{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,10,6]],"date-time":"2022-10-06T13:10:08Z","timestamp":1665061808711},"reference-count":12,"publisher":"Cambridge University Press (CUP)","issue":"3-4","license":[{"start":{"date-parts":[[2018,8,10]],"date-time":"2018-08-10T00:00:00Z","timestamp":1533859200000},"content-version":"unspecified","delay-in-days":40,"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":[[2018,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We propose an interpretation of the first-order answer set programming (FOASP) in terms of intuitionistic proof theory. It is obtained by two polynomial translations between FOASP and the bounded-arity fragment of the \u03a3<jats:sub>1<\/jats:sub> level of the Mints hierarchy in first-order intuitionistic logic. It follows that \u03a3<jats:sub>1<\/jats:sub> formulas using predicates of fixed arity (in particular unary) is of the same strength as FOASP. Our construction reveals a close similarity between constructive provability and stable entailment, or equivalently, between the construction of an answer set and an intuitionistic refutation. This paper is under consideration for publication in Theory and Practice of Logic Programming<\/jats:p>","DOI":"10.1017\/s147106841800008x","type":"journal-article","created":{"date-parts":[[2018,8,10]],"date-time":"2018-08-10T05:44:17Z","timestamp":1533879857000},"page":"673-690","source":"Crossref","is-referenced-by-count":2,"title":["First-order Answer Set Programming as Constructive Proof Search"],"prefix":"10.1017","volume":"18","author":[{"given":"ALEKSY","family":"SCHUBERT","sequence":"first","affiliation":[]},{"given":"PAWE\u0141","family":"URZYCZYN","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,8,10]]},"reference":[{"key":"S147106841800008X_ref6","doi-asserted-by":"publisher","DOI":"10.1145\/116825.116836"},{"key":"S147106841800008X_ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s00165-016-0403-1"},{"key":"S147106841800008X_ref12","article-title":"On the Mints hierarchy in first-order intuitionistic logic","volume":"12","author":"Schubert","year":"2016","journal-title":"Logical Methods in Computer Science"},{"key":"S147106841800008X_ref4","doi-asserted-by":"crossref","unstructured":"Kolaitis P. G. and Papadimitriou C. H. 1988. Why not negation by fixpoint? In Proceedings of the Seventh ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems. PODS'88. ACM, New York, NY, USA, 231\u2013239.","DOI":"10.1145\/308386.308446"},{"key":"S147106841800008X_ref2","doi-asserted-by":"publisher","DOI":"10.1145\/502807.502810"},{"key":"S147106841800008X_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/s10472-006-9028-z"},{"key":"S147106841800008X_ref7","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068403001881"},{"key":"S147106841800008X_ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.indag.2017.05.006"},{"key":"S147106841800008X_ref11","first-page":"251","volume-title":"Proc. TYPES 2014","author":"Schubert","year":"2015"},{"key":"S147106841800008X_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/S0743-1066(98)10015-8"},{"key":"S147106841800008X_ref1","doi-asserted-by":"publisher","DOI":"10.1145\/2043174.2043195"},{"key":"S147106841800008X_ref5","unstructured":"Lifschitz V. 2008. What is answer set programming? In Proceedings of the 23rd National Conference on Artificial Intelligence - Volume 3. AAAI'08. AAAI Press, 1594\u20131597."}],"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\/S147106841800008X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,14]],"date-time":"2019-04-14T15:20:06Z","timestamp":1555255206000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S147106841800008X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7]]},"references-count":12,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2018,7]]}},"alternative-id":["S147106841800008X"],"URL":"https:\/\/doi.org\/10.1017\/s147106841800008x","relation":{},"ISSN":["1471-0684","1475-3081"],"issn-type":[{"value":"1471-0684","type":"print"},{"value":"1475-3081","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,7]]}}}