{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T02:57:27Z","timestamp":1782529047489,"version":"3.54.5"},"reference-count":33,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T00:00:00Z","timestamp":1683763200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Given a three-valued definition of validity, which choice of three-valued truth tables for the connectives can ensure that the resulting logic coincides exactly with classical logic? We give an answer to this question for the five monotonic consequence relations <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020323000114_inline1.png\"\/><jats:tex-math>\n$st$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020323000114_inline2.png\"\/><jats:tex-math>\n$ss$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020323000114_inline3.png\"\/><jats:tex-math>\n$tt$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020323000114_inline4.png\"\/><jats:tex-math>\n$ss\\cap tt$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020323000114_inline5.png\"\/><jats:tex-math>\n$ts$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, when the connectives are negation, conjunction, and disjunction. For <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020323000114_inline6.png\"\/><jats:tex-math>\n$ts$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020323000114_inline7.png\"\/><jats:tex-math>\n$ss\\cap tt$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> the answer is trivial (no scheme works), and for <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020323000114_inline8.png\"\/><jats:tex-math>\n$ss$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020323000114_inline9.png\"\/><jats:tex-math>\n$tt$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> it is straightforward (they are the collapsible schemes, in which the middle value acts like one of the classical values). For <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020323000114_inline10.png\"\/><jats:tex-math>\n$st$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, the schemes in question are the Boolean normal schemes that are either monotonic or collapsible.<\/jats:p>","DOI":"10.1017\/s1755020323000114","type":"journal-article","created":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T05:03:54Z","timestamp":1683781434000},"page":"682-704","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":6,"title":["ON THREE-VALUED PRESENTATIONS OF CLASSICAL LOGIC"],"prefix":"10.1017","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2958-7840","authenticated-orcid":false,"given":"BRUNO","family":"DA R\u00c9","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7324-0908","authenticated-orcid":false,"given":"DAMIAN","family":"SZMUC","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8423-5880","authenticated-orcid":false,"given":"EMMANUEL","family":"CHEMLA","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9114-7686","authenticated-orcid":false,"given":"PAUL","family":"\u00c9GR\u00c9","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2023,5,11]]},"reference":[{"key":"S1755020323000114_r7","first-page":"2193","article-title":"Characterizing logical consequence in many-valued logic","volume":"27","author":"Chemla","year":"2017","journal-title":"Journal of Logic and Computation"},{"key":"S1755020323000114_r23","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(09)70099-0"},{"key":"S1755020323000114_r11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02120878"},{"key":"S1755020323000114_r21","volume-title":"Proof Theory and Logical Complexity","author":"Girard","year":"1987"},{"key":"S1755020323000114_r12","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-020-09549-6"},{"key":"S1755020323000114_r24","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-017-9438-x"},{"key":"S1755020323000114_r6","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-019-02344-0"},{"key":"S1755020323000114_r13","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-022-09666-4"},{"key":"S1755020323000114_r16","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-020-09568-3"},{"key":"S1755020323000114_r29","volume-title":"Many-Valued Logic","author":"Rescher","year":"1969"},{"key":"S1755020323000114_r15","doi-asserted-by":"publisher","DOI":"10.3233\/FI-1994-201234"},{"key":"S1755020323000114_r22","first-page":"49","article-title":"Q-consequence operation","volume":"24","author":"Malinowski","year":"1990","journal-title":"Reports on Mathematical Logic"},{"key":"S1755020323000114_r25","doi-asserted-by":"publisher","DOI":"10.1007\/BF00485682"},{"key":"S1755020323000114_r33","first-page":"409","author":"Cobreros","journal-title":"Unifying the Philosophy of Truth"},{"key":"S1755020323000114_r10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-25365-3_18"},{"key":"S1755020323000114_r4","doi-asserted-by":"publisher","DOI":"10.12775\/LLP.2000.008"},{"key":"S1755020323000114_r26","doi-asserted-by":"publisher","DOI":"10.2307\/2370324"},{"key":"S1755020323000114_r1","doi-asserted-by":"publisher","DOI":"10.1007\/s10992-014-9342-6"},{"key":"S1755020323000114_r17","doi-asserted-by":"publisher","DOI":"10.26686\/ajl.v18i2.6722"},{"key":"S1755020323000114_r20","doi-asserted-by":"publisher","DOI":"10.1007\/BF01201353"},{"key":"S1755020323000114_r31","doi-asserted-by":"publisher","DOI":"10.1215\/00294527-2021-0022"},{"key":"S1755020323000114_r3","doi-asserted-by":"publisher","DOI":"10.1215\/00294527-2008-010"},{"key":"S1755020323000114_r32","doi-asserted-by":"crossref","unstructured":"[33] Teijeiro, P. 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