On expanding Boolean algebra into a new dual-biform logic algebra

Some interesting problems, such as those occurring with non-coherent structure functions, require an expansion of existing Bolean algebra that can manipulate special coherent structure functions and their duals. In this paper, we formalize an algebra called A-Algebra (A New Dual Biform Logic Algebra).Some aspects of this algebra lead to the puzzling question, ‘When is the conjunction of a coherent structure function and its complemented-dual function a tautology (ƒ(x)ƒ^Δ·′(x))?′. In addition, we suggest that new algorithmic efficiencies may exist through the use of this algebra.