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 ????(A) consisting of all partial classes which contain precisely the functions of A as total functions. The cardinalities of such sets ????(A) can be finite or infinite. We state some general results on ????(A). In particular, we describe all 30 closed sets of partial Boolean functions which contain all monotone and zero-preserving total Boolean functions.