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Alpha-structures and ladders are two specific kinds of Aristotelian diagrams, which are often studied together because of their close interactions. The present paper builds upon this research line, by reformulating and investigating alpha-structures and ladders in the contemporary setting of logical geometry, a mathematically sophisticated framework for studying Aristotelian diagrams. In particular, this framework allows us to formulate well-defined functions that construct alpha-structures and ladders out of each other. In order to achieve this, we point out the crucial importance of imposing an ordering on the elements in the diagrams involved, and thus formulate all our results in terms of ordered versions of alpha-structures and ladders. These results shed interesting new light on the prospects of developing a systematic classification of Aristotelian diagrams, which is one of the main ongoing research efforts within logical geometry today.<\/jats:p>","DOI":"10.1007\/s11225-024-10142-0","type":"journal-article","created":{"date-parts":[[2024,8,27]],"date-time":"2024-08-27T04:03:11Z","timestamp":1724731391000},"page":"1713-1748","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Alpha-Structures and Ladders in Logical Geometry"],"prefix":"10.1007","volume":"113","author":[{"given":"Alexander","family":"De Klerck","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0176-1958","authenticated-orcid":false,"given":"Lorenz","family":"Demey","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,8,27]]},"reference":[{"key":"10142_CR1","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1017\/S1755020313000373","volume":"7","author":"H Ben-Yami","year":"2014","unstructured":"Ben-Yami, H., The quantified argument calculus, Review of Symbolic Logic 7:120\u2013146, 2014.","journal-title":"Review of Symbolic Logic"},{"key":"10142_CR2","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1111\/j.1755-2567.1953.tb01013.x","volume":"19","author":"R Blanch\u00e9","year":"1953","unstructured":"Blanch\u00e9, R., Sur l\u2019opposition des concepts, Theoria 19:89\u2013130, 1953.","journal-title":"Theoria"},{"key":"10142_CR3","volume-title":"Structures Intellectuelles","author":"R Blanch\u00e9","year":"1966","unstructured":"Blanch\u00e9, R., Structures Intellectuelles, Vrin, Paris, 1966."},{"key":"10142_CR4","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/978-3-0348-0379-3_3","volume-title":"Around and Beyond the Square of Opposition","author":"M Correia","year":"2012","unstructured":"Correia, M., Boethius on the square of opposition, in J.-Y. 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