{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:29:51Z","timestamp":1740122991174,"version":"3.37.3"},"reference-count":11,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2021,11,16]],"date-time":"2021-11-16T00:00:00Z","timestamp":1637020800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,11,16]],"date-time":"2021-11-16T00:00:00Z","timestamp":1637020800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["407312485"],"award-info":[{"award-number":["407312485"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stud Logica"],"published-print":{"date-parts":[[2022,6]]},"abstract":"Abstract<\/jats:title>In this paper we discuss sequent calculi for the propositional fragment of the logic of HYPE. The logic of HYPE was recently suggested by Leitgeb (Journal of Philosophical Logic<\/jats:italic> 48:305\u2013405, 2019) as a logic for hyperintensional contexts. On the one hand we introduce a simple $$\\mathbf{G1}$$<\/jats:tex-math>\n \n G<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-system employing rules of contraposition. On the other hand we present a $$\\mathbf{G3}$$<\/jats:tex-math>\n \n G<\/mml:mi>\n 3<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-system with an admissible rule of contraposition. Both systems are equivalent as well as sound and complete proof-system of HYPE. In order to provide a cut-elimination procedure, we expand the calculus by connections as introduced in Kashima and Shimura (Mathematical Logic Quarterly<\/jats:italic> 40:153\u2013172, 1994).<\/jats:p>","DOI":"10.1007\/s11225-021-09971-0","type":"journal-article","created":{"date-parts":[[2021,11,16]],"date-time":"2021-11-16T20:02:26Z","timestamp":1637092946000},"page":"643-677","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Sequent Calculi for the Propositional Logic of HYPE"],"prefix":"10.1007","volume":"110","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0841-9781","authenticated-orcid":false,"given":"Martin","family":"Fischer","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,11,16]]},"reference":[{"key":"9971_CR1","volume-title":"Entailment: The Logic of Relevance and Necessity","author":"A Anderson","year":"1975","unstructured":"Anderson, A., and N.\u00a0Belnap, Entailment: The Logic of Relevance and Necessity, Princeton University Press, Princeton, 1975."},{"key":"9971_CR2","volume-title":"Cut-Elimination Theorem for the Intermediate Logic CD. 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O., Negation as a modality in a quantified setting, Journal of Logic and Computation, https:\/\/doi.org\/10.1093\/logcom\/exab025, 2021.","journal-title":"Journal of Logic and Computation"},{"key":"9971_CR10","volume-title":"Proof Theory","author":"G Takeuti","year":"1987","unstructured":"Takeuti, G., Proof Theory, 2nd edn., North Holland, Amsterdam, 1987.","edition":"2"},{"key":"9971_CR11","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139168717","volume-title":"Basic Proof Theory","author":"AS Troelstra","year":"2000","unstructured":"Troelstra, A. 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