{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T16:02:45Z","timestamp":1721923365405},"reference-count":9,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2022,1,17]],"date-time":"2022-01-17T00:00:00Z","timestamp":1642377600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,7,25]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We investigate the fixed point properties for sublogics of the interpretability logic $\\textbf {IL}$. In our previous work, it was proved that a sublogic $\\textbf {IL}^{-}(\\textbf {J 2}_+, \\textbf {J 5})$ has the fixed point property (FPP) and that a sublogic $\\textbf {IL}^{-}(\\textbf {J 4}, \\textbf {J 5})$ has a newly introduced weaker property $\\ell $FPP. In this paper, we provide countably many sublogics of $\\textbf {IL}^{-}(\\textbf {J 2}_{+}, \\textbf {J 5})$ (resp. $\\textbf {IL}^{-}(\\textbf {J 4}, \\textbf {J 5})$) having FPP (resp. $\\ell $FPP).<\/jats:p>","DOI":"10.1093\/logcom\/exab077","type":"journal-article","created":{"date-parts":[[2021,11,22]],"date-time":"2021-11-22T20:12:28Z","timestamp":1637611948000},"page":"976-995","source":"Crossref","is-referenced-by-count":3,"title":["Countably many sublogics of the interpretability logic<b>IL<\/b>having fixed point properties"],"prefix":"10.1093","volume":"32","author":[{"given":"Yuya","family":"Okawa","sequence":"first","affiliation":[{"name":"Graduate School of Science and Engineering, Chiba University , 1-33 Yayoi-cho, Inage-ku, Chiba-shi, Chiba, 263-8522, Japan"}]}],"member":"286","published-online":{"date-parts":[[2022,1,17]]},"reference":[{"key":"2022081614301716100_ref1","volume-title":"The Logic of Provability","author":"Boolos","year":"1993"},{"key":"2022081614301716100_ref2","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/BF00370386","article-title":"Explicit fixed points in interpretability logic","volume":"50","author":"de Jongh","year":"1991","journal-title":"Studia Logica"},{"key":"2022081614301716100_ref3","doi-asserted-by":"crossref","volume-title":"The fixed point and the Craig interpolation properties for sublogics of IL","author":"Iwata","DOI":"10.1007\/s00153-023-00882-6"},{"key":"2022081614301716100_ref4","article-title":"Effectively constructible fixed points in Sacchetti\u2019s modal logics of provability","author":"Kurahashi","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"2022081614301716100_ref5","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1002\/malq.202000037","article-title":"Modal completeness of sublogics of the interpretability logic IL","volume":"67","author":"Kurahashi","year":"2021","journal-title":"Mathematical Logic Quarterly"},{"key":"2022081614301716100_ref6","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1111\/j.1755-2567.1996.tb00529.x","article-title":"Provability logic\u2014a short introduction","volume":"62","author":"Lindstr\u00f6m","year":"1996","journal-title":"Theoria"},{"key":"2022081614301716100_ref7","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1305\/ndjfl\/1054837934","article-title":"The fixed point property in modal logic","volume":"42","author":"Sacchetti","year":"2001","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"2022081614301716100_ref8","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/BF02123402","article-title":"An effective fixed-point theorem in intuitionistic diagonalizable algebras","volume":"35","author":"Sambin","year":"1976","journal-title":"Studia Logica"},{"key":"2022081614301716100_ref9","article-title":"Preliminary notes on interpretability logic","volume-title":"Technical Report 29","author":"Visser","year":"1988"}],"container-title":["Journal of Logic and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/32\/5\/976\/45445541\/exab077.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/32\/5\/976\/45445541\/exab077.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T23:56:36Z","timestamp":1699833396000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/logcom\/article\/32\/5\/976\/6507815"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,1,17]]},"references-count":9,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2022,1,17]]},"published-print":{"date-parts":[[2022,7,25]]}},"URL":"https:\/\/doi.org\/10.1093\/logcom\/exab077","relation":{},"ISSN":["0955-792X","1465-363X"],"issn-type":[{"value":"0955-792X","type":"print"},{"value":"1465-363X","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2022,7]]},"published":{"date-parts":[[2022,1,17]]}}}