{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T09:46:41Z","timestamp":1766137601677},"reference-count":0,"publisher":"IOS Press","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,2,2]]},"abstract":"<jats:p>Pseudo-Boolean and cardinality constraints are a natural generalization of clauses. While a clause expresses that at least one literal must be true, a cardinality constraint expresses that at least n literals must be true and a pseudo-Boolean constraint states that a weighted sum of literals must be greater than a constant. These contraints have a high expressive power, have been intensively studied in 0\/1 programming and are close enough to the satisfiability problem to benefit from the recents advances in this field. Besides, optimization problems are naturally expressed in the pseudo-Boolean context. This chapter presents the inference rules on pseudo-Boolean constraints and demonstrates their increased inference power in comparison with resolution. It also shows how the modern satisfiability algorithms can be extended to deal with pseudo-Boolean constraints.<\/jats:p>","DOI":"10.3233\/faia201012","type":"book-chapter","created":{"date-parts":[[2021,2,8]],"date-time":"2021-02-08T08:42:22Z","timestamp":1612773742000},"source":"Crossref","is-referenced-by-count":7,"title":["Chapter 28. Pseudo-Boolean and Cardinality Constraints"],"prefix":"10.3233","author":[{"given":"Olivier","family":"Roussel","sequence":"first","affiliation":[]},{"given":"Vasco","family":"Manquinho","sequence":"additional","affiliation":[]}],"member":"7437","container-title":["Frontiers in Artificial Intelligence and Applications","Handbook of Satisfiability"],"original-title":[],"link":[{"URL":"http:\/\/ebooks.iospress.nl\/pdf\/doi\/10.3233\/FAIA201012","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,8]],"date-time":"2021-02-08T08:42:23Z","timestamp":1612773743000},"score":1,"resource":{"primary":{"URL":"http:\/\/ebooks.iospress.nl\/doi\/10.3233\/FAIA201012"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,2,2]]},"references-count":0,"URL":"https:\/\/doi.org\/10.3233\/faia201012","relation":{},"ISSN":["0922-6389","1879-8314"],"issn-type":[{"value":"0922-6389","type":"print"},{"value":"1879-8314","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,2,2]]}}}