{"type":"ScholarlyArticle","title":"The Intricacies of Three-Valued Extensional Semantics for Higher-Order Logic Programs","authors":[{"name":"Panos Rondogiannis","slug":"panos-rondogiannis","given":"Panos","family":"Rondogiannis","affiliation":"National and Kapodistrian University of Athens"},{"name":"Ioanna Symeonidou","slug":"ioanna-symeonidou","given":"Ioanna","family":"Symeonidou","affiliation":"National and Kapodistrian University of Athens"}],"abstract":"In this paper we examine the problem of providing a purely extensional three-valued semantics for higher-order logic programs with negation. We demonstrate that a technique that was proposed by M. Bezem for providing extensional semantics to positive higher-order logic programs, fails when applied to higher-order logic programs with negation. On the positive side, we demonstrate that for stratified higher-order logic programs, extensionality is indeed achieved by the technique. We analyze the reasons of the failure of extensionality in the general case, arguing that a three-valued setting can not 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.","doi":"10.24963/ijcai.2018/750","url":"https://ijcai.org/proceedings/2018/750","pdf":"https://ijcai.org/proceedings/2018/0750.pdf","markdown":"https://ijcai.org/proceedings/2018/750.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/750","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Sister Conferences Best Papers","track":"Best Sister Conferences","number":750,"pages":{"first":5344,"last":5348},"keywords":["Knowledge Representation and Reasoning: Knowledge Representation Languages","Knowledge Representation and Reasoning: Non-monotonic Reasoning"],"videos":[],"references":[{"position":1,"raw":"[Apt et al., 1988] Krzysztof R. 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