{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,10]],"date-time":"2025-09-10T22:29:59Z","timestamp":1757543399924},"reference-count":25,"publisher":"Cambridge University Press (CUP)","issue":"4-5","license":[{"start":{"date-parts":[[2013,9,25]],"date-time":"2013-09-25T00:00:00Z","timestamp":1380067200000},"content-version":"unspecified","delay-in-days":86,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Theory and Practice of Logic Programming"],"published-print":{"date-parts":[[2013,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Answer Set Programming (ASP) is a powerful form of declarative programming used in areas such as planning or reasoning. ASP solvers enforce <jats:italic>stable model semantics<\/jats:italic>, which rule out solutions representing certain kinds of circular reasoning. Unfortunately, current ASP solvers are incapable of solving problems involving cyclic dependencies between multiple integer or continuous quantities effectively. In this paper, we generalize the notion of stable models to <jats:italic>bound founded variables<\/jats:italic> with arbitrary domains, where <jats:italic>bounds<\/jats:italic> on such variables need to be justified by some rule in the program in order for the model to be stable. We show how to handle significantly more general rule forms where bound founded variables can act as head or body variables, and where head and body variables can be related via complex constraints subject to certain monotonicity requirements. We describe a new unfounded set detection algorithm which allows us to enforce this generalization of the stable model semantics. We also show how these unfounded sets can be explained in order to allow effective conflict-directed clause learning. The new solver merges the best features of CP, SAT and ASP solvers and allows new types of problems to be solved very efficiently.<\/jats:p>","DOI":"10.1017\/s147106841300032x","type":"journal-article","created":{"date-parts":[[2013,9,25]],"date-time":"2013-09-25T16:24:58Z","timestamp":1380126298000},"page":"517-532","source":"Crossref","is-referenced-by-count":7,"title":["Stable model semantics for founded bounds"],"prefix":"10.1017","volume":"13","author":[{"given":"REHAN ABDUL","family":"AZIZ","sequence":"first","affiliation":[]},{"given":"GEOFFREY","family":"CHU","sequence":"additional","affiliation":[]},{"given":"PETER J.","family":"STUCKEY","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2013,9,25]]},"reference":[{"key":"S147106841300032X_ref16","doi-asserted-by":"publisher","DOI":"10.1109\/12.769433"},{"key":"S147106841300032X_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-34922-5_15"},{"key":"S147106841300032X_ref1","first-page":"58","volume-title":"Proceedings of the International Workshop on Nonmonotonic Reasoning","author":"Anger","year":"2006"},{"key":"S147106841300032X_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068410000220"},{"key":"S147106841300032X_ref12","first-page":"235","volume-title":"Proceedings of the 25th International Conference on Logic Programming","author":"Gebser","year":"2009"},{"key":"S147106841300032X_ref6","unstructured":"Calimeri F. , Faber W. , Gebser M. , Ianni G. , Kaminski R. , Krennwallner T. , Leone N. , Ricca F. and Schaub T. 2013. Asp-core-2 input language format. https:\/\/www.mat.unical.it\/aspcomp2013\/ASPStandardization."},{"key":"S147106841300032X_ref20","first-page":"359","volume-title":"Proceedings of Logics in Artificial Intelligence, 10th European Conference, JELIA 2006","author":"Nieuwenborgh","year":"2006"},{"key":"S147106841300032X_ref24","doi-asserted-by":"publisher","DOI":"10.1016\/S0004-3702(02)00187-X"},{"key":"S147106841300032X_ref2","first-page":"41","volume-title":"Proceedings of the Thirty-Sixth Australasian Computer Science Conference","author":"Aziz","year":"2013"},{"key":"S147106841300032X_ref23","doi-asserted-by":"publisher","DOI":"10.1145\/1452044.1452046"},{"key":"S147106841300032X_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511543357"},{"key":"S147106841300032X_ref14","first-page":"362","volume-title":"Proceedings of the 24th International Conference on Logic Programming","author":"Janssen","year":"2008"},{"key":"S147106841300032X_ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2012.04.001"},{"key":"S147106841300032X_ref10","first-page":"386","volume-title":"Proceedings of the 20th International Joint Conference on Artificial Intelligence","author":"Gebser","year":"2007"},{"key":"S147106841300032X_ref8","unstructured":"Drescher C. and Walsh T. 2012. Answer set solving with lazy nogood neneration. In Technical Communications of the 28th International Conference on Logic Programming. 188\u2013200."},{"key":"S147106841300032X_ref25","first-page":"221","volume-title":"Proceedings of the ACM Symposium on Principles of Database Systems","author":"Van Gelder","year":"1988"},{"key":"S147106841300032X_ref4","first-page":"52","volume-title":"Proceedings of the 21st International Conference on Logic Programming","author":"Baselice","year":"2005"},{"key":"S147106841300032X_ref15","first-page":"32","volume-title":"Proceedings of the 13th International Conference on Principles of Knowledge Representation and Reasoning","author":"Liu","year":"2012"},{"key":"S147106841300032X_ref9","doi-asserted-by":"crossref","DOI":"10.2200\/S00457ED1V01Y201211AIM019","volume-title":"Answer Set Solving in Practice","author":"Gebser","year":"2012"},{"key":"S147106841300032X_ref18","first-page":"530","volume-title":"Proceedings of the 38th Design Automation Conference","author":"Moskewicz","year":"2001"},{"key":"S147106841300032X_ref22","volume-title":"Handbook of Constraint Programming (Foundations of Artificial Intelligence)","author":"Rossi","year":"2006"},{"key":"S147106841300032X_ref19","first-page":"529","volume-title":"Proceedings of the 13th International Conference on the Principles and Practice of Constraint Programming","author":"Nethercote","year":"2007"},{"key":"S147106841300032X_ref13","first-page":"1070","volume-title":"Proceedings of the Fifth International Conference on Logic Programming","author":"Gelfond","year":"1988"},{"key":"S147106841300032X_ref21","first-page":"71","volume-title":"Proceedings of Non-Monotonic Extensions of Logic Programming, NMELP '96","author":"Osorio","year":"1996"},{"key":"S147106841300032X_ref17","doi-asserted-by":"publisher","DOI":"10.1007\/s10472-009-9116-y"}],"container-title":["Theory and Practice of Logic Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S147106841300032X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T09:28:43Z","timestamp":1715592523000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S147106841300032X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,7]]},"references-count":25,"journal-issue":{"issue":"4-5","published-print":{"date-parts":[[2013,7]]}},"alternative-id":["S147106841300032X"],"URL":"https:\/\/doi.org\/10.1017\/s147106841300032x","relation":{},"ISSN":["1471-0684","1475-3081"],"issn-type":[{"value":"1471-0684","type":"print"},{"value":"1475-3081","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,7]]}}}