{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T23:10:51Z","timestamp":1773097851930,"version":"3.50.1"},"publisher-location":"Cham","reference-count":21,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783030003883","type":"print"},{"value":"9783030003890","type":"electronic"}],"license":[{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2018,1,1]],"date-time":"2018-01-01T00:00:00Z","timestamp":1514764800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018]]},"DOI":"10.1007\/978-3-030-00389-0_3","type":"book-chapter","created":{"date-parts":[[2018,9,19]],"date-time":"2018-09-19T19:12:43Z","timestamp":1537384363000},"page":"13-33","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Intuitionistic Podelski-Rybalchenko Theorem and Equivalence Between Inductive Definitions and Cyclic Proofs"],"prefix":"10.1007","author":[{"given":"Stefano","family":"Berardi","sequence":"first","affiliation":[]},{"given":"Makoto","family":"Tatsuta","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,9,20]]},"reference":[{"key":"3_CR1","doi-asserted-by":"crossref","unstructured":"Afshari, B., Leigh, G.: Cut-free completeness for modal mu-calculus. In: Proceedings of LICS 2017, pp. 1\u201312 (2017)","DOI":"10.1109\/LICS.2017.8005088"},{"key":"3_CR2","unstructured":"Baelde, D., Doumane, A., Saurin, A.: Infinitary proof theory: the multiplicative additive case. In: Proceedings of 25th EACSL Annual Conference on Computer Science Logic (CSL 2016). LIPIcs, vol. 62, pp. 42:1\u201342:17 (2016)"},{"key":"3_CR3","doi-asserted-by":"publisher","first-page":"1382","DOI":"10.1016\/j.apal.2015.08.002","volume":"166","author":"S Berardi","year":"2015","unstructured":"Berardi, S., Steila, S.: An intuitionistic version of Ramsey\u2019s Theorem and its use in Program Termination. Ann. Pure Appl. Log. 166, 1382\u20131406 (2015)","journal-title":"Ann. Pure Appl. Log."},{"key":"3_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1007\/978-3-662-54458-7_18","volume-title":"Foundations of Software Science and Computation Structures","author":"S Berardi","year":"2017","unstructured":"Berardi, S., Tatsuta, M.: Classical system of Martin-L\u00f6f\u2019s inductive definitions is not equivalent to cyclic proof system. In: Esparza, J., Murawski, A.S. (eds.) FoSSaCS 2017. LNCS, vol. 10203, pp. 301\u2013317. Springer, Heidelberg (2017). https:\/\/doi.org\/10.1007\/978-3-662-54458-7_18"},{"key":"3_CR5","doi-asserted-by":"crossref","unstructured":"Berardi, S., Tatsuta, M.: Equivalence of inductive definitions and cyclic proofs under arithmetic. In: Proceedings of Thirty-Second Annual IEEE Symposium on Logic in Computer Science (LICS 2017), pp. 1\u201312 (2017)","DOI":"10.1109\/LICS.2017.8005114"},{"key":"3_CR6","doi-asserted-by":"crossref","unstructured":"Berardi, S., Tatsuta, M.: Equivalence of Intuitionistic Inductive Definitions and Intuitionistic Cyclic Proofs under Arithmetic, arXiv:1712.03502 (2017)","DOI":"10.1109\/LICS.2017.8005114"},{"key":"3_CR7","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1007\/11554554_8","volume-title":"Automated Reasoning with Analytic Tableaux and Related Methods","author":"J Brotherston","year":"2005","unstructured":"Brotherston, J.: Cyclic proofs for first-order logic with inductive definitions. In: Beckert, B. (ed.) TABLEAUX 2005. LNCS (LNAI), vol. 3702, pp. 78\u201392. Springer, Heidelberg (2005). https:\/\/doi.org\/10.1007\/11554554_8"},{"key":"3_CR8","unstructured":"Brotherston, J.: Sequent calculus proof systems for inductive definitions, PhD. thesis, University of Edinburgh (2006)"},{"key":"3_CR9","doi-asserted-by":"crossref","unstructured":"Brotherston, J., Bornat, R., Calcagno, C.: Cyclic proofs of program termination in separation logic. In: Proceedings of POPL 2008 (2008)","DOI":"10.1145\/1328438.1328453"},{"key":"3_CR10","series-title":"Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence)","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1007\/978-3-642-22438-6_12","volume-title":"Automated Deduction \u2013 CADE-23","author":"J Brotherston","year":"2011","unstructured":"Brotherston, J., Distefano, D., Petersen, R.L.: Automated cyclic entailment proofs in separation logic. In: Bj\u00f8rner, N., Sofronie-Stokkermans, V. (eds.) CADE 2011. LNCS (LNAI), vol. 6803, pp. 131\u2013146. Springer, Heidelberg (2011). https:\/\/doi.org\/10.1007\/978-3-642-22438-6_12"},{"issue":"6","key":"3_CR11","doi-asserted-by":"publisher","first-page":"1177","DOI":"10.1093\/logcom\/exq052","volume":"21","author":"J Brotherston","year":"2011","unstructured":"Brotherston, J., Simpson, A.: Sequent calculi for induction and infinite descent. J. Log. Comput. 