Abstract
In general, every logic L comes equipped with a syntax, consisting of a finite set A of symbols, called the alphabet, and an inductive definition of which strings over A are to be called formula of L; a semantics, telling the meaning of each formula, whence in particular, telling when two formula are equivalent; an algorithmic procedure whereby, given a finite set F of formula, one can in principle obtain all conse-quences of F. In certain fortunate cases-e.g., in classical logic-formula up to equivalence form an interesting class of algebraic structures. The infinite-valued calculus of ?ukasiewicz is such a fortunate case. Our aim in this paper is to review semantic-algorithmic issues for this logic, with particular reference to recent research.