{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T03:05:41Z","timestamp":1767236741583},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"4-5","license":[{"start":{"date-parts":[[2012,9,5]],"date-time":"2012-09-05T00:00:00Z","timestamp":1346803200000},"content-version":"unspecified","delay-in-days":66,"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":[[2012,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The module theorem by Janhunen <jats:italic>et al<\/jats:italic>. demonstrates how to provide a modular structure in answer set programming, where each module has a well-defined input\/output interface which can be used to establish the compositionality of answer sets. The theorem is useful in the analysis of answer set programs, and is a basis of incremental grounding and reactive answer set programming. We extend the module theorem to the general theory of stable models by Ferraris <jats:italic>et al<\/jats:italic>. The generalization applies to non-ground logic programs allowing useful constructs in answer set programming, such as choice rules, the count aggregate, and nested expressions. Our extension is based on relating the module theorem to the symmetric splitting theorem by Ferraris <jats:italic>et al<\/jats:italic>. Based on this result, we reformulate and extend the theory of incremental answer set computation to a more general class of programs.<\/jats:p>","DOI":"10.1017\/s1471068412000269","type":"journal-article","created":{"date-parts":[[2012,9,5]],"date-time":"2012-09-05T11:28:45Z","timestamp":1346844525000},"page":"719-735","source":"Crossref","is-referenced-by-count":2,"title":["Module theorem for the general theory of stable models"],"prefix":"10.1017","volume":"12","author":[{"given":"JOSEPH","family":"BABB","sequence":"first","affiliation":[]},{"given":"JOOHYUNG","family":"LEE","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2012,9,5]]},"reference":[{"key":"S1471068412000269_ref12","first-page":"717","article-title":"Achieving compositionality of the stable model semantics for smodels programs","volume":"8","author":"Oikarinen","year":"2008","journal-title":"TPLP"},{"key":"S1471068412000269_ref11","first-page":"298","volume-title":"Handbook of Logic in AI and Logic Programming","author":"Lifschitz","year":"1994"},{"key":"S1471068412000269_ref10","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1613\/jair.3489","article-title":"Reformulating the situation calculus and the event calculus in the general theory of stable models and in answer set programming","volume":"43","author":"Lee","year":"2012","journal-title":"Journal of Artificial Inteligence Research (JAIR)"},{"key":"S1471068412000269_ref9","unstructured":"Lee J. and Meng Y. 2012. Stable models of formulas with generalized quantifiers. In Proceedings of International Workshop on Nonmonotonic Reasoning (NMR). URL: http:\/\/peace.eas.asu.edu\/joolee\/papers\/smgq-nmr.pdf."},{"key":"S1471068412000269_ref7","doi-asserted-by":"crossref","first-page":"813","DOI":"10.1613\/jair.2810","article-title":"Modularity aspects of disjunctive stable models","volume":"35","author":"Janhunen","year":"2009","journal-title":"Journal of Artificial Intelligence Research"},{"key":"S1471068412000269_ref6","first-page":"1070","volume-title":"Proceedings of International Logic Programming Conference and Symposium","author":"Gelfond","year":"1988"},{"key":"S1471068412000269_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-20895-9_7"},{"key":"S1471068412000269_ref3","first-page":"797","volume-title":"Proceedings of International Joint Conference on Artificial Intelligence (IJCAI)","author":"Ferraris","year":"2009"},{"key":"S1471068412000269_ref1","first-page":"372","volume-title":"Proceedings of International Joint Conference on Artificial Intelligence (IJCAI)","author":"Ferraris","year":"2007"},{"key":"S1471068412000269_ref2","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2010.04.011"},{"key":"S1471068412000269_ref5","first-page":"190","volume-title":"Proceedings of the Twenty-fourth International Conference on Logic Programming (ICLP'08)","author":"Gebser","year":"2008"},{"key":"S1471068412000269_ref8","first-page":"472","volume-title":"Proceedings of the AAAI Conference on Artificial Intelligence (AAAI)","author":"Lee","year":"2008"}],"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\/S1471068412000269","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,25]],"date-time":"2019-04-25T20:27:11Z","timestamp":1556224031000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1471068412000269\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,7]]},"references-count":12,"journal-issue":{"issue":"4-5","published-print":{"date-parts":[[2012,7]]}},"alternative-id":["S1471068412000269"],"URL":"https:\/\/doi.org\/10.1017\/s1471068412000269","relation":{},"ISSN":["1471-0684","1475-3081"],"issn-type":[{"value":"1471-0684","type":"print"},{"value":"1475-3081","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,7]]}}}