Abstract
In this paper, we show that the classical A.I. planning problem can be modelled using simple database constructs with logic-based semantics. The approach is similar to that used to model updates and nondeterminism in active database rules. We begin by showing that planning problems can be automatically converted to Datalog1S programs with nondeterministic choice constructs, for which we provide a formal semantics using the concept of stable models. The resulting programs are characterized by a syntactic structure (XY-stratification) that makes them amenable to efficient implementation using compilation and fixpoint computation techniques developed for deductive database systems. We first develop the approach for sequential plans, and then we illustrate its flexibility and expressiveness by formalizing a model for parallel plans, where several actions can be executed simultaneously. The characterization of parallel plans as partially ordered plans allows us to develop (parallel) versions of partially ordered plans that can often be executed faster than the original partially ordered plans.
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References
Allen, J.F. (1984). Towards a General Theory of Action and Time. Artificial Intelligence, 23, 123–154.
Apt, K.R. and Bezem, M. (1990). Acyclic Programs. In D.H.D. Warren and P. Szeredi (Eds.), Proceedings Seventh International Conference on Logic Programming (pp. 617–633). The MIT Press.
Baral, C. (1997). Relating Logic Programming Theories of Actions and Partial Order Planning, Annals of Math and AI 21 (2–4).
Bonner, A.J. and Kifer, M. (1994). An Overview of Transaction Logic. Theoretical Computer Science (TCS), 133, 205–265.
Chomicki, J. (1990). Polynomial-time Computable Queries in Temporal Deductive Databases. In PODS'90.
Chomicki, J. (1993). Temporal Deductive Databases. In A. Tansel, J. Clifford, S. Gadia, S. Jagodia, A. Segev, and R. Snodgrass (Eds.), Temporal Databases: Theory, Design and Implementation, Benjamin/Cummings, pp. 294–320.
Corciulo, L. Giannotti, F., and Pedreschi, D. (1993). Datalog with Non-Deterministic Choice Compute ndb-ptime. In Procs., International Conference on Deductive and Object-Oriented Databases, DOOD'93.
Dean, T. and Boddy, M. (1988). Reasoning about Partially Ordered Events. Artificial Intelligence, 375–399.
Eiter, T., Gottlob, G., and Leone, N. (1997). Abduction from Logic Programs: Semantics and Complexity. Theoretical Computer Science, 189(1/2), 129–177.
Eiter, T., Gottlob, G., and Mannila, H. (1997). Disjunctive Datalog. ACM Transactions on Database Systems, 22(3), 364–417.
Erol, K., Nau, D.S., and Subrahmanian, V.S. (1995). Complexity, Decidability and Undecidability Results for Domain-Independent Planning. Artificial Intelligence, 76(1/2), 75–88.
Fikes, R. and Nilsson, N. (1971). Strips: A New Approach to the Application of Theorem Proving in Problem Solving. Artificial Intelligence, 2(3/4), 189–208.
Gelfond, M. and Lifschitz, V. (1988). The Stable Model Semantics for Logic Programming. In R.A. Kowalski and K. Bowen (Eds.), Logic Programming: Proceedings of the Fifth Int'l Conf. and Symposium, pp. 1070–1080.
Gelfond, M. and Lifschitz, V. (1993). Representing Action and Change by Logic Programs. Journal of Logic programming, 17, 301–322.
Georgeff, M.P. (1984). A Theory of Actions for Multiagent Planning. In Proceedings of the Third National Conference on Artificial Intelligence (pp. 121–125). The MIT Press.
Gottlob, G. (1992). Complexity Results for Nonmonotonic Logics. Journal of Logic and Computation, 2(3), 397–425.
Greco, S. and Zaniolo, C. (1998). Greedy Algorithms in Datalog with Choice and Negation, In Procs. 1998 Joint International Conference and Symposium on Logic Programming, JCSLP'98 (pp. 294–309). MIT Press.
Green, C.C. (1969a). Theorem Proving by Resolution as a Basis for Question-Answering Systems, Machine Intelligence 4, B. Meltzer and D. Michie (Eds.), Edinburgh University Press.
Green, C.C. (1969b). Application of Theorem Proving to Problem Solving, In Proc. 1969 Intl. Joint Conf. on Artificial Intelligence, pp. 219–240.
Grobe, G. and Waldinger, R. (1991). Towards a Theory of Simultaneous Actions. In J. Hertzberg (Eds.), Proceedings of European Workshop on Planning, number 522 in LNAI, pp. 78–87. Springer-Verlag.
