{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,27]],"date-time":"2025-09-27T13:20:00Z","timestamp":1758979200087,"version":"3.43.0"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2002,4,1]],"date-time":"2002-04-01T00:00:00Z","timestamp":1017619200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2002,4,1]],"date-time":"2002-04-01T00:00:00Z","timestamp":1017619200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Studia Logica"],"published-print":{"date-parts":[[2002,4]]},"DOI":"10.1023\/a:1015150314504","type":"journal-article","created":{"date-parts":[[2002,12,28]],"date-time":"2002-12-28T17:32:56Z","timestamp":1041096776000},"page":"353-372","source":"Crossref","is-referenced-by-count":3,"title":["A Cut-Free Sequent System for the Smallest Interpretability Logic"],"prefix":"10.1007","volume":"70","author":[{"given":"Katsumi","family":"Sasaki","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"5086394_CR1","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.2307\/2274474","volume":"55","author":"A. Berarducci","year":"1990","unstructured":"Berarducci, A., \u2018The interpretability logic of Peano arithmetic\u2019, The Journal of Symbolic Logic55 (1990), 1059-1089.","journal-title":"The Journal of Symbolic Logic"},{"key":"5086394_CR2","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1007\/BF01201353","volume":"39","author":"G. Gentzen","year":"1934","unstructured":"Gentzen, G., \u2018Untersuchungen \u00fcber das logisch Schliessen\u2019, Mathematische Zeitschrift39 (1934\u201335), 176-210, 405\u2013431.","journal-title":"Mathematische Zeitschrift"},{"key":"5086394_CR3","first-page":"113","volume":"30","author":"P. H\u00c1jek","year":"1990","unstructured":"H\u00c1jek, P., and F. Montagna, \u2018The logic of \u03a01-conservativity\u2019, Archiv for f\u00fcr Mathematische Logik und Grundlagenforschung30 (1990), 113-123.","journal-title":"Archiv for f\u00fcr Mathematische Logik und Grundlagenforschung"},{"key":"5086394_CR4","first-page":"57","volume":"32","author":"P. H\u00c1jek","year":"1992","unstructured":"H\u00c1jek, P., and F. Montagna, \u2018The logic of \u03a01-conservativity continued\u2019, Archiv for f\u00fcr Mathematische Logik und Grundlagenforschung32 (1992), 57-63.","journal-title":"Archiv for f\u00fcr Mathematische Logik und Grundlagenforschung"},{"doi-asserted-by":"crossref","unstructured":"Japaridze, G., and D. H. J.de Jongh, \u2018The logic of provability\u2019, pp. 475-546 in Handbook of Proof Theory, edited by S. R. Buss, University of California, 1998.","key":"5086394_CR5","DOI":"10.1016\/S0049-237X(98)80022-0"},{"doi-asserted-by":"crossref","unstructured":"de Jongh, D. H. J., and F. Veltman, \u2018Provability logics for relative interpretability\u2019, pp. 31-42 in [Pet90].","key":"5086394_CR6","DOI":"10.1007\/978-1-4613-0609-2_3"},{"key":"5086394_CR7","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/BF00370386","volume":"50","author":"D. H. J. de Jongh","year":"1991","unstructured":"de Jongh, D. H. J., and A. Visser, \u2018Explicit fixed points in interpretability logic\u2019, Studia Logica50 (1991), 39-50.","journal-title":"Studia Logica"},{"doi-asserted-by":"crossref","unstructured":"Petkov, P.(ed.), Mathematical Logic, Proceedings of the Heyting 1988 Summer School, Plenum Press, 1990.","key":"5086394_CR8","DOI":"10.1007\/978-1-4613-0609-2"},{"key":"5086394_CR9","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1305\/ndjfl\/1093636104","volume":"33","author":"M. de Rijke","year":"1992","unstructured":"de Rijke, M., \u2018Unary interpretability logic\u2019, Notre Dame Journal of Formal Logic33 (1992), 249-272.","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"5086394_CR10","first-page":"91","volume":"1","author":"K. Sasaki","year":"2001","unstructured":"Sasaki, K., \u2018L\u00f6b's axiom and cut-elimination theorem\u2019, Journal of the Nanzan Academic Society Mathematical Sciences and Information Engineering1 (2001), 91-98.","journal-title":"Journal of the Nanzan Academic Society Mathematical Sciences and Information Engineering"},{"key":"5086394_CR11","series-title":"Technical Report","volume-title":"The logic of relative interpretability over Peano arithmetic","author":"V. Y. Shavrukov","year":"1988","unstructured":"Shavrukov, V.Yu., \u2018The logic of relative interpretability over Peano arithmetic\u2019 (Russian), Technical Report No. 5, Stekhlov Mathematical Institute, Moscow, 1988."},{"doi-asserted-by":"crossref","unstructured":"Visser, A., \u2018Interpretability logic\u2019, pp. 175-209 in [Pet90].","key":"5086394_CR12","DOI":"10.1007\/978-1-4613-0609-2_13"},{"unstructured":"Visser, A., \u2018An overview of interpretability logic\u2019, in Advances in Modal Logic '96, edited by M. Kraft, M. de Rijke, and H. Wansing, CSLI Publications, 1997.","key":"5086394_CR13"}],"container-title":["Studia Logica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1015150314504.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1015150314504\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1015150314504.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,8]],"date-time":"2025-08-08T05:21:43Z","timestamp":1754630503000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1015150314504"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,4]]},"references-count":13,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2002,4]]}},"alternative-id":["5086394"],"URL":"https:\/\/doi.org\/10.1023\/a:1015150314504","relation":{},"ISSN":["0039-3215","1572-8730"],"issn-type":[{"type":"print","value":"0039-3215"},{"type":"electronic","value":"1572-8730"}],"subject":[],"published":{"date-parts":[[2002,4]]}}}