{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T11:53:58Z","timestamp":1759146838256,"version":"3.37.3"},"reference-count":25,"publisher":"Oxford University Press (OUP)","issue":"7","license":[{"start":{"date-parts":[[2021,7,5]],"date-time":"2021-07-05T00:00:00Z","timestamp":1625443200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100002341","name":"Academy of Finland","doi-asserted-by":"publisher","award":["1308664"],"award-info":[{"award-number":["1308664"]}],"id":[{"id":"10.13039\/501100002341","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,10,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Neighbourhood semantics for intuitionistic logic extended with countable conjunctions and disjunctions is introduced and shown equivalent to topological semantics, with an indirect completeness proof as payoff. The new semantics is used to obtain a labelled sequent calculus with good structural properties. In particular, admissibility of weakening and contraction, invertibility with preservation of height for each rule and cut elimination are shown. Finally, a direct Tait\u2013Sch\u00fctte\u2013Takeuti style form of completeness via the extraction of a countermodel from a failed proof search is proved.<\/jats:p>","DOI":"10.1093\/logcom\/exab040","type":"journal-article","created":{"date-parts":[[2021,6,8]],"date-time":"2021-06-08T19:54:13Z","timestamp":1623182053000},"page":"1608-1639","source":"Crossref","is-referenced-by-count":7,"title":["Neighbourhood semantics and labelled calculus for intuitionistic infinitary logic"],"prefix":"10.1093","volume":"31","author":[{"given":"Matteo","family":"Tesi","sequence":"first","affiliation":[{"name":"Classe di Lettere e Filosofia, Scuola Normale Superiore di Pisa, 56126 Pisa, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sara","family":"Negri","sequence":"additional","affiliation":[{"name":"Dipartimento di matematica, Universit\u00e0 degli Studi di Genova, 16146 Genova, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2021,7,5]]},"reference":[{"key":"2021102214141273900_ref1","first-page":"357","article-title":"Semantic construction of intuitionistic logic","volume":"19","author":"Beth","year":"1956","journal-title":"Koninklijke Nederlandse Akademie van Wetenschappen, Mededelingen, NieuweReeks"},{"key":"2021102214141273900_ref2","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1016\/j.indag.2019.01.001","article-title":"A semantic hierarchy for intuitionistic logic","volume":"30","author":"Bezhanishvili","year":"2019","journal-title":"Indagationes Mathematicae"},{"key":"2021102214141273900_ref3","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1305\/ndjfl\/1063372244","article-title":"A closer look at some subintuitionistic logics","volume":"42","author":"Celani","year":"2001","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"2021102214141273900_ref4","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s00153-011-0254-7","article-title":"Proof analysis in intermediate logic","volume":"51","author":"Dyckhoff","year":"2012","journal-title":"Archive for Mathematical Logic"},{"key":"2021102214141273900_ref5","doi-asserted-by":"crossref","first-page":"216","DOI":"10.1305\/ndjfl\/1093883041","article-title":"Infinitary propositional intuitionistic logic","volume":"21","author":"Kalicki","year":"1980","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"2021102214141273900_ref6","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/S0049-237X(08)71685-9","article-title":"Semantical analysis of intuitionistic logic I","volume":"40","author":"Kripke","year":"1965","journal-title":"Studies in Logica and the Foundations of Mathematics"},{"key":"2021102214141273900_ref7","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/978-3-319-29198-7_8","article-title":"Some remarks on the proof-theory and the semantics of infinitary modal logic","volume-title":"Advances in Proof Theory","author":"Minari","year":"2016"},{"volume-title":"A Short Introduction to Intuitionistic Logic","year":"2000","author":"Mints","key":"2021102214141273900_ref8"},{"key":"2021102214141273900_ref9","first-page":"339","article-title":"Neighborhood semantics for basic and intuitionistic logic","volume":"24","author":"Moniri","year":"2015","journal-title":"Logic and Logical Philosophy"},{"key":"2021102214141273900_ref10","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1016\/0003-4843(78)90015-3","article-title":"Infinitary intuitionistic logic from a classical point of view","volume":"14","author":"Nadel","year":"1978","journal-title":"Annals of Mathematical Logic"},{"key":"2021102214141273900_ref11","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511527340","volume-title":"Structural Proof Theory","author":"Negri","year":"2001"},{"key":"2021102214141273900_ref12","first-page":"1241","article-title":"Proof theory for non-normal modal logics: the neighbourhood formalism and basic results","volume":"4","author":"Negri","year":"2017","journal-title":"IfCoLog Journal of Logics and their Applications"},{"key":"2021102214141273900_ref13","first-page":"159","article-title":"Non-normal modal logics: bi-neighbourhood semantics and its labelled calculi","volume-title":"Advances in Modal Logic","author":"Dalmonte","year":"2018"},{"key":"2021102214141273900_ref14","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-030-71258-7_12","article-title":"Geometric rules in infinitary logic","volume-title":"Arnon Avron on Semantics and Proof Theory of Non-Classical Logics","author":"Negri","year":"2021"},{"key":"2021102214141273900_ref15","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-47012-2","volume-title":"Probability Logics. 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