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We show that in the propositional case most logics are complete but not strongly complete with respect to the corresponding class of complete Kripke frames, whereas in the predicate case there are important many\u2010valued logics like BL, \u0141 and \u03a0, which are not even complete with respect to the class of all predicate Kripke frames in which they are valid. Thus although very natural, Kripke semantics seems to be slightly less powerful than algebraic semantics. (\u00a9 2003 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200310068","type":"journal-article","created":{"date-parts":[[2003,9,11]],"date-time":"2003-09-11T13:20:26Z","timestamp":1063286426000},"page":"629-641","source":"Crossref","is-referenced-by-count":14,"title":["Kripke\u2010style semantics for many\u2010valued logics"],"prefix":"10.1002","volume":"49","author":[{"given":"Franco","family":"Montagna","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lorenzo","family":"Sacchetti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2003,9,9]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"P.Aglian\u00f3 I. M. A.Ferreirim andF.Montagna Basic hoops: an algebraic study of continuous t\u2010norms. Studia Logica (to appear)."},{"key":"e_1_2_1_3_2","unstructured":"P.Aglian\u00f3 andF.Montagna Varieties of basic algebras I: General properties. J. Pure Appl. 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