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We investigate its structural properties and provide a Gentzen-style cut-elimination procedure. The most notable feature of the calculus is that it jointly satisfies the subformula property and the property of\n                    <jats:italic>deductive purity<\/jats:italic>\n                    , to the effect that only contingent hypersequents occur in formal proofs. Moreover, since the negation of a contingent formula is also contingent, the calculus turns out to be\n                    <jats:italic>paraconsistent<\/jats:italic>\n                    , and since the conjunction of a formula with its own negation is not contingent, the paraconsistency is of the\n                    <jats:italic>non-adjunctive<\/jats:italic>\n                    kind.\n                  <\/jats:p>","DOI":"10.1007\/s10992-026-09832-y","type":"journal-article","created":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T11:15:20Z","timestamp":1771672520000},"page":"199-215","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Hypersequent Calculus for Classical Contingencies"],"prefix":"10.1007","volume":"55","author":[{"given":"Gabriele","family":"Pulcini","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Achille C.","family":"Varzi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,2,21]]},"reference":[{"key":"9832_CR1","doi-asserted-by":"crossref","unstructured":"Arruda, A. 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