{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,23]],"date-time":"2023-09-23T16:04:58Z","timestamp":1695485098828},"reference-count":24,"publisher":"Cambridge University Press (CUP)","issue":"5-6","license":[{"start":{"date-parts":[[2017,8,23]],"date-time":"2017-08-23T00:00:00Z","timestamp":1503446400000},"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":[[2017,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>M. Bezem defined an extensional semantics for positive higher-order logic programs. Recently, it was demonstrated by Rondogiannis and Symeonidou that Bezem's technique can be extended to higher-order logic programs with negation, retaining its extensional properties, provided that it is interpreted under a logic with an infinite number of truth values. Rondogiannis and Symeonidou also demonstrated that Bezem's technique, when extended under the stable model semantics, does not in general lead to extensional stable models. In this paper, we consider the problem of extending Bezem's technique under the well-founded semantics. We demonstrate that the well-founded extension<jats:italic>fails<\/jats:italic>to retain extensionality in the general case. On the positive side, we demonstrate that for stratified higher-order logic programs, extensionality is indeed achieved. We analyze the reasons of the failure of extensionality in the general case, arguing that a three-valued setting cannot distinguish between certain predicates that appear to have a different behaviour inside a program context, but which happen to be identical as three-valued relations.<\/jats:p>","DOI":"10.1017\/s1471068417000357","type":"journal-article","created":{"date-parts":[[2017,8,23]],"date-time":"2017-08-23T05:33:20Z","timestamp":1503466400000},"page":"974-991","source":"Crossref","is-referenced-by-count":1,"title":["The intricacies of three-valued extensional semantics for higher-order logic programs"],"prefix":"10.1017","volume":"17","author":[{"given":"PANOS","family":"RONDOGIANNIS","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"IOANNA","family":"SYMEONIDOU","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2017,8,23]]},"reference":[{"key":"S1471068417000357_ref5","unstructured":"Carayol A. and \u00c9sik Z. 2016. An analysis of the equational properties of the well-founded fixed point. In Proc. of Principles of Knowledge Representation and Reasoning: Proceedings of the 15th International Conference, KR 2016, Cape Town, South Africa, April 25\u201329, 2016, C. Baral , J. P. Delgrande and F. Wolter , Eds. AAAI Press, 533\u2013536."},{"key":"S1471068417000357_ref3","doi-asserted-by":"crossref","unstructured":"Bezem M. 2001. An improved extensionality criterion for higher-order logic programs. In Proc. of Computer Science Logic, 15th International Workshop, CSL 2001. 10th Annual Conference of the EACSL, Paris, France, September 10\u201313, 2001, L. Fribourg , Ed. Lecture Notes in Computer Science, vol. 2142. Springer, 203\u2013216.","DOI":"10.1007\/3-540-44802-0_15"},{"key":"S1471068417000357_ref12","doi-asserted-by":"crossref","unstructured":"\u00c9sik Z. 2015. Equational properties of stratified least fixed points (extended abstract). In Proc. of Logic, Language, Information, and Computation - 22nd International Workshop, WoLLIC 2015, Bloomington, IN, USA, July 20\u201323, 2015, V. de Paiva , R. J. G. B. de Queiroz , L. S. Moss , D. Leivant , and A. G. de Oliveira , Eds. Lecture Notes in Computer Science vol. 9160. Springer, 174\u2013188.","DOI":"10.1007\/978-3-662-47709-0_13"},{"key":"S1471068417000357_ref8","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2017.01.005"},{"key":"S1471068417000357_ref19","first-page":"321","volume-title":"Formal Techniques in Artificial Intelligence","author":"Przymusinska","year":"1990"},{"key":"S1471068417000357_ref7","first-page":"21","article-title":"Extensional higher-order logic programming","volume":"14","author":"Charalambidis","year":"2013","journal-title":"ACM Transaction on Computational