{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T13:40:15Z","timestamp":1776346815203,"version":"3.51.2"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"5","license":[{"start":{"date-parts":[[2020,6,2]],"date-time":"2020-06-02T00:00:00Z","timestamp":1591056000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2020,7,23]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The necessary condition for a calculus to be paraconsistent is that its consequence relation is not explosive. This results in rejection of the principle of ex contradictione sequitur quodlibet. In 1973, Sette presented a calculus, denoted as $P^1$, which is paraconsistent only at the atomic level, i.e. $\\alpha $ and ${\\sim }\\alpha $ yield any $\\beta $ if, and only if the formula $\\alpha $ is not a propositional variable. The calculus has been viewed as one of the noteworthy paraconsistent calculi since then. The objective of this paper is to propose a new semantics for Sette\u2019s calculus and present some hierarchies of the paraconsistent calculi, which are based on $P^1$. We demonstrate that $P^1$ is sound and complete with respect to the semantics and so are all the calculi under consideration.<\/jats:p>","DOI":"10.1093\/logcom\/exaa030","type":"journal-article","created":{"date-parts":[[2020,4,23]],"date-time":"2020-04-23T11:09:31Z","timestamp":1587640171000},"page":"1109-1124","source":"Crossref","is-referenced-by-count":6,"title":["Sette\u2019s calculus P1 and some hierarchies of paraconsistent systems"],"prefix":"10.1093","volume":"30","author":[{"given":"Janusz","family":"Ciuciura","sequence":"first","affiliation":[{"name":"Faculty of Philosophy and History, Institute of Philosophy, University of \u0141\u00f3d\u017a, Lindleya 3\/5, 90-131 \u0141\u00f3d\u017a, Poland"}]}],"member":"286","published-online":{"date-parts":[[2020,6,2]]},"reference":[{"key":"2020071310022841100_ref1","first-page":"33","article-title":"Some relations between modal and paraconsistent logic","volume":"8","author":"Araujo","year":"1987","journal-title":"Journal of Non-Classical Logic"},{"key":"2020071310022841100_ref2","volume-title":"Theory of Effective Propositional Paraconsistent Logics","author":"Avron","year":"2018"},{"key":"2020071310022841100_ref3","first-page":"373","article-title":"Sequents and bivaluations","volume":"44","author":"B\u00e9ziau","year":"2001","journal-title":"Logique et Analyse"},{"key":"2020071310022841100_ref4","article-title":"Suszko\u2019s thesis and dyadic semantics","author":"Caleiro","year":"2003"},{"key":"2020071310022841100_ref5","volume-title":"Paraconsistent Logic: Consistency, Contradiction and Negation","author":"Carnielli","year":"2016"},{"key":"2020071310022841100_ref6","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":"2020071310022841100_ref7","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1090\/conm\/235\/03464","article-title":"Society semantics and multiplevalued logics","volume-title":"Advances in Contemporary Logic and Computer Science: Proceedings of the Eleventh Brazilian Conference on Mathematical Logic, May 6\u201310, 1996, Salvador Da Bahia, Brazil","author":"Carnielli","year":"1999"},{"key":"2020071310022841100_ref8","first-page":"173","article-title":"Paraconsistent heap. 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