{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T05:22:22Z","timestamp":1776316942124,"version":"3.50.1"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,6,25]]},"abstract":"<jats:p>We prove a conservativity result for extensional type theories over propositional ones, i.e. dependent type theories with propositional computation rules, or computation axioms, using insights from homotopy type theory. The argument exploits a notion of canonical homotopy equivalence between contexts, and uses the notion of a category with attributes to phrase the semantics of theories of dependent types. Informally, our main result asserts that, for judgements essentially concerning h-sets, reasoning with extensional or propositional type theories is equivalent.<\/jats:p>","DOI":"10.46298\/lmcs-21(3:32)2025","type":"journal-article","created":{"date-parts":[[2025,9,26]],"date-time":"2025-09-26T13:05:09Z","timestamp":1758891909000},"source":"Crossref","is-referenced-by-count":1,"title":["Relating homotopy equivalences to conservativity in dependent type theories with computation axioms"],"prefix":"10.46298","volume":"Volume 21, Issue 3","author":[{"given":"Matteo","family":"Spadetto","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2025,9,26]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/2303.05623v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/2303.05623v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,26]],"date-time":"2025-09-26T13:05:09Z","timestamp":1758891909000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/11565"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,26]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-21(3:32)2025","relation":{"has-preprint":[{"id-type":"arxiv","id":"2303.05623v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2303.05623v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2303.05623","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2303.05623","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"value":"1860-5974","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9,26]]},"article-number":"11565"}}