{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:19:06Z","timestamp":1777645146727,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2019,3,14]],"date-time":"2019-03-14T00:00:00Z","timestamp":1552521600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2019,3,14]]},"abstract":"<jats:p>Rozenberg and Ehrenfeucht has shown a duality between 2-structures (a.k.a. transition systems) and (elementary) Petri nets. The tool has been the notion of a region of a 2-structure, the regions then define a Petri net. Bernardinello et al. has observed that the regions of a 2-structure form an orthomodular poset and there is a similar relation between 2-structures and orthomodular posets.<\/jats:p>\n                  <jats:p>While in the theory of 2-structures we may ask if a 2-structure is full and forward closed, the analogous notion for orthomodular posets is their regularity. In the present paper we study the problem of closing a given orthomodular poset to a regular one. This is a dual problem to closing a 2-structure, which has been studied by the author earlier. Also, as in a seminal work of Rozenberg and Ehrenfeucht, one can be interested in a concrete representation, i.e. as a family of sets. We show here an appropriate construction for orthomodular posets too.<\/jats:p>","DOI":"10.3233\/fi-2019-1792","type":"journal-article","created":{"date-parts":[[2019,3,22]],"date-time":"2019-03-22T11:53:05Z","timestamp":1553255585000},"page":"15-28","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Regular Orthomodular Posets"],"prefix":"10.1177","volume":"166","author":[{"given":"Andrzej M.","family":"Borzyszkowski","sequence":"first","affiliation":[{"name":"Institute of Informatics, Faculty of Mathematics, Physics and Informatics, University of Gda\u0144sk, Gda\u0144sk, Poland."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,3,14]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2019-1792","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2019-1792","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:31:28Z","timestamp":1777444288000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2019-1792"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,14]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,3,14]]}},"alternative-id":["10.3233\/FI-2019-1792"],"URL":"https:\/\/doi.org\/10.3233\/fi-2019-1792","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,14]]}}}