{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T23:58:27Z","timestamp":1778803107662,"version":"3.51.4"},"reference-count":16,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2007,5,1]],"date-time":"2007-05-01T00:00:00Z","timestamp":1177977600000},"content-version":"unspecified","delay-in-days":0,"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":[[2007,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This technical note describes a monotone and continuous fixpoint operator to compute the answer sets of programs with aggregates. The fixpoint operator relies on the notion of<jats:italic>aggregate solution<\/jats:italic>. Under certain conditions, this operator behaves identically to the three-valued immediate consequence operator \u03a6<jats:italic><jats:sup>aggr<\/jats:sup><jats:sub>P<\/jats:sub><\/jats:italic>for aggregate programs, independently proposed in Pelov (2004) and Pelov<jats:italic>et al.<\/jats:italic>(2004). This operator allows us to closely tie the computational complexity of the answer set checking and answer sets existence problems to the cost of checking a solution of the aggregates in the program. Finally, we relate the semantics described by the operator to other proposals for logic programming with aggregates.<\/jats:p>","DOI":"10.1017\/s1471068406002936","type":"journal-article","created":{"date-parts":[[2007,3,14]],"date-time":"2007-03-14T09:10:41Z","timestamp":1173863441000},"page":"355-375","source":"Crossref","is-referenced-by-count":42,"title":["A Constructive semantic characterization of aggregates in answer set programming"],"prefix":"10.1017","volume":"7","author":[{"given":"TRAN CAO","family":"SON","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ENRICO","family":"PONTELLI","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2007,5,1]]},"reference":[{"key":"S1471068406002936_N10217","unstructured":"Pelov N. 2004. Semantic of Logic Programs with Aggregates. Ph.D. thesis, Katholieke Universiteit Leuven."},{"key":"S1471068406002936_N1017D","unstructured":"Faber W. , Leone N. , and Pfeifer G. 2004. Recursive Aggregates in Disjunctive Logic Programs: Semantics and Complexity. In JELIA, Springer, 200\u2013212."},{"key":"S1471068406002936_N101F9","unstructured":"Mumick I. S. , Pirahesh H. , and Ramakrishnan R. 1990. The Magic of Duplicates and Aggregates. In Int. Conf. on Very Large Data Bases, Morgan Kaufmann, 264\u2013277."},{"key":"S1471068406002936_N10115","doi-asserted-by":"publisher","DOI":"10.1007\/BF03037598"},{"key":"S1471068406002936_N101AD","unstructured":"Gelfond M. and Lifschitz V. 1988. The Stable Model Semantics for Logic Programming. In International Conf. and Symp. on Logic Programming, MIT Press, 1070\u20131080."},{"key":"S1471068406002936_N100EC","volume-title":"Introduction to Algorithms, 2nd Edition","author":"Cormen","year":"2001"},{"key":"S1471068406002936_N10243","unstructured":"Pelov N. , Denecker M. , and Bruynooghe M. 2004. Partial Stable Models for Logic Programs with Aggregates. In LPNMR, Springer, 207\u2013219."},{"key":"S1471068406002936_N10261","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1997.1453"},{"key":"S1471068406002936_N101E5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-83189-8"},{"key":"S1471068406002936_N101C5","first-page":"387","volume-title":"Semantics of Logic Programs with Aggregates. In ISLP","author":"Kemp","year":"1991"},{"key":"S1471068406002936_N10287","unstructured":"Son T. C. , Pontelli E. , and Elkabani I. 2005. A Translational Semantics for Aggregates in Logic Programming. Tech. Rep. 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Translation of Aggregate Programs to Normal Logic Programs. In ASP: Advances in Theory and Implementation, CEUR Workshop Proceedings. 29\u201342."},{"key":"S1471068406002936_N102A5","doi-asserted-by":"crossref","unstructured":"Zaniolo C. , Arni N. , and Ong K. 1993. Negation and Aggregates in Recursive Rules: the LDL++ Approach. 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