{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:45:14Z","timestamp":1740123914300,"version":"3.37.3"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2023,8,7]],"date-time":"2023-08-07T00:00:00Z","timestamp":1691366400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,8,7]],"date-time":"2023-08-07T00:00:00Z","timestamp":1691366400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["436508789"],"award-info":[{"award-number":["436508789"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PID2019- 110843GA-I00"],"award-info":[{"award-number":["PID2019- 110843GA-I00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Philos Logic"],"published-print":{"date-parts":[[2023,10]]},"abstract":"Abstract<\/jats:title>In this paper we re-assess the philosophical foundation of Exactly True Logic<\/jats:italic> ($$\\mathcal {ET\\!L}$$<\/jats:tex-math>\n \n ET<\/mml:mi>\n \n L<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>), a competing variant of First Degree Entailment<\/jats:italic> ($$\\mathcal {FDE}$$<\/jats:tex-math>\n FDE<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>). In order to do this, we first rebut an argument against it. As the argument appears in an interview with Nuel Belnap himself, one of the fathers of $$\\mathcal {FDE}$$<\/jats:tex-math>\n FDE<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, we believe its provenance to be such that it needs to be taken seriously. We submit, however, that the argument ultimately fails, and that $$\\mathcal {ET\\!L}$$<\/jats:tex-math>\n \n ET<\/mml:mi>\n \n L<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> cannot easily be dismissed. We then proceed to give an overview of the research that was inspired by this logic over the last decade, thus providing further motivation for the study of $$\\mathcal {ET\\!L}$$<\/jats:tex-math>\n \n ET<\/mml:mi>\n \n L<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and, more generally, of $$\\mathcal {FDE}$$<\/jats:tex-math>\n FDE<\/mml:mi>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-related logics that result from semantical analyses alternative to Belnap\u2019s canonical one. We focus, in particular, on philosophical questions that these developments raise.<\/jats:p>","DOI":"10.1007\/s10992-023-09711-w","type":"journal-article","created":{"date-parts":[[2023,8,7]],"date-time":"2023-08-07T11:02:55Z","timestamp":1691406175000},"page":"1417-1444","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["The Value of the One Value: Exactly True Logic revisited"],"prefix":"10.1007","volume":"52","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6494-1876","authenticated-orcid":false,"given":"Andreas","family":"Kapsner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1364-5003","authenticated-orcid":false,"given":"Umberto","family":"Rivieccio","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,8,7]]},"reference":[{"issue":"6","key":"9711_CR1","doi-asserted-by":"publisher","first-page":"1051","DOI":"10.1007\/s11225-017-9739-7","volume":"105","author":"H Albuquerque","year":"2017","unstructured":"Albuquerque, H., P\u0159enosil, A., & Rivieccio, U. (2017). An algebraic view of super-Belnap logics. Studia Logica, 105(6), 1051\u20131086.","journal-title":"Studia Logica"},{"key":"9711_CR2","unstructured":"Anderson, A., & Belnap, N. (1975). Entailment The Logic of Necessity and Relevance. Princeton University Press Princeton"},{"issue":"1","key":"9711_CR3","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/S0004-3702(98)00032-0","volume":"102","author":"O Arieli","year":"1998","unstructured":"Arieli, O., & Avron, A. (1998). The value of the four values. Articial Intelligence, 102(1), 97\u2013141.","journal-title":"Articial Intelligence"},{"key":"9711_CR4","doi-asserted-by":"crossref","unstructured":"Beall, JC. (2019). FDE as the one true logic. In New essays on Belnap-Dunn