@inproceedings{AzzBelRigMAP-AIXIA-IC, author = {Azzolini, Damiano and Bellodi, Elena and Riguzzi, Fabrizio}, editor = {Dovier, Agostino and Montanari, Angelo and Orlandini, Andrea}, title = {MAP Inference in Probabilistic Answer Set Programs}, booktitle = {AIxIA 2022 -- Advances in Artificial Intelligence}, year = {2023}, publisher = {Springer International Publishing}, address = {Cham}, pages = {413--426}, abstract = {Reasoning with uncertain data is a central task in artificial intelligence. In some cases, the goal is to find the most likely assignment to a subset of random variables, named query variables, while some other variables are observed. This task is called Maximum a Posteriori (MAP). When the set of query variables is the complement of the observed variables, the task goes under the name of Most Probable Explanation (MPE). In this paper, we introduce the definitions of cautious and brave MAP and MPE tasks in the context of Probabilistic Answer Set Programming under the credal semantics and provide an algorithm to solve them. Empirical results show that the brave version of both tasks is usually faster to compute. On the brave MPE task, the adoption of a state-of-the-art ASP solver makes the computation much faster than a naive approach based on the enumeration of all the worlds.}, isbn = {978-3-031-27181-6}, url = {https://link.springer.com/chapter/10.1007/978-3-031-27181-6_29}, doi = {10.1007/978-3-031-27181-6_29} }

@inproceedings{AzzBelRigApprox-AIXIA-IC, author = {Azzolini, Damiano and Bellodi, Elena and Riguzzi, Fabrizio}, editor = {Dovier, Agostino and Montanari, Angelo and Orlandini, Andrea}, title = {Approximate Inference in Probabilistic Answer Set Programming for Statistical Probabilities}, booktitle = {AIxIA 2022 -- Advances in Artificial Intelligence}, year = {2023}, publisher = {Springer International Publishing}, address = {Cham}, pages = {33--46}, abstract = {``Type 1'' statements were introduced by Halpern in 1990 with the goal to represent statistical information about a domain of interest. These are of the form ``x{\%} of the elements share the same property''. The recently proposed language PASTA (Probabilistic Answer set programming for STAtistical probabilities) extends Probabilistic Logic Programs under the Distribution Semantics and allows the definition of this type of statements. To perform exact inference, PASTA programs are converted into probabilistic answer set programs under the Credal Semantics. However, this algorithm is infeasible for scenarios when more than a few random variables are involved. Here, we propose several algorithms to perform both conditional and unconditional approximate inference in PASTA programs and test them on different benchmarks. The results show that approximate algorithms scale to hundreds of variables and thus can manage real world domains.}, isbn = {978-3-031-27181-6}, url = {https://link.springer.com/chapter/10.1007/978-3-031-27181-6_3}, doi = {10.1007/978-3-031-27181-6_3} }

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