{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,1]],"date-time":"2025-11-01T14:37:18Z","timestamp":1762007838145,"version":"build-2065373602"},"reference-count":20,"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 define a novel, extensional, three-valued semantics for higher-order logic programs with negation. The new semantics is based on interpreting the types of the source language as three-valued Fitting-monotonic functions at all levels of the type hierarchy. We prove that there exists a bijection between such Fitting-monotonic functions and pairs of two-valued-result functions where the first member of the pair is monotone-antimonotone and the second member is antimonotone-monotone. By deriving an extension of<jats:italic>consistent approximation fixpoint theory<\/jats:italic>(Denecker<jats:italic>et al.<\/jats:italic>2004) and utilizing the above bijection, we define an iterative procedure that produces for any given higher-order logic program a distinguished extensional model. We demonstrate that this model is actually a<jats:italic>minimal<\/jats:italic>one. Moreover, we prove that our construction generalizes the familiar well-founded semantics for classical logic programs, making in this way our proposal an appealing formulation for capturing the<jats:italic>well-founded semantics for higher-order logic programs<\/jats:italic>.<\/jats:p>","DOI":"10.1017\/s1471068418000108","type":"journal-article","created":{"date-parts":[[2018,8,10]],"date-time":"2018-08-10T05:44:17Z","timestamp":1533879857000},"page":"421-437","source":"Crossref","is-referenced-by-count":8,"title":["Approximation Fixpoint Theory and the Well-Founded Semantics of Higher-Order Logic Programs"],"prefix":"10.1017","volume":"18","author":[{"given":"ANGELOS","family":"CHARALAMBIDIS","sequence":"first","affiliation":[]},{"given":"PANOS","family":"RONDOGIANNIS","sequence":"additional","affiliation":[]},{"given":"IOANNA","family":"SYMEONIDOU","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,8,10]]},"reference":[{"key":"S1471068418000108_ref14","first-page":"620","article-title":"The well-founded semantics for general logic programs","volume":"38","author":"Gelder","year":"1991","journal-title":"J. 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Extensionality of simply typed logic programs. In Logic Programming: The 1999 International Conference, Las Cruces, New Mexico, USA, November 29 - December 4, 1999, D. D. Schreye , Ed. MIT Press, 395\u2013410."},{"key":"S1471068418000108_ref15","doi-asserted-by":"crossref","unstructured":"Przymusinski T. C. 1989. Every logic program has a natural stratification and an iterated least fixed point model. In Proceedings of the Eighth ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, March 29-31, 1989, Philadelphia, Pennsylvania, USA. 11\u201321.","DOI":"10.1145\/73721.73723"},{"key":"S1471068418000108_ref12","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2015.01.032"},{"key":"S1471068418000108_ref20","first-page":"289","volume-title":"Logic Programming, Proceedings of the 1991 International Symposium, San Diego, California, USA, Oct. 28 - Nov 1, 1991","author":"Wadge","year":"1991"},{"volume-title":"Iteration Theories - The Equational Logic of Iterative Processes","year":"1993","author":"Bloom","key":"S1471068418000108_ref2"},{"key":"S1471068418000108_ref3","unstructured":"Carayol A. and \u00c9sik Z. 2016. An analysis of the equational properties of the well-founded fixed point. In Principles of Knowledge Representation and Reasoning: Proceedings of the Fifteenth International Conference, KR 2016, Cape Town, South Africa, April 25-29, 2016., C. Baral , J. P. Delgrande , and F. Wolter , Eds. AAAI Press, 533\u2013536."},{"key":"S1471068418000108_ref16","doi-asserted-by":"crossref","unstructured":"Rondogiannis P. and Symeonidou I. 2016. Extensional semantics for higher-order logic programs with negation. In Logics in Artificial Intelligence - 15th European Conference, JELIA 2016, Larnaca, Cyprus, November 9-11, 2016, Proceedings, L. Michael and A. C. Kakas , Eds. 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