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. © 2011 Springer-Verlag.
CITATION STYLE
Panella, A., & Gmytrasiewicz, P. (2011). A partition-based first-order probabilistic logic to represent interactive beliefs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6929 LNAI, pp. 233–246). https://doi.org/10.1007/978-3-642-23963-2_19
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