). Human Problem Solving. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
- Nilsson, N. (1980). Principles of Artificial Intelligence. Tioga.Google Scholar
- Pearl, J. (1983). Heuristics. Morgan Kaufmann.Google Scholar
- Pednault, E. (1989). ADL: Exploring the middle ground between Strips and the situation calcules. In Brachman, R., Levesque, H., and Reiter, R., editors, Proc. KR-89, pages 324–332. Morgan Kaufmann.Google Scholar
- Penberthy, J. and Weld, D. (1994). Temporal planning with continous change. In Proc. AAAI-94, pages 1010–1015.Google Scholar
- Reiter, R. (1991). The frame problem in the situation calculus: A simple solution (sometimes) and a completeness result for goal regression. In Lifschitz, V., editor, Artificial Intelligence and Mathematical Theory of Computation: Papers in Honor of John McCarthy, pages 359–380. Academic Press.Google Scholar
- Sandewall, E. (1994). Features and Fluents. The Representation of Knowledge about Dynamical Systems. Oxford Univ. Press.Google Scholar
- Shanahan, M. (1997). Solving the Frame Problem. MIT Press.Google Scholar
- Smith, D. and Weld, D. (1998). Conformant graphplan. In Proceedings AAAI-98, pages 889–896. AAAI Press.Google Scholar
- Van Beek, P. and Chen, X. (1999). CPlan: a constraint programming approach to planning. In Proc. National Conference on Artificial Intelligence (AAAI-99), pages 585–590. AAAI Press/MIT Press.Google Scholar
- Veloso, M. (1992). Learning by Analogical Reasoning in General Problem Solving. PhD thesis, Computer Science Department, CMU. Tech. Report CMU-CS-92-174.Google Scholar
- Wilkins, D. (1988). Practical Planning: Extending the classical AI paradigm. M. Kaufmann.Google Scholar