{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:19Z","timestamp":1753894399924,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>A distributive lattice-ordered magma ($d\\ell$-magma) $(A,\\wedge,\\vee,\\cdot)$\nis a distributive lattice with a binary operation $\\cdot$ that preserves joins\nin both arguments, and when $\\cdot$ is associative then $(A,\\vee,\\cdot)$ is an\nidempotent semiring. A $d\\ell$-magma with a top $\\top$ is unary-determined if\n$x{\\cdot} y=(x{\\cdot}\\!\\top\\wedge y)$ $\\vee(x\\wedge \\top\\!{\\cdot}y)$. These\nalgebras are term-equivalent to a subvariety of distributive lattices with\n$\\top$ and two join-preserving unary operations $\\mathsf p,\\mathsf q$. We\nobtain simple conditions on $\\mathsf p,\\mathsf q$ such that $x{\\cdot}\ny=(\\mathsf px\\wedge y)\\vee(x\\wedge \\mathsf qy)$ is associative, commutative,\nidempotent and\/or has an identity element.\n  This generalizes previous results on the structure of doubly idempotent\nsemirings and, in the case when the distributive lattice is a Heyting algebra,\nit provides structural insight into unary-determined algebraic models of\nbunched implication logic. We also provide Kripke semantics for the algebras\nunder consideration, which leads to more efficient algorithms for constructing\nfinite models. We find all subdirectly irreducible algebras up to cardinality\neight in which $\\mathsf p=\\mathsf q$ is a closure operator, as well as all\nfinite unary-determined bunched implication chains and map out the poset of\njoin-irreducible varieties generated by them.<\/jats:p>","DOI":"10.46298\/lmcs-20(1:12)2024","type":"journal-article","created":{"date-parts":[[2024,2,9]],"date-time":"2024-02-09T10:43:03Z","timestamp":1707475383000},"source":"Crossref","is-referenced-by-count":0,"title":["Varieties of unary-determined distributive $\\ell$-magmas and bunched implication algebras"],"prefix":"10.46298","volume":"Volume 20, Issue 1","author":[{"given":"Natanael","family":"Alpay","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Jipsen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Melissa","family":"Sugimoto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2024,2,7]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/13016\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/13016\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,9]],"date-time":"2024-02-09T10:43:04Z","timestamp":1707475384000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/10280"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,7]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(1:12)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2211.02804v3","asserted-by":"subject"},{"id-type":"arxiv","id":"2211.02804v2","asserted-by":"subject"},{"id-type":"arxiv","id":"2211.02804v1","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2211.02804","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2211.02804","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2024,2,7]]},"article-number":"10280"}}