On Partial Classes Containig All Monotone and Zero‐Preserving Total Boolean Functions

Source abstract

Abstract We describe sets of partial Boolean functions being closed under the operations of superposition. For any class A of total functions we define the set 𝔐( A ) consisting of all partial classes which contain precisely the functions of A as total functions. The cardinalities of such sets 𝔐( A ) can be finite or infinite. We state some general results on 𝔐( A ). In particular, we describe all 30 closed sets of partial Boolean functions which contain all monotone and zero‐preserving total Boolean functions.