{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T04:07:27Z","timestamp":1759032447731,"version":"3.37.3"},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2020,6,4]],"date-time":"2020-06-04T00:00:00Z","timestamp":1591228800000},"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\/501100003593","name":"National Council for Scientific and Technological Development","doi-asserted-by":"publisher","award":["308524\/2014-4","150064\/2018-7"],"award-info":[{"award-number":["308524\/2014-4","150064\/2018-7"]}],"id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"publisher"}]},{"name":"The S\u00e3o Paulo Research Foundation","award":["2016\/21928-0","2019\/08442-9"],"award-info":[{"award-number":["2016\/21928-0","2019\/08442-9"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,9,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (i.e. logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous approaches to quantified LFIs presented in the literature. The case of QmbC, the simpler quantified LFI expanding classical logic, will be analyzed in detail. An axiomatic extension of QmbC called $\\textbf{QLFI1}_\\circ $ is also studied, which is equivalent to the quantified version of da Costa and D\u2019Ottaviano 3-valued logic J3. The semantical structures for this logic turn out to be Tarkian structures based on twist structures. The expansion of QmbC and $\\textbf{QLFI1}_\\circ $ with a standard equality predicate is also considered.<\/jats:p>","DOI":"10.1093\/logcom\/exaa027","type":"journal-article","created":{"date-parts":[[2020,3,9]],"date-time":"2020-03-09T20:23:08Z","timestamp":1583785388000},"page":"1257-1290","source":"Crossref","is-referenced-by-count":4,"title":["First-order swap structures semantics for some logics of formal inconsistency"],"prefix":"10.1093","volume":"30","author":[{"given":"Marcelo E","family":"Coniglio","sequence":"first","affiliation":[{"name":"Institute of Philosophy and the Humanities and Centre for Logic, Epistemology and The History of Science, University of Campinas, Campinas, SP, Brazil 13083-896"}]},{"given":"Aldo","family":"Figallo-Orellano","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica, Universidad Nacional del Sur, Bahia Blanca, Argentina Centre for Logic, Epistemology and The History of Science, University of Campinas, Campinas, SP, Brazil B8000"}]},{"given":"Ana C","family":"Golzio","sequence":"additional","affiliation":[{"name":"Faculty of Philosophy and Sciences, S\u00e3o Paulo State University, Marilia Campus, Brazil 17525-900"}]}],"member":"286","published-online":{"date-parts":[[2020,6,4]]},"reference":[{"key":"2020081904464677500_ref1","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1007\/3-7643-7304-0_9","article-title":"Non-deterministic matrices and modular semantics of rules","volume-title":"Logica Universalis","author":"Avron","year":"2005"},{"key":"2020081904464677500_ref2","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.ijar.2006.06.011","article-title":"Non-deterministic semantics for logics with a consistency operator","volume":"45","author":"Avron","year":"2007","journal-title":"International Journal of Approximate Reasoning"},{"key":"2020081904464677500_ref3","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":"2020081904464677500_ref4","first-page":"529","article-title":"Canonical propositional Gentzen-type systems","volume-title":"Proceedings of the 1st International Joint Conference on Automated Reasoning (IJCAR 2001)","author":"Avron","year":"2001"},{"key":"2020081904464677500_ref5","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1093\/logcom\/exi001","article-title":"Non-deterministic multi-valued structures","volume":"15","author":"Avron","year":"2005","journal-title":"Journal of Logic and Computation"},{"key":"2020081904464677500_ref6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-3-540-75939-3_1","article-title":"Many-valued non-deterministic semantics for first-order logics of formal (in)consistency","volume-title":"Algebraic and Proof-Theoretic Aspects of Non-classical Logics","author":"Avron","year":"2007"},{"key":"2020081904464677500_ref7","article-title":"Logic, Epistemology, and the Unity of Science","volume-title":"Paraconsistent Logic: Consistency, Contradiction and Negation","author":"Carnielli","year":"2016"},{"article-title":"Twist-valued models for three-valued paraconsistent set theory","year":"2019","author":"Carnielli","key":"2020081904464677500_ref8"},{"key":"2020081904464677500_ref9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/978-1-4020-6324-4_1","article-title":"Logics of formal inconsistency","volume-title":"Handbook of Philosophical Logic","author":"Carnielli","year":"2007"},{"key":"2020081904464677500_ref10","doi-asserted-by":"crossref","first-page":"548","DOI":"10.1017\/S1755020314000148","article-title":"On the way to a wider model theory: completeness theorems for first-order logics of formal inconsistency","volume":"7","author":"Carnielli","year":"2014","journal-title":"The Review of Symbolic Logic"},{"key":"2020081904464677500_ref11","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1201\/9780203910139.pt1","article-title":"A taxonomy of C-systems","volume-title":"Paraconsistency: The Logical Way to the Inconsistent","author":"Carnielli","year":"2002"},{"volume-title":"Model