{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T16:09:46Z","timestamp":1762445386696,"version":"build-2065373602"},"reference-count":68,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,13]],"date-time":"2023-05-13T00:00:00Z","timestamp":1683936000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004040","name":"Internal Funds KU Leuven","doi-asserted-by":"publisher","award":["IDN-19-009","101040049"],"award-info":[{"award-number":["IDN-19-009","101040049"]}],"id":[{"id":"10.13039\/501100004040","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000781","name":"European Union","doi-asserted-by":"publisher","award":["IDN-19-009","101040049"],"award-info":[{"award-number":["IDN-19-009","101040049"]}],"id":[{"id":"10.13039\/501100000781","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we introduce and study AD-logic, i.e., a system of (hybrid) modal logic that can be used to reason about Aristotelian diagrams. The language of AD-logic, LAD, is interpreted on a kind of birelational Kripke frames, which we call \u201cAD-frames\u201d. We establish a sound and strongly complete axiomatization for AD-logic, and prove that there exists a bijection between finite Aristotelian diagrams (up to Aristotelian isomorphism) and finite AD-frames (up to modal isomorphism). We then show how AD-logic can express several major insights about Aristotelian diagrams; for example, for every well-known Aristotelian family A, we exhibit a formula \u03c7A\u2208LAD and show that an Aristotelian diagram D belongs to the family A iff \u03c7A is validated by D (when the latter is viewed as an AD-frame). Finally, we show that AD-logic itself gives rise to new and interesting Aristotelian diagrams, and we reflect on their profoundly peculiar status.<\/jats:p>","DOI":"10.3390\/axioms12050471","type":"journal-article","created":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T08:33:01Z","timestamp":1684139581000},"page":"471","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["The Modal Logic of Aristotelian Diagrams"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3066-249X","authenticated-orcid":false,"given":"Stef","family":"Frijters","sequence":"first","affiliation":[{"name":"Center for Logic and Philosophy of Science, 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":[[2023,5,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"B\u00e9ziau, J.Y., and Jacquette, D. 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