\input zb-basic \input zb-ioport \iteman{io-port 05994820} \itemau{P\'asztor Varga, Katalin; V\'arter\'esz, Magda} \itemti{Many-valued logics -- theorem proving problems.} \itemso{Pop, Horia F. (ed.) et al., 8th joint conference on mathematics and computer science, MaCS 2010, Kom\'arno, Slovakia, July 14--17, 2010. Selected papers. Gy\H or: NOVADAT (ISBN 978-963-9056-38-1/pbk). 91-98 (2011).} \itemab This paper contains a brief discussion on semantic vs. syntactic consequence in many-valued logic. For further developments in the last fifteen years see {\it P. H\'ajek}'s book [Metamathematics of fuzzy logic. Dordrecht: Kluwer Academic Publishers (1998; Zbl 0937.03030)] as well as the present reviewer's book [Advanced \L ukasiewicz calculus and MV-algebras. Berlin: Springer (2011; Zbl 1235.03002)]. For the special case of infinite-valued \L ukasiewicz logic see Chapter 4 in the book [Algebraic foundations of many-valued reasoning. Dordrecht: Kluwer Academic Publishers (2000; Zbl 0937.06009)] by {\it R. L. O. Cignoli}, {\it I. M. L. D'Ottaviano} and the present reviewer. \itemrv{Daniele Mundici (Firenze)} \itemcc{} \itemut{many-valued logic; semantic consequence; syntactic consequence} \itemli{} \end