{"title":"$$\\textbf{IL}子逻辑的不动点和Craig插值性质$$","authors":"Sohei Iwata, Taishi Kurahashi, Yuya Okawa","doi":"10.1007/s00153-023-00882-6","DOIUrl":null,"url":null,"abstract":"<div><p>We study the fixed point property and the Craig interpolation property for sublogics of the interpretability logic <span>\\(\\textbf{IL}\\)</span>. We provide a complete description of these sublogics concerning the uniqueness of fixed points, the fixed point property and the Craig interpolation property.\n</p></div>","PeriodicalId":48853,"journal":{"name":"Archive for Mathematical Logic","volume":"63 1-2","pages":"1 - 37"},"PeriodicalIF":0.3000,"publicationDate":"2023-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00153-023-00882-6.pdf","citationCount":"0","resultStr":"{\"title\":\"The fixed point and the Craig interpolation properties for sublogics of \\\\(\\\\textbf{IL}\\\\)\",\"authors\":\"Sohei Iwata, Taishi Kurahashi, Yuya Okawa\",\"doi\":\"10.1007/s00153-023-00882-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We study the fixed point property and the Craig interpolation property for sublogics of the interpretability logic <span>\\\\(\\\\textbf{IL}\\\\)</span>. We provide a complete description of these sublogics concerning the uniqueness of fixed points, the fixed point property and the Craig interpolation property.\\n</p></div>\",\"PeriodicalId\":48853,\"journal\":{\"name\":\"Archive for Mathematical Logic\",\"volume\":\"63 1-2\",\"pages\":\"1 - 37\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-06-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00153-023-00882-6.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archive for Mathematical Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00153-023-00882-6\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"Arts and Humanities\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for Mathematical Logic","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00153-023-00882-6","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Arts and Humanities","Score":null,"Total":0}
The fixed point and the Craig interpolation properties for sublogics of \(\textbf{IL}\)
We study the fixed point property and the Craig interpolation property for sublogics of the interpretability logic \(\textbf{IL}\). We provide a complete description of these sublogics concerning the uniqueness of fixed points, the fixed point property and the Craig interpolation property.
期刊介绍：
The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.
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