logic, pages 115\u2013125. Springer","DOI":"10.1007\/978-3-030-31136-0_8"},{"issue":"2","key":"9711_CR5","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1080\/11663081.2020.1751573","volume":"30","author":"A Belikov","year":"2020","unstructured":"Belikov, A., & Petrukhin, Y. (2020). Exactly true and non-falsity logics meeting infectious ones. Journal of Applied Non-Classical Logics, 30(2), 93\u2013122.","journal-title":"Journal of Applied Non-Classical Logics"},{"key":"9711_CR6","first-page":"30","volume-title":"Con- temporary Aspects of Philosophy","author":"ND Belnap","year":"1977","unstructured":"Belnap, N. D. (1977). How a computer should think. In G. Ryle (Ed.), Con- temporary Aspects of Philosophy (pp. 30\u201356). Boston: Oriel Press."},{"key":"9711_CR7","doi-asserted-by":"crossref","unstructured":"Belnap, N. D. Jr. (1977). A useful four-valued logic. In J. M. Dunn & G. Epstein (Eds.), Modern uses of multiple-valued logic (Fifth Internat. Sym- pos., Indiana Univ., Bloomington, Ind., 1975), pages 5\u201337. Episteme, Vol. 2. Reidel, Dordrecht","DOI":"10.1007\/978-94-010-1161-7_2"},{"key":"9711_CR8","doi-asserted-by":"crossref","unstructured":"Blok, W. J., & Pigozzi, D. (1989). Algebraizable logics, volume 396 of Mem. Amer. Math. Soc. A.M.S., Providence, January 1989","DOI":"10.1090\/memo\/0396"},{"key":"9711_CR9","doi-asserted-by":"crossref","unstructured":"Brignole, D., & Monteiro, A. (1967). Caracterisation des alg\u00e8bres de nelson par des egalit\u00e9s. i. Proceedings of the Japan Academy, 43(4), 279\u2013283","DOI":"10.3792\/pja\/1195521624"},{"key":"9711_CR10","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/j.fss.2017.10.014","volume":"345","author":"C Caleiro","year":"2018","unstructured":"Caleiro, C., Marcelino, S., & Rivieccio, U. (2018). Characterizing finite-valuedness. Fuzzy Sets and Systems, 345, 113\u2013125.","journal-title":"Fuzzy Sets and Systems"},{"key":"9711_CR11","unstructured":"Conway, J. H. (2012). Regular algebra and finite machines. Courier Corporation."},{"issue":"2","key":"9711_CR12","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1007\/BF00142493","volume":"2","author":"J Copeland","year":"1983","unstructured":"Copeland, J. (1983). Pure semantics and applied semantics. Topoi, 2(2), 197\u2013204.","journal-title":"Topoi"},{"issue":"1","key":"9711_CR13","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1093\/aristotelian\/59.1.141","volume":"59","author":"M Dummett","year":"1959","unstructured":"Dummett, M. (1959). Truth. Proceedings of the Aristotelian Society, 59(1), 141\u2013162.","journal-title":"Proceedings of the Aristotelian Society"},{"key":"9711_CR14","doi-asserted-by":"crossref","unstructured":"Fitting, M. (2021). The strict\/tolerant idea and bilattices. In Arnon Avron on Semantics and Proof Theory of Non-Classical Logics, pages 167\u2013191 Springer","DOI":"10.1007\/978-3-030-71258-7_8"},{"key":"9711_CR15","doi-asserted-by":"crossref","unstructured":"Kapsner, A. (2019). FDE as a base for constructive logic. In New essays on Belnap-Dunn logic, pages 191\u2013216. Cham: Springer","DOI":"10.1007\/978-3-030-31136-0_12"},{"key":"9711_CR16","doi-asserted-by":"crossref","unstructured":"Kapsner, A. (2019). Removing the oddity in first degree entailment. Thought A Journal of Philosophy, 8(4), 240\u2013249.","DOI":"10.1002\/tht3.428"},{"key":"9711_CR17","first-page":"277","volume-title":"Logic without Frontiers Festschrift for Walter Alexandre Carnielli on the occasion of his 60th birthday","author":"J Marcos","year":"2011","unstructured":"Marcos, J. (2011). The value of the two values. In M. E. Coniglio & J.-Y. B\u00e9ziau (Eds.), Logic without Frontiers Festschrift for Walter Alexandre Carnielli on the occasion of his 60th birthday (pp. 277\u2013294). London: College Publications."