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However, several real-world scenarios require a combination of both discrete and continuous random variables. In this paper, we extend the PASP framework to support continuous random variables and propose Hybrid Probabilistic Answer Set Programming. Moreover, we discuss, implement, and assess the performance of two exact algorithms based on projected answer set enumeration and knowledge compilation and two approximate algorithms based on sampling. Empirical results, also in line with known theoretical results, show that exact inference is feasible only for small instances, but knowledge compilation has a huge positive impact on performance. Sampling allows handling larger instances but sometimes requires an increasing amount of memory.<\/jats:p>","DOI":"10.1017\/s1471068424000437","type":"journal-article","created":{"date-parts":[[2024,11,8]],"date-time":"2024-11-08T07:29:00Z","timestamp":1731050940000},"page":"1-32","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["Probabilistic Answer Set Programming with Discrete and Continuous Random Variables"],"prefix":"10.1017","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7133-2673","authenticated-orcid":false,"given":"DAMIANO","family":"AZZOLINI","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1654-9703","authenticated-orcid":false,"given":"FABRIZIO","family":"RIGUZZI","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2024,11,8]]},"reference":[{"key":"S1471068424000437_ref9","first-page":"3","volume-title":"The Structure and Complexity of Credal Semantics","author":"Cozman","year":"2016"},{"key":"S1471068424000437_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2020.07.004"},{"key":"S1471068424000437_ref15","first-page":"2462","volume-title":"IJCAI\u201807: Proceedings of the 20th international joint conference on Artifical intelligence","volume":"7","author":"De RAEDT","year":"2007"},{"key":"S1471068424000437_ref29","doi-asserted-by":"publisher","DOI":"10.1017\/S147106842200014X"},{"key":"S1471068424000437_ref52","doi-asserted-by":"publisher","DOI":"10.1038\/s41592-019-0686-2"},{"key":"S1471068424000437_ref20","unstructured":"Gelfond, M. and Lifschitz, V. 1988, The stable model semantics for logic programming. 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