{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T13:27:54Z","timestamp":1770038874477,"version":"3.49.0"},"reference-count":31,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T00:00:00Z","timestamp":1751587200000},"content-version":"unspecified","delay-in-days":184,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2025]]},"abstract":"<jats:title>Abstract<\/jats:title>\n\t  <jats:p>Often in Software Engineering, a modeling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such formalism: states evolve through two accessibility relations capturing weighted evidence of a transition or its absence, respectively. Their weights come, parametrically, from a residuated lattice. This paper explores both i) a category of these systems, and the corresponding compositional operators and ii) a modal logic to reason upon them. Furthermore, two notions of <jats:italic>crisp<\/jats:italic> and <jats:italic>graded<\/jats:italic> simulation and bisimulation are introduced in order to relate two paraconsistent transition systems. Finally, results of modal invariance, for specific subsets of formulas, are discussed.<\/jats:p>","DOI":"10.1017\/s0960129525100170","type":"journal-article","created":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T05:11:48Z","timestamp":1751605908000},"update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":1,"title":["Paraconsistent transition structures: compositional principles and a modal logic"],"prefix":"10.1017","volume":"35","author":[{"given":"Juliana","family":"Cunha","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0646-2017","authenticated-orcid":false,"given":"Alexandre","family":"Madeira","sequence":"additional","affiliation":[]},{"given":"Luis S.","family":"Barbosa","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2025,7,4]]},"reference":[{"key":"S0960129525100170_ref6","volume-title":"Process Aalgebra: Eequational theories of communicating processes. 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In: Klin, B. and Pimentel, E. , 31st EACSL Annual Conference on Computer ScienceLogic (CSL 2023), volume 252 of Leibniz International Proceedings in Informatics (LIPIcs), Dagstuhl, Germany, 2023, Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00a8ur Informatik, 12:1\u201312:18."},{"key":"S0960129525100170_ref2","doi-asserted-by":"publisher","DOI":"10.1093\/logcom\/exp072"},{"key":"S0960129525100170_ref11","doi-asserted-by":"publisher","DOI":"10.1007\/s11225-010-9230-1"},{"key":"S0960129525100170_ref13","doi-asserted-by":"publisher","DOI":"10.1023\/A:1005296018904"},{"key":"S0960129525100170_ref19","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-014-0472-8"},{"key":"S0960129525100170_ref15","doi-asserted-by":"publisher","DOI":"10.4204\/EPTCS.358.20"},{"key":"S0960129525100170_ref5","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2019.03.002"},{"key":"S0960129525100170_ref22","doi-asserted-by":"crossref","unstructured":"Jain, M. , Madeira, A. and Martins, M. A. (2019). A fuzzy modal logic for fuzzy transition systems. Felty, A. P. and Marcos, J. (eds.) 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S. (2022). Paraconsistent transition systems. In: Nantes-Sobrinho, D. and Fontaine, P. (eds.) Proceedings 17th International Workshop on Logical and SemanticFrameworks with Applications, LSFA 2022, Belo Horizonte, Brazil (hybrid), 23\u201324 September 2022, Volume 376 of EPTCS, 3\u201315."},{"key":"S0960129525100170_ref21","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-0114(01)00098-7"},{"key":"S0960129525100170_ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.fss.2021.08.009"},{"key":"S0960129525100170_ref25","doi-asserted-by":"publisher","DOI":"10.1016\/j.jlamp.2016.03.004"},{"key":"S0960129525100170_ref3","volume-title":"Towards Paraconsistent Engineering, Volume 110 of Intelligent Systems Reference Library","author":"Akama","year":"2016"}],"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129525100170","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T05:11:54Z","timestamp":1751605914000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129525100170\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"references-count":31,"alternative-id":["S0960129525100170"],"URL":"https:\/\/doi.org\/10.1017\/s0960129525100170","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"\u00a9 The Author(s), 2025. 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