{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T19:59:39Z","timestamp":1762459179209},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"4-5","license":[{"start":{"date-parts":[[2014,7,21]],"date-time":"2014-07-21T00:00:00Z","timestamp":1405900800000},"content-version":"unspecified","delay-in-days":20,"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":[[2014,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Extensional higher-order logic programming has been introduced as a generalization of classical logic programming. An important characteristic of this paradigm is that it preserves all the well-known properties of traditional logic programming. In this paper we consider the semantics of negation in the context of the new paradigm. Using some recent results from non-monotonic fixed-point theory, we demonstrate that every higher-order logic program with negation has a unique <jats:italic>minimum<\/jats:italic> infinite-valued model. In this way we obtain the first purely model-theoretic semantics for negation in extensional higher-order logic programming. Using our approach, we resolve an old paradox that was introduced by W. W. Wadge in order to demonstrate the semantic difficulties of higher-order logic programming.<\/jats:p>","DOI":"10.1017\/s1471068414000313","type":"journal-article","created":{"date-parts":[[2014,7,21]],"date-time":"2014-07-21T11:52:50Z","timestamp":1405943570000},"page":"725-737","source":"Crossref","is-referenced-by-count":9,"title":["Minimum Model Semantics for Extensional Higher-order Logic Programming with Negation"],"prefix":"10.1017","volume":"14","author":[{"given":"ANGELOS","family":"CHARALAMBIDIS","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ZOLT\u00c1N","family":"\u00c9SIK","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"PANOS","family":"RONDOGIANNIS","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,7,21]]},"reference":[{"key":"S1471068414000313_ref9","doi-asserted-by":"publisher","DOI":"10.1145\/1055686.1055694"},{"key":"S1471068414000313_ref1","first-page":"203","volume-title":"Proceedings of the 15th International Workshop on Computer Science Logic (CSL)","author":"Bezem","year":"2001"},{"key":"S1471068414000313_ref4","volume-title":"Proceedings of 13th Panhellenic Logic Symposium","author":"\u00c9sik","year":"2013"},{"key":"S1471068414000313_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-83189-8"},{"key":"S1471068414000313_ref3","doi-asserted-by":"publisher","DOI":"10.1145\/2499937.2499942"},{"key":"S1471068414000313_ref10","doi-asserted-by":"publisher","DOI":"10.1145\/116825.116838"},{"key":"S1471068414000313_ref2","first-page":"91","volume-title":"JELIA","author":"Charalambidis","year":"2010"},{"key":"S1471068414000313_ref7","first-page":"57","volume-title":"NMELP","author":"Pearce","year":"1996"},{"key":"S1471068414000313_ref5","unstructured":"\u00c9sik Z. and Rondogiannis P. 2014. A fixed point theorem for non-monotonic functions. CoRR abs\/1402.0299."},{"key":"S1471068414000313_ref8","first-page":"11","volume-title":"PODS","author":"Przymusinski","year":"1989"},{"key":"S1471068414000313_ref11","unstructured":"Wadge W. W. 1991. Higher-order Horn logic programming. In ISLP. 289\u2013303."}],"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\/S1471068414000313","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,22]],"date-time":"2019-04-22T19:06:07Z","timestamp":1555959967000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1471068414000313\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,7]]},"references-count":11,"journal-issue":{"issue":"4-5","published-print":{"date-parts":[[2014,7]]}},"alternative-id":["S1471068414000313"],"URL":"https:\/\/doi.org\/10.1017\/s1471068414000313","relation":{},"ISSN":["1471-0684","1475-3081"],"issn-type":[{"value":"1471-0684","type":"print"},{"value":"1475-3081","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,7]]}}}