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To be more detailed, in this paper the latter is adapted to Weir\u2019s non-transitive trivalent logic <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathbf{NC}}_{\\mathbf{3}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>NC<\/mml:mi>\n                    <mml:mn>3<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. As a result, for each binary extension of <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathbf{NC}}_{\\mathbf{3}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>NC<\/mml:mi>\n                    <mml:mn>3<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, we present a sound and complete Lemmon-style natural deduction system. Last, but not least, we stress the fact that Avron and his co-authors\u2019 general method of obtaining <jats:italic>n<\/jats:italic>-sequent proof systems for any <jats:italic>n<\/jats:italic>-valent logic with deterministic or non-deterministic matrices is not applicable to <jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathbf{NC}}_{\\mathbf{3}}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:msub>\n                    <mml:mi>NC<\/mml:mi>\n                    <mml:mn>3<\/mml:mn>\n                  <\/mml:msub>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and its binary extensions.\n<\/jats:p>","DOI":"10.1007\/s10849-022-09382-x","type":"journal-article","created":{"date-parts":[[2022,9,19]],"date-time":"2022-09-19T07:13:41Z","timestamp":1663571621000},"page":"247-273","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Non-transitive Correspondence Analysis"],"prefix":"10.1007","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7731-1339","authenticated-orcid":false,"given":"Yaroslav","family":"Petrukhin","sequence":"first","affiliation":[]},{"given":"Vasily","family":"Shangin","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,9,19]]},"reference":[{"issue":"1","key":"9382_CR1","doi-asserted-by":"publisher","first-page":"102","DOI":"10.1017\/jsl.2018.51","volume":"84","author":"JP Aguilera","year":"2019","unstructured":"Aguilera, J. 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