Note on Słupecki T-functions

Extract

For the m-valued (2<w<∞) logics of Łukasiewicz as described in [2] using the values 1,2, …, m and based on the functions f(p, q) = max(1,q—p+1) and g(p) = m—p+1, Evans and Schwartz have essentially² proved in [1] that the addition of a constant function i, 1<i<m, yields functional completeness if and only if (m—1, i—1)= 1.³ In this note it will be shown that if n constant functions i₁, …, i_n, 1<i_k<m and 1≦k≦n, are added, functional completeness obtains if and only if (m—1, i₁—1, …, i_n—1) = 1.