PRODUCTION-LOGICAL EQUATIONS ON BOOLEAN LATTICES
The concept of production-logical equation on boolean lattice is introduced which is based on general production-logical relations theory. Some properties of such equations are considered in case of finite lattice. The solution process of an arbitrary production-logical equation on a finite boolean lattice is reduced to solving a set of equations with elementary right-hand members. The concept of canonical relation on distributive lattice is introduced in order to simplify the study of logical connections. An existance of logically equivalent canonical relation for an arbitrary relation is proved in case of finite distributive lattice.