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Our method extends the classical first-order sequent calculus by incorporating a specialized framework to manage both <jats:italic>negative<\/jats:italic> extra-logical information (explicit exceptions) and <jats:italic>positive<\/jats:italic> information (background assumptions). We prove that the resulting sequent calculi satisfy the cut-elimination theorem, thereby ensuring strong analytical properties. Furthermore, we show how this framework effectively models traditional reasoning patterns involving conflicting information and typicality. Finally, we establish a natural correspondence between our approach and the Kraus-Lehmann-Magidor postulates, further grounding our work within established theoretical foundations.<\/jats:p>","DOI":"10.1007\/s10849-025-09437-9","type":"journal-article","created":{"date-parts":[[2025,6,11]],"date-time":"2025-06-11T21:35:14Z","timestamp":1749677714000},"page":"341-369","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Exception and typicality, logically framed"],"prefix":"10.1007","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9545-3912","authenticated-orcid":false,"given":"Mario","family":"Piazza","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2810-5835","authenticated-orcid":false,"given":"Matteo","family":"Tesi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,6,12]]},"reference":[{"issue":"3\u20134","key":"9437_CR1","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/BF01531058","volume":"4","author":"A Avron","year":"1991","unstructured":"Avron, A. 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