This is a revised version of the paper with the same title appeared in the Proc. of the Estylf'98 Conference, September 8-10, 1998, Pamplona (Spain).In this paper we investigate a propositional fuzzy logical system LΠ which contains the well-known Lukasiewicz, Product and Gödel fuzzy logics as sublogics. We define the corresponding algebraic structures, called LΠ-algebras and prove the following completeness result: a formula φ is provable in the LΠ logic iff it is a tautology for all linear LΠ-algebras. Moreover, linear LΠ-algebras are shown to be embeddable in linearly ordered abelian rings with a strong unit and cancellation law.The authors acknowledge partial support of this work through CICYT Project SMASH (TIC96-1138-C04-01/04) and of the COST Action 15 of the European Union.Peer reviewed