Pairs of Boolean elements based on a 'concrete' Rauszer Boolean algebra

With the development of practical applications in the domain of information systems, a wide variety of non-classical logics are part of current studies. Most of these systems have a natural algebraic model (namely their Lindenbaum algebra) which is a distributive lattice with additional operators. In order to find examples of these models, one way is to consider pairs of elements. The purpose of this paper is to provide a general framework, built from a pair of Boolean operators-a quantifier and a co-quantifier-on a complete Heyting-Brouwer algebra, focusing on the lattice part, which is common to all these structures.