The implicatively implicit bases in implicatively closed classes of three-valued logic
Sergey Seraphimovich Marchenkov · Mathematical Problems of Cybernetics · 2023
It is proved that for any k ≥ 3, any implicatively implicit extension in Pk contains a class of Hk homogeneous functions. In each of the 17 implicatively closed classes in P3, an implicatively implicitly generating system of functions is constructed. With the exception of the H3 class, each of the systems consists of one or two no more than two-place functions. A one-place function is specified, the implicatively implicit extension of which is different from any implicatively closed class in P3.