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This logic displays a number of unusual features: <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathcal{O}\\mathcal{L}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>O<\/mml:mi>\n                    <mml:mi>L<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> is not weaker but incomparable with classical logic, it is connexive, paraconsistent and contradictory. As a non-structural logic, <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathcal{O}\\mathcal{L}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>O<\/mml:mi>\n                    <mml:mi>L<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> cannot be algebraized by the standard methods. However, we show that <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathcal{O}\\mathcal{L}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>O<\/mml:mi>\n                    <mml:mi>L<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> has an algebraizable structural companion, and determine its equivalent semantics, which turns out to be a finitely-generated discriminator variety. We provide an equational and a twist presentation for this class of algebras, which allow us to compare it with other well-known algebras of non-classical logics. In this way we establish that <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$$\\mathcal{O}\\mathcal{L}$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>O<\/mml:mi>\n                    <mml:mi>L<\/mml:mi>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> is definitionally equivalent to an expansion of the three-valued logic <jats:inline-formula>\n              <jats:alternatives>\n                <jats:tex-math>$${\\mathcal {J}}3$$<\/jats:tex-math>\n                <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mrow>\n                    <mml:mi>J<\/mml:mi>\n                    <mml:mn>3<\/mml:mn>\n                  <\/mml:mrow>\n                <\/mml:math>\n              <\/jats:alternatives>\n            <\/jats:inline-formula> of D\u2019Ottaviano and da Costa, itself a schematic extension of paraconsistent Nelson logic.<\/jats:p>","DOI":"10.1007\/s00153-024-00961-2","type":"journal-article","created":{"date-parts":[[2025,1,27]],"date-time":"2025-01-27T13:02:40Z","timestamp":1737982960000},"page":"795-817","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["The algebra of ordinary discourse. On the semantics of Cooper\u2019s logic"],"prefix":"10.1007","volume":"64","author":[{"given":"Umberto","family":"Rivieccio","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,1,27]]},"reference":[{"key":"961_CR1","unstructured":"Greati, V., Greco, G., Marcelino, S., Palmigiano, A., Rivieccio, U.: Generating proof systems for three-valued propositional logics. In: Egr\u00e9, P., Rossi, L. (eds.) Handbook of Three-Valued Logics (to Appear). MIT Press, ( 2024)"},{"issue":"( 1\u20134)","key":"961_CR2","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1080\/00201746808601531","volume":"11","author":"W.S Cooper","year":"1968","unstructured":"Cooper, W..S.: The propositional logic of ordinary discourse. Inquiry: Interdiscip J. Philos. 11(( 1\u20134)), 295\u2013320 (1968)","journal-title":"Inquiry: Interdiscip J. 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