{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T01:12:24Z","timestamp":1747185144469},"reference-count":23,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2023,8,4]],"date-time":"2023-08-04T00:00:00Z","timestamp":1691107200000},"content-version":"vor","delay-in-days":95,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/501100004488","name":"Hrvatska Zaklada za Znanost","doi-asserted-by":"publisher","award":["IP-2018-01-7459","UIP-2017-05-9219"],"award-info":[{"award-number":["IP-2018-01-7459","UIP-2017-05-9219"]}],"id":[{"id":"10.13039\/501100004488","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2023,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Interpretability logic is a modal formalization of relative interpretability between first\u2010order arithmetical theories. Verbrugge semantics is a generalization of Veltman semantics, the basic semantics for interpretability logic. Bisimulation is the basic equivalence between models for modal logic. We study various notions of bisimulation between Verbrugge models and develop a new one, which we call w\u2010bisimulation. We show that the new notion, while keeping the basic property that bisimilarity implies modal equivalence, is weak enough to allow the converse to hold in the finitary case. To do this, we develop and use an appropriate notion of bisimulation games between Verbrugge\u00a0models.<\/jats:p>","DOI":"10.1002\/malq.202200042","type":"journal-article","created":{"date-parts":[[2023,8,4]],"date-time":"2023-08-04T07:17:14Z","timestamp":1691133434000},"page":"231-243","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Bisimulations and bisimulation games between Verbrugge models"],"prefix":"10.1002","volume":"69","author":[{"given":"Sebastijan","family":"Horvat","sequence":"first","affiliation":[{"name":"University of Zagreb Faculty of Science Department of Mathematics  Croatia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tin","family":"Perkov","sequence":"additional","affiliation":[{"name":"University of Zagreb, Faculty of Teacher Education Chair of Mathematics and Statistics  Croatia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mladen","family":"Vukovi\u0107","sequence":"additional","affiliation":[{"name":"University of Zagreb Faculty of Science Department of Mathematics  Croatia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2023,8,4]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"publisher","DOI":"10.2307\/2274474"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781107050884"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511625183"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-011-9366-7"},{"key":"e_1_2_8_6_1","doi-asserted-by":"crossref","unstructured":"D. H. J.deJonghandF.Veltman.Provability logics for relative interpretability in:Mathematical Logic Proceedings of the 1988 Heyting Conference edited byP. P.Petkov(Plenum Press 1990) pp.31\u201342.","DOI":"10.1007\/978-1-4613-0609-2_3"},{"key":"e_1_2_8_7_1","first-page":"249","volume-title":"Handbook of Modal Logic","author":"Goranko V.","year":"2006"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1093\/jigpal\/jzp082"},{"key":"e_1_2_8_9_1","first-page":"667","article-title":"Interpretability in theories containing arithmetic II","volume":"22","author":"H\u00e1jek P.","year":"1981","journal-title":"Commentationes Mathematicae Universitatis Carolinae"},{"volume-title":"Dick de Jongh on Intuitionistic and Provability Logic","author":"Joosten J. 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Yu.Shavrukov The logic of relative interpretability over Peano arithmetic[in Russian] Technical Report No. 5 (Steklov Mathematical Institute Moscow 1988)."},{"key":"e_1_2_8_18_1","doi-asserted-by":"publisher","DOI":"10.2307\/2273663"},{"key":"e_1_2_8_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370385"},{"key":"e_1_2_8_20_1","first-page":"307","volume-title":"Advances in Modal Logic","author":"Visser A.","year":"1998"},{"key":"e_1_2_8_21_1","doi-asserted-by":"crossref","unstructured":"A.Visser Interpretability logic in:Mathematical Logic Proceedings of the 1988 Heyting Conference edited byP. P.Petkov(Plenum Press 1990) pp.175\u2013210.","DOI":"10.1007\/978-1-4613-0609-2_13"},{"key":"e_1_2_8_22_1","doi-asserted-by":"publisher","DOI":"10.1093\/jigpal\/jzp067"},{"key":"e_1_2_8_23_1","first-page":"7","article-title":"Characteristic classes and bisimulations of generalized Veltman models","volume":"341","author":"Vukovi\u0107 M.","year":"2000","journal-title":"Grazer Math. 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Log."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.202200042","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T16:06:21Z","timestamp":1691769981000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.202200042"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5]]},"references-count":23,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2023,5]]}},"alternative-id":["10.1002\/malq.202200042"],"URL":"https:\/\/doi.org\/10.1002\/malq.202200042","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"type":"print","value":"0942-5616"},{"type":"electronic","value":"1521-3870"}],"subject":[],"published":{"date-parts":[[2023,5]]},"assertion":[{"value":"2022-07-24","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-04-26","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2023-08-04","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}