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Following B\u00fcring and others we assume that the main difference between comparative and superlative modifiers is that only the latter convey disjunctive meanings. We further argue that the inference patterns triggered by disjunction and superlative modifiers are hard to capture in existing semantic and pragmatic analyses of these phenomena (neo-Gricean or grammatical alike), and we propose a novel account of these inferences in the framework of bilateral state-based modal logic defining a first order extension of Aloni (Semant Pragmat 15:5-EA, 2022. <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" ext-link-type=\"uri\" xlink:href=\"https:\/\/doi.org\/10.3765\/sp.15.5\">https:\/\/doi.org\/10.3765\/sp.15.5<\/jats:ext-link>)\u2019s .<\/jats:p>","DOI":"10.1007\/s10849-023-09399-w","type":"journal-article","created":{"date-parts":[[2023,6,12]],"date-time":"2023-06-12T14:02:12Z","timestamp":1686578532000},"page":"539-567","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Modified Numerals and Split Disjunction: The First-Order Case"],"prefix":"10.1007","volume":"32","author":[{"given":"Maria","family":"Aloni","sequence":"first","affiliation":[]},{"given":"Peter","family":"van Ormondt","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,6,12]]},"reference":[{"key":"9399_CR1","unstructured":"Aloni, M. 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