{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T12:44:38Z","timestamp":1765457078071,"version":"3.46.0"},"reference-count":14,"publisher":"Oxford University Press (OUP)","issue":"8","license":[{"start":{"date-parts":[[2025,11,4]],"date-time":"2025-11-04T00:00:00Z","timestamp":1762214400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/501100004263","name":"FAPERGS","doi-asserted-by":"publisher","award":["14\/2022\u2014ARD\/ARC\u201472212.751.70585.15022023"],"award-info":[{"award-number":["14\/2022\u2014ARD\/ARC\u201472212.751.70585.15022023"]}],"id":[{"id":"10.13039\/501100004263","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,11,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>This paper revisits the model theory of logics of formal inconsistency. I investigate how adopting the minimal system QmbC as a foundational framework affects the standard logical conditions of mathematical definability. In a classical setting, mathematical definability is tied to the validity of the Fra\u00efss\u00e9 definability property. This property states that a concept is first-order definable if, and only if, its satisfiability is preserved under partial isomorphism. In QmbC, Fra\u00efss\u00e9 definability property fails. Instead, we only recover a weaker version of this theorem. To demonstrate this, I elaborate on preliminary results from Mendon\u00e7a and Carnielli (2020, Logic J. IGPL, 28, 10601072) and Mendon\u00e7a (Traditional Theory of Semantic Information without Scandal of Deduction: A Moderately Externalist Reassessment of the Topic Based on Urn Semantics and a Paraconsistent Application. PhD Thesis. Unicamp, Brazil, 2018) . The present findings indicate that, in a paraconsistent context, the universe of mathematically definable notions is significantly restricted.<\/jats:p>","DOI":"10.1093\/logcom\/exaf065","type":"journal-article","created":{"date-parts":[[2025,11,7]],"date-time":"2025-11-07T13:05:32Z","timestamp":1762520732000},"source":"Crossref","is-referenced-by-count":0,"title":["Logics of formal inconsistency and mathematical definability"],"prefix":"10.1093","volume":"35","author":[{"given":"Bruno Ramos","family":"Mendon\u00e7a","sequence":"first","affiliation":[{"name":"Federal University of Southern Border (UFFS\/Brazil) , SC 484, Km 02, Chapec\u00f3, SC 89815-899 ,","place":["Brazil"]}]}],"member":"286","published-online":{"date-parts":[[2025,12,1]]},"reference":[{"key":"2025121107423185400_ref1","article-title":"Ludwig Wittgenstein","volume-title":"The Stanford Encyclopedia of Philosophy","author":"Biletzki","year":"2023"},{"volume-title":"Paraconsistent Logic: Consistency, Contradiction and Negation","year":"2016","author":"Carnielli","key":"2025121107423185400_ref2"},{"key":"2025121107423185400_ref3","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"},{"volume-title":"Mathematical Knowledge and the Interplay of Practices","year":"2015","author":"Ferreir\u00f3s","key":"2025121107423185400_ref4"},{"volume-title":"On Mathematical Defining","year":"","author":"Freire","key":"2025121107423185400_ref5"},{"volume-title":"A Shorter Model Theory","year":"1997","author":"Hodges","key":"2025121107423185400_ref6"},{"key":"2025121107423185400_ref7","doi-asserted-by":"crossref","first-page":"1060","DOI":"10.1093\/jigpal\/jzy073","article-title":"Fra\u00efss\u00e9\u2019s theorem for logics of formal inconsistency","volume":"28","author":"Mendon\u00e7a","year":"2020","journal-title":"Logic Journal of the IGPL"},{"key":"2025121107423185400_ref8","doi-asserted-by":"crossref","DOI":"10.47749\/T\/UNICAMP.2018.1045091","volume-title":"Traditional Theory of Semantic Information without Scandal of Deduction: A Moderately Externalist Reassessment of the Topic Based on Urn Semantics and a Paraconsistent Application","author":"Mendon\u00e7a","year":"2018"},{"key":"2025121107423185400_ref9","article-title":"Paraconsistent logic","volume-title":"The Stanford Encyclopedia of Philosophy","author":"Priest","year":"2008"},{"key":"2025121107423185400_ref10","article-title":"Notes on middle Wittgenstein on contradiction as conflicting rules","volume-title":"Epistemologia, Mente, Matem\u00e1tica e Linguagem: Discuss\u00f5es Do X Simp\u00f3sio Internacional Principia","author":"Silva","year":"2018"},{"key":"2025121107423185400_ref11","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511974885","volume-title":"Models and Games","author":"V\u00e4\u00e4n\u00e4nen","year":"2011"},{"volume-title":"Wittgenstein Und der Wiener Kreis (1929\u20131932)","year":"1984","author":"Wittgenstein","key":"2025121107423185400_ref12"},{"volume-title":"Philosophical Investigations: The German Text, with a Revised English Translation","year":"2003","author":"Wittgenstein","key":"2025121107423185400_ref13"},{"key":"2025121107423185400_ref14","article-title":"Hilbert\u2019s program","volume-title":"The Stanford Encyclopedia of Philosophy","author":"Zach","year":"2023"}],"container-title":["Journal of Logic and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/35\/8\/exaf065\/65666242\/exaf065.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/logcom\/article-pdf\/35\/8\/exaf065\/65666242\/exaf065.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T12:42:40Z","timestamp":1765456960000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/logcom\/article\/doi\/10.1093\/logcom\/exaf065\/8362160"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,4]]},"references-count":14,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2025,11,4]]}},"URL":"https:\/\/doi.org\/10.1093\/logcom\/exaf065","relation":{},"ISSN":["0955-792X","1465-363X"],"issn-type":[{"type":"print","value":"0955-792X"},{"type":"electronic","value":"1465-363X"}],"subject":[],"published-other":{"date-parts":[[2025,12]]},"published":{"date-parts":[[2025,11,4]]},"article-number":"exaf065"}}