{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T15:32:57Z","timestamp":1747150377241,"version":"3.40.5"},"reference-count":25,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2023,7,24]],"date-time":"2023-07-24T00:00:00Z","timestamp":1690156800000},"content-version":"vor","delay-in-days":84,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2023,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A class of ordered relational topological spaces is described, which we call <jats:italic>orthomodular spaces<\/jats:italic>. Our construction of these spaces involves adding a topology to the class of orthomodular frames introduced by Hartonas, along the lines of Bimb\u00f3's topologization of the class of orthoframes employed by Goldblatt in his representation of ortholattices. We then prove that the category of orthomodular lattices and homomorphisms is dually equivalent to the category of orthomodular spaces and certain continuous frame morphisms, which we call <jats:italic>continuous weak p\u2010morphisms<\/jats:italic>. It is well\u2010known that orthomodular lattices provide an algebraic semantics for the quantum logic . Hence, as an application of our duality, we develop a topological semantics for  using orthomodular spaces and prove soundness and\u00a0completeness.<\/jats:p>","DOI":"10.1002\/malq.202200044","type":"journal-article","created":{"date-parts":[[2023,7,24]],"date-time":"2023-07-24T11:57:45Z","timestamp":1690199865000},"page":"174-191","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Topological duality for orthomodular lattices"],"prefix":"10.1002","volume":"69","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3824-1988","authenticated-orcid":false,"given":"Joseph","family":"McDonald","sequence":"first","affiliation":[{"name":"Department of Philosophy University of Alberta Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Katalin","family":"Bimb\u00f3","sequence":"additional","affiliation":[{"name":"Department of Philosophy University of Alberta Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2023,7,24]]},"reference":[{"volume-title":"Category Theory","year":"2010","author":"Awodey S.","key":"e_1_2_9_2_1"},{"volume-title":"Orthomodular Lattices: Algebraic Approach","year":"1984","author":"Beran L.","key":"e_1_2_9_3_1"},{"key":"e_1_2_9_4_1","doi-asserted-by":"crossref","unstructured":"N.Bezhanishvili G.Grilletti andW.Holliday Algebraic and topological semantics for inquisitive logic via choice\u2010free duality preprint (accessed September 15 2022).","DOI":"10.1017\/S175502032100054X"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107050884"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.2307\/1968621"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1215\/00294527-2008-025"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11787-007-0016-9"},{"volume-title":"Generalized Galois Logics: Relational Semantics of Nonclassical Logical Calculi","year":"2008","author":"Bimb\u00f3 K.","key":"e_1_2_9_9_1"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-71430-7_12"},{"key":"e_1_2_9_11_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-981-13-2487-1_1"},{"volume-title":"Natural Dualities for the Working Algebraist","year":"1998","author":"Clark D.","key":"e_1_2_9_12_1"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8841-8"},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511809088"},{"key":"e_1_2_9_15_1","first-page":"21","article-title":"An algebraic approach to orthologic","volume":"5","author":"Feitosa H.","year":"2019","journal-title":"South Amer. 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