Hanks, S. and McDermott, D. (1987). Nonmonotonic Logic and Temporal Projection. Artificial Intelligence, 33, 379–412.
Horz, A. (1993). On the Relation of Classical and Temporal Planning. In Proc. of the Spring Symposium on Foundations of Automated Planning.
Kowalski, R.A. (1974). Logic for Problem Solving. North Holland Elsevier.
Marek, V. and Subrahmanian, V.S. (1992). The Relationship Between Stable, Supported, Default and Autoepistemic Semantics for General Logic Programs. Theoretical Computer Science, 103, 365–386.
Marek, V.W. and Truszczynski, M. (1995). Nonmonotonic Logic. Springer-Verlag.
McAllester, D. and Rosenblitt, D. (1991). Systematic Nonlinear Planning. In Proceedings of the Ninth National Conference on Artificial Intelligence (pp. 634–639). The MIT Press.
McCarthy, J. (1986). Applications of Circumscription to Formalising Common Sense Reasoning. Artificial Intelligence, 26, 89–116.
Pednault, E. (1986). Solving Multiagent Dynamic World Problems in the Classical Planning Framework. In Reasoning about Actions and Plans: Proceedings of the 1986 Workshop (pp. 42–82). Morgan Kaufmann.
Pinto, J. and Reiter, R. (1993). Temporal Reasoning in Logic Programming: A Case for the Situation Calculus. In Proc. 1993 Intl. Conf. on Logic Programming (pp. 203–221). MIT Press.
Regnier, P. and Fade, B. (1991). Complete Determination of Parallel Actions and Temporal Optimization in Linear Plans of Action. In J. Hertzberg (Eds.), Proceedings of European Workshop on Planning (pp. 100–111). Springer-Verlag.
Saccà, D. and Zaniolo, C. (1990). Stable Models and Non-Determinism in Logic Programs with Negation. In Proc. 9th ACM Symp. on Principles of Database Systems.
Saccà, D. and Zaniolo, C. (1997). Deterministic and Non-Deterministic Stable Models, Journal of Logic and Computation (JLC).
Sacerdoti, E.D. (1990). The Nonlinear Nature of Plans. In J. Allen, J. Hendler, and A. Tate (Eds.), Readings in Planning (pp. 162–170). Morgan Kaufman.
Sellis, T.K. and Ghosh, S. (1990). On the Multiple-Query Optimization Problem. IEEE Transactions on Knowledge and Data Engineering, 2(2), 262–266.
Tate, A. (1977). Generating Project Networks. In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI-77) (pp. 889–900).
Vaghani, J., Ramamohanarao, K., Kemp, D.B., Somogyi, Z., Stuckey, P.J., Leask, T.S., and Harland, J. (1994). The Aditi Deductive Database System. VLDB Journal, 3, 245–288.
Wang, H. and Carlo Zaniolo (2000) Nonmonotonic Reasoning in \({\mathcal{L}}{\mathcal{D}}{\mathcal{L}} + + \). In J. Minker (Ed.), Logic-Based Artificial Intelligence (pp. 523–542). Kluwer Academic Publishers.
Weld, D.S. (1995). An Introduction to Least Commitment Planning. A.I. Magazine.
Zaniolo, C. (1993). A Unified Semantics for Active and Deductive Databases. In Proceedings of the 1st International Workshop on Rules in Database Systems (pp. 271–287).
Zaniolo, C. (1995). Transaction-Conscious Stable Model Semantics for Active Database Rules. In Procs., International Conference on Deductive Object-Oriented Databases, DOOD'95.
Zaniolo, C., Arni, N., and Ong, K. (1993). Negation and Aggregates in Recursive Rules: the \({\mathcal{L}}{\mathcal{D}}{\mathcal{L}} + + \) approach. In Procs. International Conference on Deductive and Object-Oriented Databases, DOOD'93.
Zaniolo, C. et al. (1998) \({\mathcal{L}}{\mathcal{D}}{\mathcal{L}} + + \) Documentation and Web Demo, 1988: http://www.cs.ucla.edu/ldl
Zaniolo, C., Ceri, S., Faloutsos, C., Snodgrass, R., Subrahmanian, VS., and Zicari, R. (1997). Advanced Database Systems. Morgan Kaufmann Publisher, San Francisco.
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Brogi, A., Subrahmanian, V. & Zaniolo, C. A Deductive Database Approach to A.I. Planning. Journal of Intelligent Information Systems 20, 215–253 (2003). https://doi.org/10.1023/A:1022808724136
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DOI: https://doi.org/10.1023/A:1022808724136