{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T08:01:48Z","timestamp":1771315308203,"version":"3.50.1"},"reference-count":11,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T00:00:00Z","timestamp":1769472000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,1,27]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Windows have been introduced in [1] as a tool for designing polynomial algorithms to check satisfiability of a bimodal logic of weak-density. In this paper, after revisiting the \u201cfolklore\u201d case of bimodal ${\\textbf{K}}4$ already treated in [8], but which is worth a fresh review, we show that windows allow to polynomially solve the satisfiability problem when adding transitivity to weak-density, by mixing algorithms for bimodal ${\\textbf{K}}4$ together with windows-approach. The conclusion is that both satisfiability and validity are $\\textbf{PSPACE}$-complete for these logics.<\/jats:p>","DOI":"10.1093\/jigpal\/jzaf097","type":"journal-article","created":{"date-parts":[[2025,12,13]],"date-time":"2025-12-13T12:53:57Z","timestamp":1765630437000},"source":"Crossref","is-referenced-by-count":0,"title":["PSPACE-completeness of bimodal transitive weak-density logic"],"prefix":"10.1093","volume":"34","author":[{"given":"Olivier","family":"Gasquet","sequence":"first","affiliation":[{"name":"IRIT, Universit\u00e9 de Toulouse , CNRS, France"}]}],"member":"286","published-online":{"date-parts":[[2026,2,17]]},"reference":[{"key":"2026021702052224100_ref1","article-title":"Complexity of some modal logics of density","volume-title":"Festschrift for Andreas Herzig on the Occasion of his 65th Birthday","author":"Balbiani","year":"2025"},{"key":"2026021702052224100_ref2","doi-asserted-by":"crossref","DOI":"10.1007\/3-540-69778-0_13","article-title":"A tableau calculus for multimodal logics and some (un)decidability results","volume-title":"Proceedings of TABLEAUX\u201998, LNAI 1397","author":"Baldoni","year":"1998"},{"key":"2026021702052224100_ref5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511621192","volume-title":"Modal Logic an Introduction","author":"Chellas","year":"1980"},{"key":"2026021702052224100_ref6","article-title":"Complexity of simple dependent bimodal logics. 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Synthese Library","author":"Spaan","year":"1993"}],"container-title":["Logic Journal of the IGPL"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/34\/1\/jzaf097\/66952707\/jzaf097.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/34\/1\/jzaf097\/66952707\/jzaf097.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,17]],"date-time":"2026-02-17T07:05:30Z","timestamp":1771311930000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jigpal\/article\/doi\/10.1093\/jigpal\/jzaf097\/8488132"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,1,27]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1,27]]}},"URL":"https:\/\/doi.org\/10.1093\/jigpal\/jzaf097","relation":{},"ISSN":["1367-0751","1368-9894"],"issn-type":[{"value":"1367-0751","type":"print"},{"value":"1368-9894","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2026,2]]},"published":{"date-parts":[[2026,1,27]]},"article-number":"jzaf097"}}