Logic"},{"key":"S1471068417000357_ref13","doi-asserted-by":"publisher","DOI":"10.1016\/0743-1066(89)90032-0"},{"key":"S1471068417000357_ref22","doi-asserted-by":"crossref","unstructured":"Rondogiannis P. and Symeonidou I. 2017. Extensional semantics for higher-order logic programs with negation. CoRR abs\/1701.08622.","DOI":"10.24963\/ijcai.2018\/750"},{"key":"S1471068417000357_ref14","first-page":"620","article-title":"The well-founded semantics for general logic programs","volume":"38","author":"Gelder","year":"1991","journal-title":"Journal of ACM"},{"key":"S1471068417000357_ref21","unstructured":"Rondogiannis P. and Symeonidou I. 2016. Extensional semantics for higher-order logic programs with negation. In Proc. of Logics in Artificial Intelligence - 15th European Conference, JELIA 2016, Larnaca, Cyprus, November 9\u201311, 2016, L. Michael and A. C. Kakas , Eds. Lecture Notes in Computer Science, vol. 10021, 447\u2013462."},{"key":"S1471068417000357_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-934613-40-8.50006-3"},{"key":"S1471068417000357_ref2","unstructured":"Bezem M. 1999. Extensionality of simply typed logic programs. In Proc. Logic Programming: The 1999 International Conference, Las Cruces, New Mexico, USA, November 29\u2013December 4, 1999, D. D. Schreye , Ed. MIT Press, 395\u2013410."},{"key":"S1471068417000357_ref18","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139021326"},{"key":"S1471068417000357_ref6","doi-asserted-by":"publisher","DOI":"10.1017\/S1471068414000313"},{"key":"S1471068417000357_ref17","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-83189-8"},{"key":"S1471068417000357_ref11","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1007\/978-3-642-30743-0_13","volume-title":"Correct Reasoning - Essays on Logic-Based AI in Honour of Vladimir Lifschitz","author":"Denecker","year":"2012"},{"key":"S1471068417000357_ref24","unstructured":"Wadge W. W. 1991. Higher-order horn logic programming. In Proc. the 1991 International Symposium on Logic Programming, Larnaca, Cyprus, San Diego, California, USA, Oct. 28\u2013Nov 1, 1991, V. A. Saraswat and K. Ueda , Eds. MIT Press, 289\u2013303."},{"key":"S1471068417000357_ref4","volume-title":"Iteration Theories - The Equational Logic of Iterative Processes","author":"Bloom","year":"1993"},{"key":"S1471068417000357_ref10","doi-asserted-by":"publisher","DOI":"10.1145\/958942.958946"},{"key":"S1471068417000357_ref16","unstructured":"Kountouriotis V. , Rondogiannis P. and Wadge W. W. 2005. Extensional higher-order datalog. In Short Paper Proc. of the 12th International Conference on Logic for Programming, Artificial Intelligence and Reasoning (LPAR), 1\u20135."},{"key":"S1471068417000357_ref20","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-934613-40-8.50009-9"},{"key":"S1471068417000357_ref23","doi-asserted-by":"publisher","DOI":"10.1145\/1055686.1055694"},{"key":"S1471068417000357_ref9","doi-asserted-by":"publisher","DOI":"10.1016\/0743-1066(93)90039-J"},{"key":"S1471068417000357_ref15","unstructured":"Gelfond M. and Lifschitz V. 1988. The stable model semantics for logic programming. In Proc. of the 5th International Conference and Symposium Logic Programming, Seattle, Washington, August 15\u201319, 1988 (2 Volumes), R. A. Kowalski and K. A. Bowen , Eds. MIT Press, 1070\u20131080."}],"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\/S1471068417000357","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,2]],"date-time":"2019-10-02T14:10:07Z","timestamp":1570025407000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1471068417000357\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,23]]},"references-count":24,"journal-issue":{"issue":"5-6","published-print":{"date-parts":[[2017,9]]}},"alternative-id":["S1471068417000357"],"URL":"https:\/\/doi.org\/10.1017\/s1471068417000357","relation":{},"ISSN":["1471-0684","1475-3081"],"issn-type":[{"value":"1471-0684","type":"print"},{"value":"1475-3081","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8,23]]}}}