{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T22:01:09Z","timestamp":1747173669663,"version":"3.40.5"},"reference-count":28,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T00:00:00Z","timestamp":1658448000000},"content-version":"unspecified","delay-in-days":21,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Theory and Practice of Logic Programming"],"published-print":{"date-parts":[[2022,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Aggregates provide a concise way to express complex knowledge. The problem of selecting an appropriate formalization of aggregates for answer set programming (ASP) remains unsettled. This paper revisits it from the viewpoint of Approximation Fixpoint Theory (AFT). We introduce an AFT formalization equivalent with the Gelfond\u2013Lifschitz reduct for basic ASP programs and we extend it to handle aggregates. We analyze how existing approaches relate to our framework. We hope this work sheds some new light on the issue of a proper formalization of aggregates.<\/jats:p>","DOI":"10.1017\/s1471068422000126","type":"journal-article","created":{"date-parts":[[2022,7,22]],"date-time":"2022-07-22T10:03:50Z","timestamp":1658484230000},"page":"523-537","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":4,"title":["Analyzing Semantics of Aggregate Answer Set Programming Using Approximation Fixpoint Theory"],"prefix":"10.1017","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0700-7099","authenticated-orcid":false,"given":"LINDE","family":"VANBESIEN","sequence":"first","affiliation":[]},{"given":"MAURICE","family":"BRUYNOOGHE","sequence":"additional","affiliation":[]},{"given":"MARC","family":"DENECKER","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2022,7,22]]},"reference":[{"key":"S1471068422000126_ref16","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139342124"},{"key":"S1471068422000126_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2004.02.004"},{"key":"S1471068422000126_ref27","doi-asserted-by":"publisher","DOI":"10.1613\/jair.2171"},{"volume-title":"Introduction to Metamathematics","year":"1952","author":"Kleene","key":"S1471068422000126_ref22"},{"key":"S1471068422000126_ref9","doi-asserted-by":"crossref","unstructured":"Denecker, M. , Pelov, N. and Bruynooghe, M. 2001. Ultimate well-founded and stable semantics for logic programs with aggregates. In Logic Programming, 17th International Conference, ICLP 2001, Paphos, Cyprus, 26 November\u20131 December 2001, Proceedings, P. Codognet, Ed., Lecture Notes in Computer Science, vol. 2237. Springer, 212\u2013226.","DOI":"10.1007\/3-540-45635-X_22"},{"key":"S1471068422000126_ref15","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068415000150"},{"key":"S1471068422000126_ref3","doi-asserted-by":"publisher","DOI":"10.1080\/11663081.2018.1439358"},{"key":"S1471068422000126_ref18","first-page":"28","volume-title":"Artificial Intelligence 275","author":"Gelfond","year":"2019"},{"key":"S1471068422000126_ref17","unstructured":"Gelfond, M. and Lifschitz, V. 1988. The stable model semantics for logic programming. In The Stable Model Semantics for Logic Programming. ICLP\/SLP, 1070\u20131080."},{"key":"S1471068422000126_ref19","unstructured":"G\u00d6del, K. 1932. Zum intuitionistischen aussagenkalk\u00fcl. 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