Abstract
In the first part of the talk we shall try to evaluate Tarski's
contribution to the development of infititely-valued Lukasiewicz
propositional logic, nowadays one of the most important fuzzy
propositional logic. In the second part we shall survey fuzzy
propositional and predicate calculi based on the notion of
continuous t-norm as the truth function of conjunction and
its residuum as the truth function of negation. We shall show
how to apply "Tarskian" semantics to fuzzy predicate logic to get
G"odel's style completeness and describe its variant for
which completeness fails dramatically.
Main references:
J. Lukasiewicz, A. Tarski: Untersuchungen ueber den
Aussagenkalk"ul. Comp. Rend. Soc. des Sci. et Lettres de
Varsovie cl. iii 23 (1930), 1-21
P. Hajek: Metamathematics of fuzzy logic. Kluwer 1998.
P. Hajek: Fuzzy logic and arithmetical hierarchy III. Studia
logica (to appear 2001).