Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Algebraic decision diagrams and their applications
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Practical solution techniques for first-order MDPs
Artificial Intelligence
FLUCAP: a heuristic search planner for first-order MDPs
Journal of Artificial Intelligence Research
First order decision diagrams for relational MDPs
Journal of Artificial Intelligence Research
Symbolic dynamic programming for first-order MDPs
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
SPUDD: stochastic planning using decision diagrams
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Planning with noisy probabilistic relational rules
Journal of Artificial Intelligence Research
Probabilistic relational planning with first order decision diagrams
Journal of Artificial Intelligence Research
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First order decision diagrams (FODD) were recently introduced as a compact knowledge representation expressing functions over relational structures. FODDs represent numerical functions that, when constrained to the Boolean range, use only existential quantification. Previous work developed a set of operations over FODDs, showed how they can be used to solve relational Markov decision processes (RMDP) using dynamic programming algorithms, and demonstrated their success in solving stochastic planning problems from the International Planning Competition in the system FODD-Planner. A crucial ingredient of this scheme is a set of operations to remove redundancy in decision diagrams, thus keeping them compact. This paper makes three contributions. First, we introduce Generalized FODDs (GFODD) and combination algorithms for them, generalizing FODDs to arbitrary quantification. Second, we show how GFODDs can be used in principle to solve RMDPs with arbitrary quantification, and develop a particularly promising case where an arbitrary number of existential quantifiers is followed by an arbitrary number of universal quantifiers. Third, we develop a new approach to reduce FODDs and GFODDs using model checking. This yields a reduction that is complete for FODDs and provides a sound reduction procedure for GFODDs.