{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:55:23Z","timestamp":1760147723151,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2023,2,24]],"date-time":"2023-02-24T00:00:00Z","timestamp":1677196800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Internal Funds KU Leuven","award":["IDN-19-009","101040049"],"award-info":[{"award-number":["IDN-19-009","101040049"]}]},{"name":"ERC Starting Grant","award":["IDN-19-009","101040049"],"award-info":[{"award-number":["IDN-19-009","101040049"]}]},{"name":"European Union","award":["IDN-19-009","101040049"],"award-info":[{"award-number":["IDN-19-009","101040049"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we study the interaction between the square of opposition for the Aristotelian quantifiers (\u2018all\u2019, \u2018some\u2019, \u2018no\u2019, and \u2018not all\u2019) and the square of opposition generated by the proportional quantifier \u2018most\u2019 (in its standard generalized quantifier theory reading of \u2018more than half\u2019). In a first step, we provide an analysis in terms of bitstring semantics for the two squares independently. The classical square for \u2018most\u2019 involves a tripartition of logical space, whereas the degenerate square for \u2018all\u2019 in first-order logic (FOL) involves a quadripartition, due to FOL\u2019s lack of existential import. In a second move, we combine these two squares into an octagon of opposition, which was hitherto unattested in logical geometry, while the meet of the original tri- and quadripartitions yields a hexapartition for this octagon. In a final step, we switch from FOL to a logical system, which does assume existential import. This yields an octagon of the well known Lenzen type, and its bitstring semantics is reduced to a pentapartition.<\/jats:p>","DOI":"10.3390\/axioms12030236","type":"journal-article","created":{"date-parts":[[2023,2,24]],"date-time":"2023-02-24T03:57:35Z","timestamp":1677211055000},"page":"236","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Aristotelian Diagrams for the Proportional Quantifier \u2018Most\u2019"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8186-0170","authenticated-orcid":false,"given":"Hans","family":"Smessaert","sequence":"first","affiliation":[{"name":"Department of Linguistics, KU Leuven, 3000 Leuven, Belgium"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0176-1958","authenticated-orcid":false,"given":"Lorenz","family":"Demey","sequence":"additional","affiliation":[{"name":"Center for Logic and Philosophy of Science, KU Leuven, 3000 Leuven, Belgium"},{"name":"KU Leuven Institute for Artificial Intelligence, KU Leuven, 3000 Leuven, Belgium"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s10992-017-9430-5","article-title":"Combinatorial Bitstring Semantics for Arbitrary Logical Fragments","volume":"47","author":"Demey","year":"2018","journal-title":"J. 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