{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T14:11:31Z","timestamp":1775484691733,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2022,12,20]],"date-time":"2022-12-20T00:00:00Z","timestamp":1671494400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>In this paper we try to find a computational interpretation for a strong form\nof extensionality, which we call \"converse extensionality\". Converse\nextensionality principles, which arise as the Dialectica interpretation of the\naxiom of extensionality, were first studied by Howard. In order to give a\ncomputational interpretation to these principles, we reconsider Brouwer's\napartness relation, a strong constructive form of inequality. Formally, we\nprovide a categorical construction to endow every typed combinatory algebra\nwith an apartness relation. We then exploit that functions reflect apartness,\nin addition to preserving equality, to prove that the resulting categories of\nassemblies model a converse extensionality principle.<\/jats:p>","DOI":"10.46298\/lmcs-18(4:13)2022","type":"journal-article","created":{"date-parts":[[2022,12,27]],"date-time":"2022-12-27T09:14:06Z","timestamp":1672132446000},"source":"Crossref","is-referenced-by-count":1,"title":["Converse extensionality and apartness"],"prefix":"10.46298","volume":"Volume 18, Issue 4","author":[{"given":"Benno van den","family":"Berg","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robert","family":"Passmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2022,12,20]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/10511\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/10511\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:19:41Z","timestamp":1687292381000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/7306"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,20]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-18(4:13)2022","relation":{"has-preprint":[{"id-type":"arxiv","id":"2103.14482v5","asserted-by":"subject"},{"id-type":"arxiv","id":"2103.14482v4","asserted-by":"subject"},{"id-type":"arxiv","id":"2103.14482v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2103.14482v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2103.14482","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2103.14482","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,20]]},"article-number":"7306"}}