{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T21:57:40Z","timestamp":1747173460359,"version":"3.40.5"},"reference-count":29,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2024,4,11]],"date-time":"2024-04-11T00:00:00Z","timestamp":1712793600000},"content-version":"unspecified","delay-in-days":41,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2024,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, the notion of locally algebraic intersection structure is introduced for algebraic L-domains. Essentially, every locally algebraic intersection structure is a family of sets, which forms an algebraic L-domain ordered by inclusion. It is shown that there is a locally algebraic intersection structure which is order-isomorphic to a given algebraic L-domain. This result extends the classic Stone\u2019s representation theorem for Boolean algebras to the case of algebraic L-domains. In addition, it can be seen that many well-known representations of algebraic L-domains, such as logical algebras, information systems, closure spaces, and formal concept analysis, can be analyzed in the framework of locally algebraic intersection structures. Then, a set-theoretic uniformity across different representations of algebraic L-domains is established.<\/jats:p>","DOI":"10.1017\/s0960129524000069","type":"journal-article","created":{"date-parts":[[2024,4,11]],"date-time":"2024-04-11T09:24:00Z","timestamp":1712827440000},"page":"244-257","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["A set-theoretic approach to algebraic L-domains"],"prefix":"10.1017","volume":"34","author":[{"given":"Juan","family":"Zou","sequence":"first","affiliation":[]},{"given":"Yuhan","family":"Zhao","sequence":"additional","affiliation":[]},{"given":"Cuixia","family":"Miao","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2382-936X","authenticated-orcid":false,"given":"Longchun","family":"Wang","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2024,4,11]]},"reference":[{"key":"S0960129524000069_ref20","first-page":"37","article-title":"The theory of representations for Boolean algebras","volume":"40","author":"Stone","year":"1936","journal-title":"Transactions of the American Mathematical Society"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref27","DOI":"10.1016\/j.tcs.2015.11.037"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref19","DOI":"10.1016\/j.tcs.2020.12.044"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref23","DOI":"10.1016\/j.ic.2022.104958"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref17","DOI":"10.1007\/BFb0012801"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref14","DOI":"10.3233\/FI-1999-37403"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref2","DOI":"10.1016\/0168-0072(91)90065-T"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref16","DOI":"10.1006\/inco.2001.3073"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref7","DOI":"10.1007\/978-3-642-59830-2"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref5","DOI":"10.1016\/j.tcs.2006.09.005"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref15","DOI":"10.1016\/0890-5401(91)90068-D"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref22","DOI":"10.1016\/j.ipl.2020.106036"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref24","DOI":"10.1007\/s11225-022-10024-3"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref9","DOI":"10.1016\/j.dam.2017.12.016"},{"key":"S0960129524000069_ref11","first-page":"1","article-title":"A categorical view on algebraic lattices in formal concept analysis","volume":"74","author":"Hitzler","year":"2006","journal-title":"Fundamenta Informaticae"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref26","DOI":"10.1016\/j.tcs.2022.02.020"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref6","DOI":"10.1017\/CBO9780511809088"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref8","DOI":"10.1017\/CBO9780511542725"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref10","DOI":"10.1016\/j.tcs.2019.01.042"},{"unstructured":"Abramsky, S. (1987). Domain Theory and the Logic of Observable Properties. Phd thesis, University of London.","key":"S0960129524000069_ref1"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref25","DOI":"10.1007\/s00153-023-00903-4"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref4","DOI":"10.1016\/S0898-1221(97)00096-5"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref18","DOI":"10.1016\/j.tcs.2008.06.032"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref12","DOI":"10.1016\/j.entcs.2014.01.007"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref3","DOI":"10.1215\/S0012-7094-37-00334-X"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref29","DOI":"10.1007\/978-1-4612-0445-9"},{"key":"S0960129524000069_ref13","volume-title":"CWI Tracts","volume":"66","author":"Jung","year":"1989"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref28","DOI":"10.1007\/s00233-021-10209-7"},{"doi-asserted-by":"publisher","key":"S0960129524000069_ref21","DOI":"10.1016\/j.tcs.2004.01.033"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129524000069","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,3]],"date-time":"2024-06-03T11:02:06Z","timestamp":1717412526000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129524000069\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3]]},"references-count":29,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,3]]}},"alternative-id":["S0960129524000069"],"URL":"https:\/\/doi.org\/10.1017\/s0960129524000069","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"type":"print","value":"0960-1295"},{"type":"electronic","value":"1469-8072"}],"subject":[],"published":{"date-parts":[[2024,3]]},"assertion":[{"value":"\u00a9 The Author(s), 2024. Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}