{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T15:56:48Z","timestamp":1770825408618,"version":"3.50.1"},"reference-count":9,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2020,7,27]],"date-time":"2020-07-27T00:00:00Z","timestamp":1595808000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"name":"Spanish Ministry of Economy, Industry and Competitiveness","award":["FFI2017-82878-P"],"award-info":[{"award-number":["FFI2017-82878-P"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,1,11]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A classical result by S\u0142upecki states that a logic L is functionally complete for the 3-element set of truth-values THREE if, in addition to functionally including \u0141ukasiewicz\u2019s 3-valued logic \u01413, what he names the \u2018$T$-function\u2019 is definable in L. By leaning upon this classical result, we prove a general theorem for defining binary expansions (i.e. expansions with a binary connective) of Kleene\u2019s strong logic that are functionally complete for THREE.<\/jats:p>","DOI":"10.1093\/jigpal\/jzaa028","type":"journal-article","created":{"date-parts":[[2020,6,25]],"date-time":"2020-06-25T11:25:14Z","timestamp":1593084314000},"page":"21-33","source":"Crossref","is-referenced-by-count":4,"title":["A remark on functional completeness of binary expansions of Kleene\u2019s strong 3-valued logic"],"prefix":"10.1093","volume":"30","author":[{"given":"Gemma","family":"Robles","sequence":"first","affiliation":[{"name":"Departamento de Psicolog\u00eda, Sociolog\u00eda y Filosof\u00eda, Universidad de Le\u00f3n, Campus de Vegazana, s\/n, 24071, Le\u00f3n, Spain"}]},{"given":"Jos\u00e9 M","family":"M\u00e9ndez","sequence":"additional","affiliation":[{"name":"Universidad de Salamanca, Edificio FES, Campus Unamuno, 37007, Salamanca, Spain"}]}],"member":"286","published-online":{"date-parts":[[2020,7,27]]},"reference":[{"key":"2022011721250451300_ref1","article-title":"La idea de un c\u00e1lculo de antinomias","volume-title":"Seminario Matem\u00e1tico","author":"Asenjo","year":"1953"},{"key":"2022011721250451300_ref2","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1026740726955","article-title":"Partiality and its dual","volume":"65","author":"Dunn","year":"2000","journal-title":"Studia Logica"},{"key":"2022011721250451300_ref3","article-title":"MaTest","author":"Gonz\u00e1lez","year":"2012"},{"key":"2022011721250451300_ref4","doi-asserted-by":"crossref","first-page":"81","DOI":"10.12775\/LLP.1999.006","article-title":"Ja\u015bkowski\u2019s criterion and three-valued paraconsistent logics","volume":"7","author":"Karpenko","year":"1999","journal-title":"Logic and Logical Philosophy"},{"key":"2022011721250451300_ref5","volume-title":"Introduction to Metamathematics","author":"Kleene","year":"2009"},{"key":"2022011721250451300_ref6","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1007\/BF00258428","article-title":"Logic of paradox","volume":"8","author":"Priest","year":"1979","journal-title":"Journal of Philosophical Logic"},{"key":"2022011721250451300_ref7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s10849-019-09306-2","article-title":"The class of all natural implicative expansions of Kleene\u2019s strong logic functionally equivalent to \u0141ukasiewicz\u2019s 3-valued logic \u01413","author":"Robles","year":"2019","journal-title":"Journal of Logic, Language and Information"},{"key":"2022011721250451300_ref8","first-page":"9","article-title":"Der volle dreiwertige Aussagenkalk\u00fcl","volume-title":"Comptes Rendus des S\u00e9ances de La Soci\u00e9t\u00e9 des Sciences et des Lettres de Varsovie","author":"S\u0142upecki","year":"1936"},{"key":"2022011721250451300_ref9","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1007\/BF02120845","article-title":"A criterion of fullness of many-valued systems of propositional logic","volume":"30","author":"S\u0142upecki","year":"1972","journal-title":"Studia Logica"}],"container-title":["Logic Journal of the IGPL"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/30\/1\/21\/42198228\/jzaa028.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jigpal\/article-pdf\/30\/1\/21\/42198228\/jzaa028.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,17]],"date-time":"2022-01-17T21:25:22Z","timestamp":1642454722000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jigpal\/article\/30\/1\/21\/5875438"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,7,27]]},"references-count":9,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,7,27]]},"published-print":{"date-parts":[[2022,1,11]]}},"URL":"https:\/\/doi.org\/10.1093\/jigpal\/jzaa028","relation":{},"ISSN":["1367-0751","1368-9894"],"issn-type":[{"value":"1367-0751","type":"print"},{"value":"1368-9894","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2022,2]]},"published":{"date-parts":[[2020,7,27]]}}}