{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T04:15:15Z","timestamp":1759032915366},"reference-count":16,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":4334,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1995,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A many\u2010valued sentential logic with truth values in an injective MV\u2010algebra is introduced and the axiomatizability of this logic is proved. The paper develops some ideas of Goguen and generalizes the results of Pavelka on the unit interval. The proof for completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if and only if the algebra of the truth values is a complete MV\u2010algebra. In the well\u2010defined fuzzy sentential logic holds the Compactness Theorem, while the Deduction Theorem and the Finiteness Theorem in general do not hold. Because of its generality and good\u2010behaviour, MV\u2010valued logic can be regarded as a mathematical basis of fuzzy reasoning.<\/jats:p>","DOI":"10.1002\/malq.19950410209","type":"journal-article","created":{"date-parts":[[2007,6,2]],"date-time":"2007-06-02T20:57:34Z","timestamp":1180817854000},"page":"236-248","source":"Crossref","is-referenced-by-count":22,"title":["Well\u2010Defined Fuzzy Sentential Logic"],"prefix":"10.1002","volume":"41","author":[{"given":"Esko","family":"Turunen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Models and Ultraproducts. An Introduction","author":"Bell J. L.","year":"1971"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190751"},{"key":"e_1_2_1_4_2","article-title":"Triangular norms","author":"Belluce L. P.","journal-title":"Math. Japonice."},{"key":"e_1_2_1_5_2","volume-title":"Lattice Theory","author":"Birkhoff G.","year":"1967"},{"key":"e_1_2_1_6_2","volume-title":"Residuation Theory","author":"Blyth T. S.","year":"1972"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1938-06736-5"},{"key":"e_1_2_1_8_2","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1090\/S0002-9947-1939-1501995-3","article-title":"Residuated lattices","volume":"45","author":"Dilworth R. P.","year":"1939","journal-title":"Trans. Amer. Math. Soc."},{"key":"e_1_2_1_9_2","first-page":"5","article-title":"Wajsberg algebras","volume":"8","author":"Font J. C.","year":"1984","journal-title":"Stochastica"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01212438"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00485654"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(80)90013-5"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-1236(86)90015-7"},{"key":"e_1_2_1_14_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19790250304"},{"key":"e_1_2_1_15_2","volume-title":"The Mathematics of Metamathematics","author":"Rasiowa H.","year":"1963"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1016\/0165-0114(92)90048-9"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90241-X"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19950410209","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19950410209","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T19:52:00Z","timestamp":1698349920000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19950410209"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,1]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1995,1]]}},"alternative-id":["10.1002\/malq.19950410209"],"URL":"https:\/\/doi.org\/10.1002\/malq.19950410209","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,1]]}}}