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Defining a satisfactory semantics of aggregates turned out to be a difficult problem, and in this article we propose a new approach, based on an analogy between aggregates and propositional connectives. First we extend the definition of an answer set\/stable model to cover arbitrary propositional theories; then we define aggregates on top of them both as primitive constructs and as abbreviations for formulas. Our definition of an aggregate combines expressiveness and simplicity, and it inherits many theorems about programs with nested expressions, such as theorems about strong equivalence and splitting.<\/jats:p>","DOI":"10.1145\/1970398.1970401","type":"journal-article","created":{"date-parts":[[2011,7,21]],"date-time":"2011-07-21T13:27:09Z","timestamp":1311254829000},"page":"1-40","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":35,"title":["Logic programs with propositional connectives and aggregates"],"prefix":"10.1145","volume":"12","author":[{"given":"Paolo","family":"Ferraris","sequence":"first","affiliation":[{"name":"Google Inc., Mountain View, CA"}]}],"member":"320","published-online":{"date-parts":[[2011,7,22]]},"reference":[{"volume":"2173","volume-title":"Proceedings of the 6th International Conference on Logic Programming and Nonmonotonic Reasoning. 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Leone N. and Pfeifer G. 2004. Recursive aggregates in disjunctive logic programs: Semantics and complexity. 17 In Proceedings of the European Conference on Logics in Artificial Intelligence (JELIA).","DOI":"10.1007\/978-3-540-30227-8_19"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1007\/11546207_10"},{"volume-title":"Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI). 366--371","year":"2007","author":"Ferraris P.","key":"e_1_2_1_14_1"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10472-006-9025-2"},{"volume-title":"Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI). 372--379","author":"Ferraris P.","key":"e_1_2_1_16_1"},{"key":"e_1_2_1_17_1","unstructured":"Ferraris P. and Lifschitz V. 2005a. Mathematical foundations of answer set programming. In We Will Show Them&excl; Essays in Honour of Dov Gabbay King's College Publications London U.K. 615--664.  Ferraris P. and Lifschitz V. 2005a. Mathematical foundations of answer set programming. In We Will Show Them&excl; Essays in Honour of Dov Gabbay King's College Publications London U.K. 615--664."},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068403001923"},{"volume-title":"Proceedings of the International Logic Programming Conference and Symposium, R. Kowalski and K. 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Stable models and an alternative logic programming paradigm. In The Logic Programming Paradigm: A 25-Year Perspective Springer Verlag Berlin Germany 375--398.  Marek V. and Truszczy\u0144ski M. 1999. Stable models and an alternative logic programming paradigm. In The Logic Programming Paradigm: A 25-Year Perspective Springer Verlag Berlin Germany 375--398.","DOI":"10.1007\/978-3-642-60085-2_17"},{"volume-title":"Proceedings of the National Conference on Artificial Intelligence (AAAI). 460--465","author":"McCain N.","key":"e_1_2_1_33_1"},{"key":"e_1_2_1_34_1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1018930122475"},{"key":"e_1_2_1_35_1","doi-asserted-by":"crossref","unstructured":"Niemel\u00e4 I. and Simons P. 2000. Extending the Smodels system with cardinality and weight constraints. In Logic-Based Artificial Intelligence J. Minker Ed. Kluwer Dordrecht The Netherlands 491--521.   Niemel\u00e4 I. and Simons P. 2000. 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