Artificial Intelligence
Knowledge and common knowledge in a distributed environment
Journal of the ACM (JACM)
Representing and reasoning with probabilistic knowledge: a logical approach to probabilities
Representing and reasoning with probabilistic knowledge: a logical approach to probabilities
Reasoning about knowledge and probability
Journal of the ACM (JACM)
Probabilistic frame-based systems
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Probalilistic Logic Programming under Maximum Entropy
ECSQARU '95 Proceedings of the European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty
Reasoning about Uncertainty
Exploiting structure to efficiently solve large scale partially observable markov decision processes
Exploiting structure to efficiently solve large scale partially observable markov decision processes
Machine Learning
Practical solution techniques for first-order MDPs
Artificial Intelligence
Generalized point based value iteration for interactive POMDPs
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
Factored models for probabilistic modal logic
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
A framework for sequential planning in multi-agent settings
Journal of Artificial Intelligence Research
First order decision diagrams for relational MDPs
Journal of Artificial Intelligence Research
Monte Carlo sampling methods for approximating interactive POMDPs
Journal of Artificial Intelligence Research
An analysis of first-order logics of probability
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
Symbolic dynamic programming for first-order MDPs
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Artificial Intelligence: A Modern Approach
Artificial Intelligence: A Modern Approach
Computing optimal policies for partially observable decision processes using compact representations
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
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Being able to compactly represent large state spaces is crucial in solving a vast majority of practical stochastic planning problems. This requirement is even more stringent in the context of multi-agent systems, in which the world to be modeled also includes the mental state of other agents. This leads to a hierarchy of beliefs that results in a continuous, unbounded set of possible interactive states, as in the case of Interactive POMDPs. In this paper, we describe a novel representation for interactive belief hierarchies that combines first-order logic and probability. The semantics of this new formalism is based on recursively partitioning the belief space at each level of the hierarchy; in particular, the partitions of the belief simplex at one level constitute the vertices of the simplex at the next higher level. Since in general a set of probabilistic statements only partially specifies a probability distribution over the space of interest, we adopt the maximum entropy principle in order to convert it to a full specification.