Theory","year":"1990","author":"Chang","key":"2020081904464677500_ref12"},{"key":"2020081904464677500_ref13","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1007\/BF01230621","article-title":"The class of Kleene algebras satisfying an interpolation property and Nelson algebras","volume":"23","author":"Cignoli","year":"1986","journal-title":"Algebra Universalis"},{"key":"2020081904464677500_ref14","doi-asserted-by":"crossref","DOI":"10.1093\/jigpal\/jzy072","article-title":"Non-deterministic algebraization of logics by swap structures","author":"Coniglio","year":"2018","journal-title":"Logic Journal of the IGPL"},{"key":"2020081904464677500_ref15","first-page":"62","article-title":"First-order swap structures semantics for QmbC (extended abstract)","volume-title":"SYSMICS 2019: Syntax Meets Semantics\u2014Book of Abstracts","author":"Coniglio","year":"2019"},{"key":"2020081904464677500_ref16","doi-asserted-by":"crossref","first-page":"341","DOI":"10.1017\/jsl.2014.19","article-title":"A Henkin-style proof of completeness for first-order algebraizable logics","volume":"80","author":"Cintula","year":"2015","journal-title":"The Journal of Symbolic Logic"},{"volume-title":"Sobre Uma Teoria de Modelos Trivalente (on a Three-Valued Model Theory, in Portuguese)","year":"1982","author":"D\u2019Ottaviano","key":"2020081904464677500_ref17"},{"key":"2020081904464677500_ref18","first-page":"77","article-title":"The completeness and compactness of a three-valued first-order logic","volume":"XIX","author":"D\u2019Ottaviano","year":"1985","journal-title":"Revista Colombiana de Matem\u00e1ticas"},{"key":"2020081904464677500_ref19","first-page":"157","article-title":"The model extension theorems for J3-theories","volume-title":"Methods in Mathematical Logic. Proceedings of the 6th Latin American Symposium on Mathematical Logic","author":"D\u2019Ottaviano","year":"1985"},{"key":"2020081904464677500_ref20","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/BF00396904","article-title":"Definability and quantifier elimination for J3-theories","volume":"46","author":"D\u2019Ottaviano","year":"1987","journal-title":"Studia Logica"},{"key":"2020081904464677500_ref21","doi-asserted-by":"crossref","DOI":"10.1093\/jigpal\/jzy067","article-title":"The Keisler-Shelah theorem for QmbC through semantical atomization","author":"Ferguson","year":"2018","journal-title":"Logic Journal of the IGPL"},{"key":"2020081904464677500_ref22","first-page":"99","article-title":"An algebraic study of a propositional system of Nelson","volume-title":"Mathematical Logic. Proceedings of the First Brazilian Conference on Mathematical Logic, Campinas 1977","author":"Fidel","year":"1978"},{"volume-title":"Introduction to Boolean Algebras","year":"2009","author":"Givant","key":"2020081904464677500_ref23"},{"key":"2020081904464677500_ref24","doi-asserted-by":"crossref","first-page":"63","DOI":"10.4064\/fm-37-1-63-74","article-title":"An algebraic characterization of quantifiers","volume":"37","author":"Henkin","year":"1950","journal-title":"Fundamenta Mathematicae"},{"key":"2020081904464677500_ref25","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1090\/S0002-9947-1958-0095135-X","article-title":"Lattices with involution","volume":"87","author":"Kalman","year":"1958","journal-title":"Transactions of the American Mathematical Society"},{"volume-title":"Introduction to Mathematical Logic","year":"1997","author":"Mendelson","key":"2020081904464677500_ref26"},{"key":"2020081904464677500_ref27","doi-asserted-by":"crossref","first-page":"204","DOI":"10.2307\/2267135","article-title":"Proofs of non-deducibility in intuitionistic functional calculus","volume":"13","author":"Mostowski","year":"1948","journal-title":"The Journal of Symbolic Logic"},{"volume-title":"An Algebraic Approach to Non-Classical Logics","year":"1974","author":"Rasiowa","key":"2020081904464677500_ref28"},{"volume-title":"The Mathematics of Metamathematics","year":"1963","author":"Rasiowa","key":"2020081904464677500_ref29"},{"key":"2020081904464677500_ref30","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1007\/BF02121118","article-title":"Notes on N-lattices and constructive logic with strong negation","volume":"36","author":"Vakarelov","year":"1977","journal-title":"Studia Logica"}],"container-title":["Journal of Logic and Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/logcom\/article-pdf\/30\/6\/1257\/33663166\/exaa027.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/academic.oup.com\/logcom\/article-pdf\/30\/6\/1257\/33663166\/exaa027.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,19]],"date-time":"2020-08-19T08:47:10Z","timestamp":1597826830000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/logcom\/article\/30\/6\/1257\/5851162"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,4]]},"references-count":30,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2020,6,4]]},"published-print":{"date-parts":[[2020,9,4]]}},"URL":"https:\/\/doi.org\/10.1093\/logcom\/exaa027","relation":{},"ISSN":["0955-792X","1465-363X"],"issn-type":[{"type":"print","value":"0955-792X"},{"type":"electronic","value":"1465-363X"}],"subject":[],"published-other":{"date-parts":[[2020,9]]},"published":{"date-parts":[[2020,6,4]]}}}