{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T00:38:51Z","timestamp":1783643931371,"version":"3.55.0"},"reference-count":22,"publisher":"Oxford University Press (OUP)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The finite model property is a key step in proving decidability of modal logics. By adapting the filtration method to the generalized Veltman semantics for interpretability logics, we have been able to prove the finite model property of interpretability logic ILM0 w.r.t. generalized Veltman models. We use the same technique to prove the finite model property of interpretability logic ILW* w.r.t. generalized Veltman models. The missing link needed to prove the decidability of ILM0 was completeness w.r.t. generalized Veltman models, which we obtain in this article. Thus, we prove the decidability of ILM0, which was an open problem. Using the same technique, we prove that ILW* is also decidable.<\/jats:p>","DOI":"10.1093\/jigpal\/jzx027","type":"journal-article","created":{"date-parts":[[2017,7,6]],"date-time":"2017-07-06T03:12:14Z","timestamp":1499310734000},"page":"758-772","source":"Crossref","is-referenced-by-count":12,"title":["Decidability of interpretability logics ILM0 and ILW*"],"prefix":"10.1093","volume":"25","author":[{"given":"Luka","family":"Mikec","sequence":"first","affiliation":[{"name":"University of Rijeka, Department of Mathematics, Radmile Matej\u010di\u0107 2, HR-51000 Rijeka."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tin","family":"Perkov","sequence":"additional","affiliation":[{"name":"University of Zagreb, Faculty of Teacher Education, Savska 77, HR-10000 Zagreb."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mladen","family":"Vukovi\u0107","sequence":"additional","affiliation":[{"name":"University of Zagreb, Department of Mathematics, Bijeni\u010dka 30, HR-10000 Zagreb."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2017,7,29]]},"reference":[{"key":"2020021310031729900_B1","first-page":"1","article-title":"Smart labels.","volume-title":"Liber Amicorum for Dick de Jongh","author":"Bilkova","year":"2004"},{"key":"2020021310031729900_B2","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107050884","volume-title":"Modal Logic","author":"Blackburn","year":"2001"},{"key":"2020021310031729900_B3","first-page":"31","article-title":"Provability logics for relative interpretability.","volume-title":"Mathematical Logic, Proceedings of the 1988 Heyting Conference","author":"de Jongh","year":"1990"},{"key":"2020021310031729900_B4","first-page":"1","article-title":"Modal completeness of ILW,","volume-title":"Essays dedicated to Johan van Benthem on the occasion of his 50th birthday","author":"de Jongh","year":"1999"},{"key":"2020021310031729900_B5","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1093\/jigpal\/jzn013","article-title":"Modal matters in interpretability logics.","volume":"16","author":"Goris","year":"2008","journal-title":"Logic Journal of the IGPL"},{"key":"2020021310031729900_B6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/jigpal\/jzp082","article-title":"A new principle in the interpretability logic of all reasonable arithmetical theories.","volume":"19","author":"Goris","year":"2011","journal-title":"Logic Journal of the IGPL"},{"key":"2020021310031729900_B7","volume-title":"Two series of formalized interpretability principles for weak systems of arithmetic.","author":"Goris","year":"2015"},{"key":"2020021310031729900_B8","first-page":"667","article-title":"Interpretability in theories containing arithmetic II,","volume":"22","author":"H\u00e1jek.","year":"1981","journal-title":"Commentationes Mathematicae Univ. 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