{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T22:59:28Z","timestamp":1773097168280,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":16,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540008972","type":"print"},{"value":"9783540365761","type":"electronic"}],"license":[{"start":{"date-parts":[[2003,1,1]],"date-time":"2003-01-01T00:00:00Z","timestamp":1041379200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2003]]},"DOI":"10.1007\/3-540-36576-1_27","type":"book-chapter","created":{"date-parts":[[2007,6,11]],"date-time":"2007-06-11T22:42:17Z","timestamp":1181601737000},"page":"425-440","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["On the Structure of Inductive Reasoning: Circular and Tree-Shaped Proofs in the \u03bcCalculus"],"prefix":"10.1007","author":[{"given":"Christoph","family":"Sprenger","sequence":"first","affiliation":[]},{"given":"Mads","family":"Dam","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2003,2,28]]},"reference":[{"key":"27_CR1","unstructured":"T. Arts, G. Chuganov, M. Dam, L.-\u00e5. Fredlund, D. Gurov, and T. Noll. A tool for verifying software written in Erlang. Accepted for publication in STTT Journal, 2001."},{"key":"27_CR2","unstructured":"G. Barthe, M. J. Frade, E. Gim\u00e9nez, L. Pinto, and T. Uustalu. Type-based termination of recursive definitions. Mathematical Structures in Computer Science, 2000. to appear."},{"key":"27_CR3","doi-asserted-by":"crossref","unstructured":"H. Comon. Inductionless induction. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, volume 1, chapter 14. Elsevier Science, 2001.","DOI":"10.1016\/B978-044450813-3\/50016-3"},{"issue":"2","key":"27_CR4","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1093\/logcom\/12.2.255","volume":"12","author":"M. Dam","year":"2002","unstructured":"M. Dam and D. Gurov. \u03bc-calculus with explicit points and approximations. Journal of Logic and Computation, 12(2):43\u201357, 2002. Previously appeared in Fixed Points in Computer Science, FICS\u2019 02.","journal-title":"Journal of Logic and Computation"},{"key":"27_CR5","unstructured":"L. Fredlund. A Framework for Reasoning about Erlang Code. PhD thesis, Royal Institute of Technology, Stockholm, Sweden, 2001."},{"key":"27_CR6","doi-asserted-by":"crossref","unstructured":"R. Gor\u00e9. Tableau methods for modal and temporal logics. In Handbook of Tableau Methods. Kluwer, 1999.","DOI":"10.1007\/978-94-017-1754-0_6"},{"key":"27_CR7","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1016\/0304-3975(82)90125-6","volume":"27","author":"D. Kozen","year":"1983","unstructured":"D. Kozen. Results on the propositional \u03bc-calculus. Theoretical Computer Science, 27:333\u2013354, 1983.","journal-title":"Theoretical Computer Science"},{"issue":"2","key":"27_CR8","doi-asserted-by":"publisher","first-page":"173","DOI":"10.1016\/0304-3975(76)90022-0","volume":"3","author":"D. Park","year":"1976","unstructured":"D. Park. Finiteness is mu-ineffable. Theoretical Computer Science, 3(2):173\u2013181, 1976.","journal-title":"Theoretical Computer Science"},{"key":"27_CR9","unstructured":"C. Paulin-Mohring. Inductive definitions in the system Coq-rules and properties. Technical Report 92-49, Laboratoire de l\u2019Informatique du Parall\u00e9lisme, ENS Lyon, France, Dec. 1992."},{"key":"27_CR10","unstructured":"U. Sch\u00f6pp. Formal verification of processes. Master\u2019s thesis, University of Edinburgh, 2001."},{"key":"27_CR11","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"372","DOI":"10.1007\/3-540-45931-6_26","volume-title":"FOSSACS\u2019 02, Grenoble, France","author":"U. Sch\u00f6pp","year":"2002","unstructured":"U. Sch\u00f6pp and A. Simpson. Verifying temporal properties using explicit approximants: Completeness for context-free processes. In FOSSACS\u2019 02, Grenoble, France, volume 2303 of LNCS, pages 372\u2013386. Springer-Verlag, 2002."},{"key":"27_CR12","unstructured":"A. Simpson and U. Sch\u00f6pp. Private communication."},{"key":"27_CR13","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1016\/0304-3975(90)90110-4","volume":"89","author":"C. Stirling","year":"1991","unstructured":"C. Stirling and D. Walker. Local model checking in the modal \u03bc-calculus. Theoretical Computer Science, 89:161\u2013177, 1991.","journal-title":"Theoretical Computer Science"},{"key":"27_CR14","first-page":"133","volume-title":"Handbook of Theoretical Computer Science","author":"W. Thomas","year":"1990","unstructured":"W. Thomas. Automata on infinite objects. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B, pages 133\u2013191. Elsevier Science Publishers, Amsterdam, 1990."},{"key":"27_CR15","unstructured":"M. Vardi and P. Wolper. An automata-theoretic approach to automatic program verification. In Logic in Computer Science, LICS\u2019 86, pages 322\u2013331, 1986."},{"key":"27_CR16","unstructured":"I. Walukiewicz. Completeness of Kozen\u2019s axiomatisation of the propositional \u03bc-calculus. In Logic in Computer Science, LICS\u2019 95, pages 14\u201324, 1995."}],"container-title":["Lecture Notes in Computer Science","Foundations of Software Science and Computation Structures"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-36576-1_27","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,2,9]],"date-time":"2020-02-09T23:23:29Z","timestamp":1581290609000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-36576-1_27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003]]},"ISBN":["9783540008972","9783540365761"],"references-count":16,"URL":"https:\/\/doi.org\/10.1007\/3-540-36576-1_27","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003]]},"assertion":[{"value":"28 February 2003","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}