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The classical sequent calculus without Cut is sometimes advocated as an appropriate proof-theoretic presentation of $$\\textrm{ST}$$<\/jats:tex-math>\n ST<\/mml:mtext>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. Unfortunately, there is only a partial correspondence between its derivability relation and the relation of local metainferential $$\\textrm{ST}$$<\/jats:tex-math>\n ST<\/mml:mtext>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-validity \u2013 these relations coincide only upon the addition of elimination rules and only within the propositional fragment of the calculus, due to the non-invertibility of the quantifier rules. In this paper, we present two calculi for first-order $$\\textrm{ST}$$<\/jats:tex-math>\n ST<\/mml:mtext>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> with an eye to recapturing this correspondence in full. The first calculus is close in spirit to the Epsilon calculus. The other calculus includes rules for the discharge of sequent-assumptions; moreover, it is normalisable and admits interpolation.<\/jats:p>","DOI":"10.1007\/s10992-024-09766-3","type":"journal-article","created":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T10:03:08Z","timestamp":1719914588000},"page":"1291-1320","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Sequent Calculi for First-order $$\\textrm{ST}$$"],"prefix":"10.1007","volume":"53","author":[{"given":"Francesco","family":"Paoli","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Adam","family":"P\u0159enosil","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,7,2]]},"reference":[{"issue":"1","key":"9766_CR1","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1017\/jsl.2018.51","volume":"84","author":"JP Aguilera","year":"2019","unstructured":"Aguilera, J. 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