{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T19:05:50Z","timestamp":1766084750413,"version":"3.41.2"},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T00:00:00Z","timestamp":1723161600000},"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":[[2025,5,23]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we deal with the problem of putting together modal worlds that operate in different logic systems. When evaluating a modal sentence $\\Box \\varphi $, we argue that it is not sufficient to inspect the truth of $\\varphi $ in accessed worlds (possibly in different logics). Instead, ways of transferring more subtle semantic information between logical systems must be established. Thus, we will introduce modal structures that accommodate communication between logic systems by fixing a common lattice $L$ that contains as sublattices the semantics operating in each world. The value of a formula $\\Box \\varphi $ in a world with lattice $L^{\\prime}$ will be defined in terms of the values of $\\varphi $ in accessible worlds relativized to $L^{\\prime}$ using the common order of $L$. We will investigate natural instances where formulas $\\varphi $ can be said to be necessary\/possible even though all the accessible world falsify $\\varphi $. Further, we will discuss frames that characterize dynamic relations between logic systems: classically increasing, classically decreasing and dialectic frames. Finally, we formalize the semantics of considering worlds operating in classical logic or logic of paradox, exemplifying the kind of issue one should face in this kind of formalization.<\/jats:p>","DOI":"10.1093\/jigpal\/jzae082","type":"journal-article","created":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T02:49:29Z","timestamp":1723171769000},"source":"Crossref","is-referenced-by-count":4,"title":["Modality across different logics"],"prefix":"10.1093","volume":"33","author":[{"given":"Alfredo Roque","family":"Freire","sequence":"first","affiliation":[{"name":"University of Brasilia , Brasilia, Federal District, Brazil, alfrfreire@gmail.com"}]},{"given":"Manuel A","family":"Martins","sequence":"additional","affiliation":[{"name":"CIDMA, Dep . Mathematics, University of Aveiro, Portugal, martins@ua.pt"}]}],"member":"286","published-online":{"date-parts":[[2024,8,9]]},"reference":[{"key":"2025052605515444700_ref1","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s10849-013-9184-6","article-title":"A Hilbert-style axiomatisation for equational hybrid logic","volume":"23","author":"Barbosa","year":"2014","journal-title":"Journal of Logic, Language and Information"},{"key":"2025052605515444700_ref2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/2269159","article-title":"A functional calculus of first order based on strict implication","volume":"11","author":"Barcan","year":"1946","journal-title":"The Journal of Symbolic Logic"},{"key":"2025052605515444700_ref3","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198812791.001.0001","volume-title":"Impossible Worlds","author":"Berto","year":"2019"},{"key":"2025052605515444700_ref4","doi-asserted-by":"crossref","DOI":"10.1090\/memo\/0396","volume-title":"Algebraizable Logics","author":"Blok","year":"1989"},{"volume-title":"Meaning and Necessity: A Study in Semantics and Modal Logic","year":"1947","author":"Carnap","key":"2025052605515444700_ref5"},{"key":"2025052605515444700_ref6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-1-4020-6324-4_1","article-title":"Logics of formal inconsistency","author":"Carnielli","year":"2007","journal-title":"Handbook of Philosophical Logic"},{"key":"2025052605515444700_ref7","doi-asserted-by":"publisher","first-page":"115","DOI":"10.12775\/LLP.2000.008","article-title":"Formal inconsistency and evolutionary databases","volume":"8","author":"Carnielli","year":"2004","journal-title":"Logic and Logical Philosophy"},{"key":"2025052605515444700_ref8","doi-asserted-by":"crossref","first-page":"187","DOI":"10.12775\/LLP.2020.015","article-title":"Twist-valued models for three-valued paraconsistent set theory","volume":"30","author":"Carnielli","year":"2021","journal-title":"Logic and Logical Philosophy"},{"volume-title":"Paraconsistent Logic: Consistency, Contradiction and Negation","year":"2016","author":"Carnielli","key":"2025052605515444700_ref9"},{"key":"2025052605515444700_ref10","doi-asserted-by":"crossref","first-page":"385","DOI":"10.1093\/jigpal\/jzz010","article-title":"Editors\u2019 introduction: Special issue on non-classical modal and predicate logics","volume":"27","author":"Cintula","year":"2019","journal-title":"Logic Journal of the IGPL"},{"key":"2025052605515444700_ref11","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.tcs.2007.02.068","article-title":"Ultraproducts and possible worlds semantics in institutions","volume":"379","author":"Diaconescu","year":"2007","journal-title":"Theor. 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