## Constructing Conditional Plans by a Theorem-Prover (1999)

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Venue: | Journal of Artificial Intelligence Research |

Citations: | 141 - 6 self |

### BibTeX

@ARTICLE{Rintanen99constructingconditional,

author = {Jussi Rintanen},

title = {Constructing Conditional Plans by a Theorem-Prover},

journal = {Journal of Artificial Intelligence Research},

year = {1999},

volume = {10},

pages = {323--352}

}

### Years of Citing Articles

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### Abstract

The research on conditional planning rejects the assumptions that there is no uncertainty or incompleteness of knowledge with respect to the state and changes of the system the plans operate on. Without these assumptions the sequences of operations that achieve the goals depend on the initial state and the outcomes of nondeterministic changes in the system. This setting raises the questions of how to represent the plans and how to perform plan search. The answers are quite different from those in the simpler classical framework. In this paper, we approach conditional planning from a new viewpoint that is motivated by the use of satisfiability algorithms in classical planning. Translating conditional planning to formulae in the propositional logic is not feasible because of inherent computational limitations. Instead, we translate conditional planning to quantified Boolean formulae. We discuss three formalizations of conditional planning as quantified Boolean formulae, and pr...

### Citations

958 | Fast planning through planning graph analysis - Blum, Furst - 1997 |

881 | Symbolic Boolean Manipulation with Ordered Binary Decision Diagrams
- Bryant
- 1992
(Show Context)
Citation Context ...the number of states, problem instances with big state spaces consume more memory than is likely to be available. To alleviate this problem Cimatti et al. propose the use of binary decision diagrams (=-=Bryant, 1992-=-) for encoding the state-action tables. BDDs are in general not capable of representing exponential size data structures in polynomial space. Smith and Weld (1998) extend Graphplan (Blum & Furst, 1997... |

740 | A machine program for theorem proving - Davis, Logemann, et al. - 1962 |

522 | Pushing the envelope: planning, propositional logic, and stochastic search - Kautz, Selman - 1201 |

431 | Planning as satisfiability - Kautz, Selman - 1992 |

386 | D.: Systematic nonlinear planning - McAllester, Rosenblitt - 1991 |

294 | The computational complexity of propositional STRIPS planning - Bylander - 1994 |

211 | Conditional nonlinear planning - Peot, Smith - 1992 |

174 | Structural Complexity I - Balcazar, az, et al. - 1988 |

160 | Improvements to Propositional Satisfiability Search Algorithms
- Freeman
- 1995
(Show Context)
Citation Context ...e new techniques disabled cannot solve any of the benchmarks in Table 3 in less than 4 hours (14400 seconds.) The techniques for improving the obvious algorithm are based on failed literal detection (=-=Freeman, 1995-=-; Li & Anbulagan, 1997), and for formulae 9X8Y \Phi on performing computation with the universal variables Y before all variables in X have been assigned a truth-value. First, before performing exhaus... |

145 | Complexity results for SAS+ planning - Backstrom, Nebel - 1995 |

139 | An Algorithm to Evaluate Quantified Boolean Formulae - Cadoli, Giovanardi, et al. - 1998 |

99 | G.: Planning for contingencies: A decision-based approach - Pryor, Collins - 1996 |

87 | Automatic OBDD-based generation of universal plans in non-deterministic domains - Cimatti, Roveri, et al. - 1998 |

81 | Inferring state constraints for domain-independent planning - Gerevini, Schubert - 1998 |

73 | Improvements to the Evaluation of Quantified Boolean Formulae
- Rintanen
- 1999
(Show Context)
Citation Context ... decide(e; hM 1 ; : : : ; M n i; C [ f:xg) END Figure 6: A decision procedure for quantified Boolean formulae 6. The Theorem-Prover We have developed a theorem-prover for quantified Boolean formulae (=-=Rintanen, 1999-=-) as an extension of the Davis-Putnam procedure for the satisfiability of formulae in the propositional logic (Davis, Logemann, & Loveland, 1962). It is straightforward to extend the Davis-Putnam proc... |

48 |
Plan synthesis: A logical perspective
- Rosenschein
- 1981
(Show Context)
Citation Context ...ng existing algorithms that produce non-conditional plans, we view conditional planning as an automated reasoning task, like in the pioneering work on planning by Green (1969), in deductive planning (=-=Rosenschein, 1981-=-), and in recent work on planning by satisfiability algorithms (Kautz & Selman, 1992, 1996). Instead of using a very general framework like the first-order predicate logic or a dynamic logic, we choos... |

46 | A planning algorithm not based on directional search
- Rintanen
- 1998
(Show Context)
Citation Context ...rs and the formulae that describe the initial and goal states. This program includes the automatic generation of invariants for the problem instance. The use of invariants (Gerevini & Schubert, 1998; =-=Rintanen, 1998-=-) and related techniques for pruning search spaces is one of the distinguishing features of recent classical planners. By invariants we mean formulae that are true in all reachable states of a problem... |

8 | Application of theorem-proving to problem solving - Green - 1969 |