{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,13]],"date-time":"2025-12-13T23:07:20Z","timestamp":1765667240959,"version":"3.37.3"},"reference-count":43,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2018,11,27]],"date-time":"2018-11-27T00:00:00Z","timestamp":1543276800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["817\/15"],"award-info":[{"award-number":["817\/15"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,9,25]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Paraconsistent logics are logics that, in contrast to classical and intuitionistic logic, do not trivialize inconsistent theories. In this paper we take a paraconsistent view on two famous modal logics: B and S5. We use for this a well-known general method for turning modal logics to paraconsistent logics by defining a new (paraconsistent) negation as $\\neg \\varphi =_{Def} \\sim \\Box \\varphi$ (where $\\sim$ is the classical negation). We show that while that makes both B and S5 members of the well-studied family of paraconsistent C-systems, they differ from most other C-systems in having the important replacement property (which means that equivalence of formulas implies their congruence). We further show that B is a very robust C-system in the sense that almost any axiom which has been considered in the context of C-systems is either already a theorem of B or its addition to B leads to a logic that is no longer paraconsistent. There is exactly one notable exception, and the result of adding this exception to B leads to the other logic studied here, S5.<\/jats:p>","DOI":"10.1093\/jigpal\/jzy064","type":"journal-article","created":{"date-parts":[[2018,11,7]],"date-time":"2018-11-07T20:10:25Z","timestamp":1541621425000},"page":"851-880","source":"Crossref","is-referenced-by-count":3,"title":["Paraconsistency, self-extensionality, modality"],"prefix":"10.1093","volume":"28","author":[{"given":"Arnon","family":"Avron","sequence":"first","affiliation":[{"name":"School of Computer Science, Tel Aviv University, Ramat Aviv, Israel"}]},{"given":"Anna","family":"Zamansky","sequence":"additional","affiliation":[{"name":"Department of Information Systems, University of Haifa, Abba Khoushy, Haifa, Israel"}]}],"member":"286","published-online":{"date-parts":[[2018,11,27]]},"reference":[{"key":"2020092508544127000_ref1","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s11225-011-9346-y","article-title":"Ideal paraconsistent logics","volume":"99","author":"Arieli","year":"2011","journal-title":"Studia Logica"},{"key":"2020092508544127000_ref2","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s11225-010-9296-9","article-title":"Maximal and premaximal paraconsistency in the framework of three-valued semantics","volume":"97","author":"Arieli","year":"2011","journal-title":"Studia Logica"},{"key":"2020092508544127000_ref3","first-page":"706","article-title":"What is an ideal logic for reasoning with inconsistency?","volume-title":"Proceedings of 22nd International Joint Conference on Artificial Intelligence (IJCAI 2011)","author":"Arieli","year":"2011"},{"key":"2020092508544127000_ref4","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/0890-5401(91)90023-U","article-title":"Simple consequence relations","volume":"92","author":"Avron","year":"1991","journal-title":"Information and Computation"},{"key":"2020092508544127000_ref5","first-page":"304","article-title":"On strong maximality of paraconsistent finite-valued logics","volume":"2010","author":"Avron","journal-title":"Proceedings of 2010 25th Annual IEEE Symposium on Logic in Computer Science (LICS)"},{"key":"2020092508544127000_ref6","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1093\/logcom\/exs039","article-title":"Cut-free sequent calculi for C-systems with generalized finite-valued semantics","volume":"23","author":"Avron","year":"2013","journal-title":"Journal of Logic and Computation"},{"key":"2020092508544127000_ref7","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1016\/j.ins.2014.11.003","article-title":"Efficient reasoning with inconsistent information using C-systems","volume":"296","author":"Avron","year":"2015","journal-title":"Information Sciences"},{"key":"2020092508544127000_ref8","first-page":"21","article-title":"A paraconsistent view on B and S5","volume-title":"Proceedings of the 11th Conference on \u201cAdvances in Modal Logic\u201d","author":"Avron","year":"2016"},{"key":"2020092508544127000_ref9","first-page":"195","article-title":"Paraconsistent extensional propositional logics","volume":"23","author":"Batens","year":"1980","journal-title":"Logique et Analyse Louvain"},{"key":"2020092508544127000_ref10","first-page":"445","article-title":"Inconsistency-adaptive logics","volume-title":"Logic at Work","author":"Batens","year":"1998"},{"key":"2020092508544127000_ref11","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1201\/9780203910139.ch12","article-title":"On some remarkable relations between paraconsistent logics, modal logics, and ambiguity logics","volume-title":"Paraconsistency: The Logical Way to the Inconsistent","author":"Batens","year":"2002"},{"key":"2020092508544127000_ref12","first-page":"29","article-title":"Embedding and interpolation for some paralogics. 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