Closure operators with positive connectives and quantifiers

Abstract

Closure operators based on the logical connectives & and ∨ and the quantifiers ∃ and ∀ and extend the superposition operator are classified. The (&∃∀)-closure operator, which uses only the connective & and both quantifiers, is considered. The basic properties of the (&∃∀)-closure operator are determined. All of the 15 (&∃∀)-closed classes of Boolean functions are found.