21(6), 1177\u20131216 (2011)","journal-title":"J. Log. Comput."},{"key":"3_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"350","DOI":"10.1007\/978-3-642-35182-2_25","volume-title":"Programming Languages and Systems","author":"J Brotherston","year":"2012","unstructured":"Brotherston, J., Gorogiannis, N., Petersen, R.L.: A generic cyclic theorem prover. In: Jhala, R., Igarashi, A. (eds.) APLAS 2012. LNCS, vol. 7705, pp. 350\u2013367. Springer, Heidelberg (2012). https:\/\/doi.org\/10.1007\/978-3-642-35182-2_25"},{"key":"3_CR13","doi-asserted-by":"crossref","unstructured":"Doumane, A.: Constructive completeness for the linear-time $$\\mu $$-calculus. In: Proceedings of LICS 2017, pp. 1\u201312 (2017)","DOI":"10.1109\/LICS.2017.8005075"},{"key":"3_CR14","unstructured":"Fortier, J., Santocanale, L.: Cuts for circular proofs: semantics and cut-elimination. In: Proceedings of Computer Science Logic 2013 (CSL 2013). LIPIcs, vol. 23, pp. 248\u2013262 (2013)"},{"key":"3_CR15","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1016\/0304-3975(82)90125-6","volume":"27","author":"D Kozen","year":"1983","unstructured":"Kozen, D.: Results on the propositional $$\\mu $$-calculus. Theor. Comput. Sci. 27, 333\u2013354 (1983)","journal-title":"Theor. Comput. Sci."},{"key":"3_CR16","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1016\/S0049-237X(08)70847-4","volume-title":"Proceedings of the Second Scandinavian Logic Symposium","author":"Per Martin-L\u00f6f","year":"1971","unstructured":"Martin-L\u00f6f, P.: Haupstatz for the intuitionistic theory of iterated inductive definitions. In: Proceedings of the Second Scandinavian Logic Symposium, North-Holland, pp. 179\u2013216 (1971)"},{"key":"3_CR17","doi-asserted-by":"publisher","first-page":"99","DOI":"10.1016\/0304-3975(95)00136-0","volume":"163","author":"D Niwi\u0144ski","year":"1997","unstructured":"Niwi\u0144ski, D., Walukiewicz, I.: Games for the $$\\mu $$-calculus. Theor. Comput. Sci. 163, 99\u2013116 (1997)","journal-title":"Theor. Comput. Sci."},{"key":"3_CR18","doi-asserted-by":"crossref","unstructured":"Podelski, A., Rybalchenko, A.: Transition invariants. In: Proceedings of 19th IEEE Symposium on Logic in Computer Science (LICS 2004), pp. 32\u201341 (2004)","DOI":"10.1109\/LICS.2004.1319598"},{"key":"3_CR19","volume-title":"Mathematical Logic","author":"JR Shoenfield","year":"1967","unstructured":"Shoenfield, J.R.: Mathematical Logic. Addison-Wesley, Boston (1967)"},{"key":"3_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/978-3-662-54458-7_17","volume-title":"Foundations of Software Science and Computation Structures","author":"A Simpson","year":"2017","unstructured":"Simpson, A.: Cyclic arithmetic is equivalent to Peano arithmetic. In: Esparza, J., Murawski, A.S. (eds.) FoSSaCS 2017. LNCS, vol. 10203, pp. 283\u2013300. Springer, Heidelberg (2017). https:\/\/doi.org\/10.1007\/978-3-662-54458-7_17"},{"key":"3_CR21","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1006\/inco.1999.2836","volume":"157","author":"I Walukiewicz","year":"2000","unstructured":"Walukiewicz, I.: Completeness of Kozen\u2019s axiomatisation of the propositional $$\\mu $$-calculus. Inf. Comput. 157, 142\u2013182 (2000)","journal-title":"Inf. Comput."}],"container-title":["Lecture Notes in Computer Science","Coalgebraic Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-00389-0_3","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,9,19]],"date-time":"2022-09-19T00:03:07Z","timestamp":1663545787000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-00389-0_3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"ISBN":["9783030003883","9783030003890"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-00389-0_3","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018]]},"assertion":[{"value":"20 September 2018","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CMCS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on Coalgebraic Methods in Computer Science","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Thessaloniki","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Greece","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2018","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14 April 2018","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"15 April 2018","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"14","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"cmcs2018","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/www.coalg.org\/cmcs18\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}