},{"issue":"240","key":"9711_CR18","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1515\/sem-2021-0011","volume":"2021","author":"J Mart\u00ednez-Fern\u00e1ndez","year":"2021","unstructured":"Mart\u00ednez-Fern\u00e1ndez, J., & Mart\u00ed, G. (2021). The representation of gappy sentences in four-valued semantics. Semiotica, 2021(240), 145\u2013163.","journal-title":"Semiotica"},{"issue":"5","key":"9711_CR19","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1007\/s10992-014-9337-3","volume":"44","author":"R Muskens","year":"2015","unstructured":"Muskens, R., & Wintein, S. (2015). Analytic tableaux for all of sixteen 3. Journal of philosophical logic, 44(5), 473\u2013487.","journal-title":"Journal of philosophical logic"},{"issue":"3","key":"9711_CR20","doi-asserted-by":"publisher","first-page":"407","DOI":"10.1007\/s11225-009-9181-6","volume":"91","author":"SP Odintsov","year":"2009","unstructured":"Odintsov, S. P. (2009). On axiomatizing Shramko-Wansing\u2019s logic. Studia Logica, 91(3), 407\u2013428.","journal-title":"Studia Logica"},{"key":"9711_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-31136-0","volume-title":"New Essays on Belnap-Dunn Logic","author":"H Omori","year":"2019","unstructured":"Omori, H., & Wansing, H. (2019). New Essays on Belnap-Dunn Logic. Springer."},{"issue":"1","key":"9711_CR22","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1007\/s10992-011-9215-1","volume":"42","author":"AP Kapsner","year":"2013","unstructured":"Kapsner, A. P., & Rivieccio, U. (2013). Nothing but the truth. J. Philos. Logic, 42(1), 125\u2013135.","journal-title":"J. Philos. Logic"},{"key":"9711_CR23","doi-asserted-by":"publisher","unstructured":"P\u0159enosil, A. (2023). Logics of upsets of De Morgan lattices. Mathematical Logic Quarterly. https:\/\/doi.org\/10.1002\/malq.202100076","DOI":"10.1002\/malq.202100076"},{"issue":"6","key":"9711_CR24","doi-asserted-by":"publisher","first-page":"1255","DOI":"10.1007\/s11225-017-9746-8","volume":"105","author":"A P\u0159enosil","year":"2017","unstructured":"P\u0159enosil, A. (2017). Cut elimination, identity elimination, and interpolation in super-Belnap logics. Studia Logica, 105(6), 1255\u20131289.","journal-title":"Studia Logica"},{"issue":"4","key":"9711_CR25","doi-asserted-by":"publisher","first-page":"601","DOI":"10.1215\/00294527-2020-0025","volume":"61","author":"A P\u0159enosil","year":"2020","unstructured":"P\u0159enosil, A. (2020). Four-valued logics of truth, nonfalsity, exact truth, and material equivalence. Notre Dame Journal of Formal Logic, 61(4), 601\u2013621.","journal-title":"Notre Dame Journal of Formal Logic"},{"issue":"1","key":"9711_CR26","doi-asserted-by":"publisher","first-page":"114","DOI":"10.1017\/S1755020321000204","volume":"16","author":"A P\u0159enosil","year":"2023","unstructured":"P\u0159enosil, A. (2023). The lattice of super-Belnap logics. The Review of Symbolic Logic, 16(1), 114\u2013163.","journal-title":"The Review of Symbolic Logic"},{"key":"9711_CR27","doi-asserted-by":"crossref","unstructured":"Restall, G. (2006). Relevant and substructural logics. In Handbook of the History of Logic, volume\u00a07, pages 289\u2013398 Elsevier","DOI":"10.1016\/S1874-5857(06)80030-0"},{"issue":"4","key":"9711_CR28","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1080\/11663081.2012.737154","volume":"22","author":"U Rivieccio","year":"2012","unstructured":"Rivieccio, U. (2012). An infinity of super-Belnap logics. J. Appl. Non-Class. Log., 22(4), 319\u2013335.","journal-title":"J. Appl. Non-Class. Log."