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# Specifying credal sets with probabilistic answer set programming

*Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications*, PMLR 215:321-332, 2023.

#### Abstract

Probabilistic Answer Set Programming offers an intuitive and powerful declarative language to represent uncertainty about combinatorial structures. Remarkably, under the credal semantics, such programs can specify any infinitely monotone Choquet Capacity in an intuitive way. Yet, one might be interested in specifying more general credal sets. We examine how probabilistic answer set programs can be extended to represent more general credal sets with constructs that allow for imprecise probability values. We characterize the credal sets that can be captured with various languages, and discuss the expressivity and complexity added by the use of imprecision in probabilistic constructs.