Specifying credal sets with probabilistic answer set programming

Denis Deratani Mauá, Fabio Gagliardi Cozman
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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v215-maua23a, title = {Specifying credal sets with probabilistic answer set programming}, author = {Mau\'a, Denis Deratani and Cozman, Fabio Gagliardi}, booktitle = {Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications}, pages = {321--332}, year = {2023}, editor = {Miranda, Enrique and Montes, Ignacio and Quaeghebeur, Erik and Vantaggi, Barbara}, volume = {215}, series = {Proceedings of Machine Learning Research}, month = {11--14 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v215/maua23a/maua23a.pdf}, url = {https://proceedings.mlr.press/v215/maua23a.html}, 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.} }
Endnote
%0 Conference Paper %T Specifying credal sets with probabilistic answer set programming %A Denis Deratani Mauá %A Fabio Gagliardi Cozman %B Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications %C Proceedings of Machine Learning Research %D 2023 %E Enrique Miranda %E Ignacio Montes %E Erik Quaeghebeur %E Barbara Vantaggi %F pmlr-v215-maua23a %I PMLR %P 321--332 %U https://proceedings.mlr.press/v215/maua23a.html %V 215 %X 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.
APA
Mauá, D.D. & Cozman, F.G.. (2023). Specifying credal sets with probabilistic answer set programming. Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications, in Proceedings of Machine Learning Research 215:321-332 Available from https://proceedings.mlr.press/v215/maua23a.html.

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