{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T11:15:25Z","timestamp":1778670925822,"version":"3.51.4"},"reference-count":17,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2007,11,1]],"date-time":"2007-11-01T00:00:00Z","timestamp":1193875200000},"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":[[2007,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper presents a property of propositional theories under the answer sets semantics (called <jats:italic>Equilibrium Logic<\/jats:italic> for this general syntax): any theory can always be reexpressed as a strongly equivalent disjunctive logic program, possibly with negation in the head. We provide two different proofs for this result: one involving a syntactic transformation, and one that constructs a program starting from the countermodels of the theory in the intermediate logic of here-and-there.<\/jats:p>","DOI":"10.1017\/s1471068407003110","type":"journal-article","created":{"date-parts":[[2007,5,25]],"date-time":"2007-05-25T13:30:57Z","timestamp":1180099857000},"page":"745-759","source":"Crossref","is-referenced-by-count":40,"title":["Propositional theories are strongly equivalent to logic programs"],"prefix":"10.1017","volume":"7","author":[{"given":"PEDRO","family":"CABALAR","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"PAOLO","family":"FERRARIS","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2007,11,1]]},"reference":[{"key":"S1471068407003110_ref16","doi-asserted-by":"crossref","unstructured":"Pearce D. 1997. A new logical characterisation of stable models and answer sets. In Non monotonic extensions of logic programming. Proceedings of NMELP'96. (LNAI 1216). Springer-Verlag.","DOI":"10.1007\/BFb0023801"},{"key":"S1471068407003110_ref15","doi-asserted-by":"publisher","DOI":"10.1002\/j.1538-7305.1956.tb03835.x"},{"key":"S1471068407003110_ref14","first-page":"82","article-title":"Die logik und das grundlagenproblem","volume":"12","author":"Lukasiewicz","year":"1941","journal-title":"Les Entries de Z\u00fcrich sur les Fondaments et la M\u00e9thode des Sciences Math\u00e9matiques"},{"key":"S1471068407003110_ref13","first-page":"603","volume-title":"Proceedings of Third International Conference on Principles of Knowledge Representation and Reasoning","author":"Lifschitz","year":"1992"},{"key":"S1471068407003110_ref12","doi-asserted-by":"publisher","DOI":"10.1023\/A:1018978005636"},{"key":"S1471068407003110_ref10","first-page":"259","article-title":"Characterization of strongly equivalent logic programs in intermediate logics","volume":"3","author":"Jongh","year":"2003","journal-title":"TPLP"},{"key":"S1471068407003110_ref8","first-page":"42","volume-title":"Sitzungsberichte der Preussischen Akademie der Wissenschaften, Physikalisch-mathematische Klasse","author":"Heyting","year":"1930"},{"key":"S1471068407003110_ref6","first-page":"1070","volume-title":"Proceedings of the 5th International Conference on Logic Programming","author":"Gelfond","year":"1988"},{"key":"S1471068407003110_ref3","unstructured":"Cabalar P. , Pearce D. and Valverde A. 2006. Minimal logic programs. Unpublished draft."},{"key":"S1471068407003110_ref11","doi-asserted-by":"publisher","DOI":"10.1145\/383779.383783"},{"key":"S1471068407003110_ref2","doi-asserted-by":"crossref","unstructured":"Cabalar P. , Pearce D. and Valverde A. 2005. Reducing propositional theories in equilibrium logic to logic programs. In Proceedings of the 12th Portuguese Conference on Artificial Intelligence (EPIA'05). Lecture Notes in Computer Science, vol. 3808. Springer-Verlag, Berlin, Heidelberg, 4\u201317.","DOI":"10.1007\/11595014_2"},{"key":"S1471068407003110_ref1","first-page":"67","volume-title":"The Handbook of Logic in AI and Logic Programming","author":"Bibel","year":"1993"},{"key":"S1471068407003110_ref17","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1952.11988183"},{"key":"S1471068407003110_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068403001923"},{"key":"S1471068407003110_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/11546207_10"},{"key":"S1471068407003110_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/BF03037169"},{"key":"S1471068407003110_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/S0743-1066(97)10001-2"}],"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\/S1471068407003110","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,1]],"date-time":"2019-04-01T19:09:50Z","timestamp":1554145790000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1471068407003110\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,11]]},"references-count":17,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2007,11]]}},"alternative-id":["S1471068407003110"],"URL":"https:\/\/doi.org\/10.1017\/s1471068407003110","relation":{},"ISSN":["1471-0684","1475-3081"],"issn-type":[{"value":"1471-0684","type":"print"},{"value":"1475-3081","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,11]]}}}