{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,29]],"date-time":"2026-06-29T14:01:10Z","timestamp":1782741670814,"version":"3.54.5"},"reference-count":63,"publisher":"Cambridge University Press (CUP)","issue":"5-6","license":[{"start":{"date-parts":[[2008,11,1]],"date-time":"2008-11-01T00:00:00Z","timestamp":1225497600000},"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":[[2008,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, a Gaifman\u2013Shapiro-style module architecture is tailored\n                    to the case of <jats:sc>smodels<\/jats:sc> programs under the stable model semantics. The\n                    composition of <jats:sc>smodels<\/jats:sc> program modules is suitably limited by module\n                    conditions which ensure the compatibility of the module system with stable\n                    models. Hence the semantics of an entire <jats:sc>smodels<\/jats:sc> program depends\n                    directly on stable models assigned to its modules. This result is formalized as\n                    a <jats:italic>module theorem<\/jats:italic> which truly strengthens V. Lifschitz and H.\n                    Turner's splitting-set theorem (June 1994, Splitting a logic program. In\n                        <jats:italic>Logic Programming: Proceedings of the Eleventh International\n                        Conference on Logic Programming<\/jats:italic>, Santa Margherita Ligure, Italy, P.\n                    V. Hentenryck, Ed. MIT Press, 23\u201337) for the class of <jats:sc>smodels<\/jats:sc>\n                    programs. To streamline generalizations in the future, the module theorem is\n                    first proved for normal programs and then extended to cover <jats:sc>smodels<\/jats:sc>\n                    programs using a translation from the latter class of programs to the former\n                    class. Moreover, the respective notion of module-level equivalence, namely\n                        <jats:italic>modular equivalence<\/jats:italic>, is shown to be a proper congruence\n                    relation: it is preserved under substitutions of modules that are modularly\n                    equivalent. Principles for program decomposition are also addressed. The\n                    strongly connected components of the respective dependency graph can be\n                    exploited in order to extract a module structure when there is no explicit\n                        <jats:italic>a priori<\/jats:italic> knowledge about the modules of a program. The\n                    paper includes a practical demonstration of tools that have been developed for\n                    automated (de)composition of <jats:sc>smodels<\/jats:sc> programs.<\/jats:p>","DOI":"10.1017\/s147106840800358x","type":"journal-article","created":{"date-parts":[[2008,11,20]],"date-time":"2008-11-20T04:35:46Z","timestamp":1227155746000},"page":"717-761","source":"Crossref","is-referenced-by-count":25,"title":["Achieving compositionality of the stable model semantics for\n                        <scp>smodels<\/scp> programs"],"prefix":"10.1017","volume":"8","author":[{"given":"EMILIA","family":"OIKARINEN","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"TOMI","family":"JANHUNEN","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2008,11,1]]},"reference":[{"key":"S147106840800358X_ref63","first-page":"13","volume-title":"Proceedings of the\n                        LPNMR'07 Workshop on Correspondence and Equivalence for Nonmonotonic\n                        Theories (CENT2007)","author":"Woltran","year":"2007"},{"key":"S147106840800358X_ref61","doi-asserted-by":"publisher","DOI":"10.1137\/0208032"},{"key":"S147106840800358X_ref60","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068403001819"},{"key":"S147106840800358X_ref59","doi-asserted-by":"publisher","DOI":"10.1137\/0201010"},{"key":"S147106840800358X_ref58","unstructured":"Tari L. , Baral C. and Anwar S. September 2005. A language for modular answer set programming: Application to ACC tournament scheduling. In Answer Set Programming, Advances in Theory and Implementation, Proceedings of the Third International ASP'05 Workshop, Bath, UK, Vos M. D. and Provetti A. , Eds. CEUR Workshop Proceedings, vol. 142. 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In Proceedings of the 1985 Symposium on Logic Programming, Boston, MA, 152\u2013160."},{"key":"S147106840800358X_ref51","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/exn039"},{"key":"S147106840800358X_ref50","first-page":"167","volume-title":"Artificial Intelligence:\n                        Methodology, Systems, and Applications, Thirteenth International Conference,\n                        AIMSA 2008","author":"Oikarinen","year":"2008"},{"key":"S147106840800358X_ref47","first-page":"169","volume-title":"Practical Aspects of Declarative Languages, Third\n                        International Symposium, PADL 2001","author":"Nogueira","year":"2001"},{"key":"S147106840800358X_ref44","doi-asserted-by":"publisher","DOI":"10.1016\/0743-1066(89)90031-9"},{"key":"S147106840800358X_ref43","doi-asserted-by":"publisher","DOI":"10.1109\/LICS.1988.5123"},{"key":"S147106840800358X_ref38","doi-asserted-by":"publisher","DOI":"10.1016\/j.artint.2004.04.004"},{"key":"S147106840800358X_ref41","doi-asserted-by":"publisher","DOI":"10.1145\/116825.116836"},{"key":"S147106840800358X_ref35","first-page":"121","volume-title":"Proceedings of the Ninth International Joint Conference on\n                        Artificial Intelligence","author":"Lifschitz","year":"1985"},{"key":"S147106840800358X_ref33","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-74610-2_10"},{"key":"S147106840800358X_ref32","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-72200-7_16"},{"key":"S147106840800358X_ref31","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068407003031"},{"key":"S147106840800358X_ref30","first-page":"493","volume-title":"Logics in Artificial Intelligence,\n                        Eighth European Conference, JELIA 2002","author":"Janhunen","year":"2002"},{"key":"S147106840800358X_ref28","doi-asserted-by":"publisher","DOI":"10.3166\/jancl.16.35-86"},{"key":"S147106840800358X_ref25","first-page":"78","volume-title":"Fifth International Conference on Application of\n                        Concurrency to System Design, ACSD 2005","author":"Heljanko","year":"2005"},{"key":"S147106840800358X_ref24","unstructured":"Heljanko K. and \u015etef\u0103nescu A. 2004. 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