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From various axioms for betweenness, we chose those that are most common, which makes our work applicable to a wide range of betweenness structures studied in the literature. On the algebraic side, we work with two operators of\n                    <jats:italic>possibility<\/jats:italic>\n                    and of\n                    <jats:italic>sufficiency<\/jats:italic>\n                    .\n                  <\/jats:p>","DOI":"10.1017\/jsl.2023.86","type":"journal-article","created":{"date-parts":[[2024,2,6]],"date-time":"2024-02-06T01:35:10Z","timestamp":1707183310000},"page":"574-598","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["BETWEENNESS ALGEBRAS"],"prefix":"10.1017","volume":"91","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8907-2382","authenticated-orcid":false,"given":"IVO","family":"D\u00dcNTSCH","sequence":"first","affiliation":[{"name":"BROCK UNIVERSITY"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3379-0577","authenticated-orcid":false,"given":"RAFA\u0141","family":"GRUSZCZY\u0143SKI","sequence":"additional","affiliation":[{"name":"NICOLAUS COPERNICUS UNIVERSITY"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9395-107X","authenticated-orcid":false,"given":"PAULA","family":"MENCH\u00d3N","sequence":"additional","affiliation":[{"name":"NICOLAUS COPERNICUS UNIVERSITY"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2023,11,15]]},"reference":[{"key":"S0022481223000865_r23","doi-asserted-by":"publisher","DOI":"10.2307\/2372123"},{"key":"S0022481223000865_r28","unstructured":"[28] Tehlikeli, S. , An alternative modal logic, internal semantics and external syntax (a philosophical abstract of a mathematical essay), manuscript, 1985."},{"key":"S0022481223000865_r27","doi-asserted-by":"publisher","DOI":"10.2307\/421089"},{"key":"S0022481223000865_r8","unstructured":"[8] D\u00fcntsch, I. and Or\u0142owska, E. , Betweenness structures, manuscript, 2019."},{"key":"S0022481223000865_r25","volume-title":"Dualities for Structures of Applied Logics","volume":"56","author":"Or\u0142owska","year":"2015"},{"key":"S0022481223000865_r18","unstructured":"[18] Gruszczy\u0144ski, R. and Mench\u00f3n, P. , Notes on betweenness properties, unpublished manuscript, 2023."},{"key":"S0022481223000865_r11","doi-asserted-by":"publisher","DOI":"10.1007\/BF03322885"},{"key":"S0022481223000865_r19","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093870378"},{"key":"S0022481223000865_r12","unstructured":"[12] Freese, R. , Kiss, E. , and Valeriote, M. , Universal algebra calculator, 2011. Available at http:\/\/www.uacalc.org."},{"key":"S0022481223000865_r29","doi-asserted-by":"publisher","DOI":"10.1515\/9783112733332"},{"key":"S0022481223000865_r17","first-page":"163","volume-title":"Algebra and Logic (Fourteenth Summer Res. Inst., Austral. Math. Soc., Monash Univ., Clayton, 1974)","volume":"450","author":"Goldblatt","year":"1975"},{"key":"S0022481223000865_r4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107050884"},{"key":"S0022481223000865_r7","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2003.11.009"},{"key":"S0022481223000865_r2","first-page":"36","article-title":"Minimal deontic logics","volume":"8","author":"van Benthem","year":"1979","journal-title":"Polish Acad. Sci. Inst. Philos. Sociol. Bull. Sect. 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Published by Cambridge University Press on behalf of The Association for Symbolic Logic","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}