{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,19]],"date-time":"2026-06-19T16:29:25Z","timestamp":1781886565126,"version":"3.54.5"},"reference-count":0,"publisher":"IOS Press","isbn-type":[{"value":"9781643682440","type":"print"},{"value":"9781643682457","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,12,22]]},"abstract":"<jats:p>Tractable Boolean and arithmetic circuits have been studied extensively in AI for over two decades now. These circuits were initially proposed as \u201ccompiled objects,\u201d meant to facilitate logical and probabilistic reasoning, as they permit various types of inference to be performed in linear time and a feed-forward fashion like neural networks. In more recent years, the role of tractable circuits has significantly expanded as they became a computational and semantical backbone for some approaches that aim to integrate knowledge, reasoning and learning. In this chapter, we review the foundations of tractable circuits and some associated milestones, while focusing on their core properties and techniques that make them particularly useful for the broad aims of neuro-symbolic AI.<\/jats:p>","DOI":"10.3233\/faia210353","type":"book-chapter","created":{"date-parts":[[2022,1,3]],"date-time":"2022-01-03T10:43:27Z","timestamp":1641206607000},"source":"Crossref","is-referenced-by-count":5,"title":["Chapter 6. Tractable Boolean and Arithmetic Circuits"],"prefix":"10.3233","author":[{"given":"Adnan","family":"Darwiche","sequence":"first","affiliation":[{"name":"Computer Science Department, UCLA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"7437","container-title":["Frontiers in Artificial Intelligence and Applications","Neuro-Symbolic Artificial Intelligence: The State of the Art"],"original-title":[],"link":[{"URL":"https:\/\/ebooks.iospress.nl\/pdf\/doi\/10.3233\/FAIA210353","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,3]],"date-time":"2022-01-03T10:43:29Z","timestamp":1641206609000},"score":1,"resource":{"primary":{"URL":"https:\/\/ebooks.iospress.nl\/doi\/10.3233\/FAIA210353"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,22]]},"ISBN":["9781643682440","9781643682457"],"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/faia210353","relation":{},"ISSN":["0922-6389","1879-8314"],"issn-type":[{"value":"0922-6389","type":"print"},{"value":"1879-8314","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,22]]}}}