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This paper is a contribution to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and ∆-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics -namely the class of algebras defined overdoi:10.1016/j.apal.2009.01.012 fatcat:m2jmypf4brbnpa7np4ymtae5d4