On free annotated algebras

In Lewin et al. (Studia Logica 59(3) (1997) 359-386) the authors proved tha t certain systems of annotated logics are algebraizable in the sense of Blo ck and Rigozzi (Memoirs AMS 77 (1989) 396). Later in Lewin et al. (Proceedi ngs of the X SLALM, Bagota, 1995, Marcel Dekker, New York, 1998, pp. 279-29 3; Proceedings of the WAAL, Barcelona, 1997, submitted for publication) the study of the associated quasi-varieties of annotated algebras is initiated . In this paper we continue the study of the these classes of algebras, in particular, we report some recent results about the free annotated algebras . (C) 2001 Elsevier Science B.V. All rights reserved.