Functional completeness and canonical forms in many-valued logics1

This paper examines the questions of functional completeness and canonical completeness in many-valued logics, offering proofs for several theorems on these topics. A skeletal description of the domain for these theorems is as follows. We are concerned with a proper logic L , containing a denumerably infinite class of propositional symbols, P, Q, R, …, a finite set of unary operations, U 1 , U 2 ,…, U b , and a finite set of binary operations, B 1 , B 2 , …, B c . Well-formed formulas in L are recursively defined by the conventional set of rules. With L there is associated an integer, M ≧ 2, and the integers m , where (1 ≦ m ≦M), are the truth values of L .