{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,17]],"date-time":"2025-11-17T14:32:40Z","timestamp":1763389960824,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2020,2,17]],"date-time":"2020-02-17T00:00:00Z","timestamp":1581897600000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,2,17]],"date-time":"2020-02-17T00:00:00Z","timestamp":1581897600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2020,2,17]],"date-time":"2020-02-17T00:00:00Z","timestamp":1581897600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"accepted":{"date-parts":[[2025,4,1]]},"abstract":"<jats:p>We propose a new axiomatisation of the alpha-equivalence relation for nominal terms, based on a primitive notion of fixed-point constraint. We show that the standard freshness relation between atoms and terms can be derived from the more primitive notion of permutation fixed-point, and use this result to prove the correctness of the new $\\alpha$-equivalence axiomatisation. This gives rise to a new notion of nominal unification, where solutions for unification problems are pairs of a fixed-point context and a substitution. Although it may seem less natural than the standard notion of nominal unifier based on freshness constraints, the notion of unifier based on fixed-point constraints behaves better when equational theories are considered: for example, nominal unification remains finitary in the presence of commutativity, whereas it becomes infinitary when unifiers are expressed using freshness contexts. We provide a definition of $\\alpha$-equivalence modulo equational theories that take into account A, C and AC theories. Based on this notion of equivalence, we show that C-unification is finitary and we provide a sound and complete C-unification algorithm, as a first step towards the development of nominal unification modulo AC and other equational theories with permutative properties.<\/jats:p>","DOI":"10.23638\/lmcs-16(1:19)2020","type":"journal-article","created":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:44:28Z","timestamp":1743702268000},"source":"Crossref","is-referenced-by-count":3,"title":["On Nominal Syntax and Permutation Fixed Points"],"prefix":"10.23638","volume":"Volume 16, Issue 1","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0089-3905","authenticated-orcid":false,"given":"Mauricio","family":"Ayala-Rinc\u00f3n","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8325-5815","authenticated-orcid":false,"given":"Maribel","family":"Fern\u00e1ndez","sequence":"additional","affiliation":[]},{"given":"Daniele","family":"Nantes-Sobrinho","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2020,2,17]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/arxiv.org\/pdf\/1902.08345v4","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/arxiv.org\/pdf\/1902.08345v4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,3]],"date-time":"2025-04-03T17:44:28Z","timestamp":1743702268000},"score":1,"resource":{"primary":{"URL":"http:\/\/lmcs.episciences.org\/5209"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,17]]},"references-count":0,"URL":"https:\/\/doi.org\/10.23638\/lmcs-16(1:19)2020","relation":{"has-preprint":[{"id-type":"arxiv","id":"1902.08345v2","asserted-by":"subject"},{"id-type":"arxiv","id":"1902.08345v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"1902.08345","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1902.08345","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2020,2,17]]},"article-number":"5209"}}