},{"key":"9711_CR29","unstructured":"Shramko, Y. (2019). Dual-Belnap logic and anything but falsehood. Journal of Applied Logics-IfCoLog Journal of Logics and their Applications, 6(2)"},{"key":"9711_CR30","doi-asserted-by":"crossref","unstructured":"Shramko, Y. (2021). Hilbert-style axiomatization of first-degree entailment and a family of its extensions. Annals of Pure and Applied Logic, page 103011","DOI":"10.1016\/j.apal.2021.103011"},{"issue":"6","key":"9711_CR32","doi-asserted-by":"publisher","first-page":"761","DOI":"10.1093\/logcom\/11.6.761","volume":"11","author":"Y Shramko","year":"2001","unstructured":"Shramko, Y., Dunn, J. M., & Takenaka, T. (2001). The trilattice of constructive truth values. Journal of Logic and Computation, 11(6), 761\u2013788.","journal-title":"Journal of Logic and Computation"},{"issue":"2","key":"9711_CR33","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/s10992-005-0556-5","volume":"34","author":"Y Shramko","year":"2005","unstructured":"Shramko, Y., & Wansing, H. (2005). Some useful 16-valued logics: How a computer network should think. Journal of Philosophical Logic, 34(2), 121\u2013153.","journal-title":"Journal of Philosophical Logic"},{"issue":"6","key":"9711_CR34","doi-asserted-by":"publisher","first-page":"1291","DOI":"10.1007\/s11225-017-9747-7","volume":"105","author":"Y Shramko","year":"2017","unstructured":"Shramko, Y., Zaitsev, D., & Belikov, A. (2017). First-degree entailment and its relatives. Studia Logica, 105(6), 1291\u20131317.","journal-title":"Studia Logica"},{"issue":"5","key":"9711_CR35","doi-asserted-by":"publisher","first-page":"787","DOI":"10.1007\/s10992-018-9494-x","volume":"48","author":"Y Shramko","year":"2019","unstructured":"Shramko, Y., Zaitsev, D., & Belikov, A. (2019). The Fmla-Fmla axiomatizations of the exactly true and non-falsity logics and some of their cousins. Journal of Philosophical Logic, 48(5), 787\u2013808.","journal-title":"Journal of Philosophical Logic"},{"issue":"3","key":"9711_CR36","doi-asserted-by":"publisher","first-page":"503","DOI":"10.1007\/s11225-015-9649-5","volume":"104","author":"S Wintein","year":"2016","unstructured":"Wintein, S. (2016). On all strong Kleene generalizations of classical logic. Studia Logica, 104(3), 503\u2013545.","journal-title":"Studia Logica"},{"issue":"4","key":"9711_CR37","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1007\/s10992-015-9385-3","volume":"45","author":"S Wintein","year":"2016","unstructured":"Wintein, S., & Muskens, R. (2016). Gentzen calculus for nothing but the truth. Journal of Philosophical Logic, 45(4), 451\u2013465.","journal-title":"Journal of Philosophical Logic"},{"issue":"6","key":"9711_CR38","doi-asserted-by":"publisher","first-page":"1319","DOI":"10.1007\/s11225-017-9720-5","volume":"105","author":"S Wintein","year":"2017","unstructured":"Wintein, S., & Muskens, R. (2017). Interpolation methods for Dunn logics and their extensions. Studia Logica, 105(6), 1319\u20131347.","journal-title":"Studia Logica"}],"container-title":["Journal of Philosophical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10992-023-09711-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10992-023-09711-w\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10992-023-09711-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,5]],"date-time":"2023-10-05T04:06:33Z","timestamp":1696478793000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10992-023-09711-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,7]]},"references-count":37,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2023,10]]}},"alternative-id":["9711"],"URL":"https:\/\/doi.org\/10.1007\/s10992-023-09711-w","relation":{},"ISSN":["0022-3611","1573-0433"],"issn-type":[{"type":"print","value":"0022-3611"},{"type":"electronic","value":"1573-0433"}],"subject":[],"published":{"date-parts":[[2023,8,7]]},"assertion":[{"value":"21 January 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 May 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 August 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"None","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}},{"value":"Not applicable","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical Approval"}}]}}