Hyperidentities are important formulae of second-order logic, and
research in hyperidentities paves way for the study of second-order
logic and second-order model theory.This book illustrates many
important current trends and perspectives for the field of
hyperidentities and their applications, of interest to researchers
in modern algebra and discrete mathematics. It covers a number of
directions, including the characterizations of the Boolean algebra
of n-ary Boolean functions and the distributive lattice of n-ary
monotone Boolean functions; the classification of hyperidentities
of the variety of lattices, the variety of distributive (modular)
lattices, the variety of Boolean algebras, and the variety of De
Morgan algebras; the characterization of algebras with
aforementioned hyperidentities; the functional representations of
finitely-generated free algebras of various varieties of lattices
and bilattices via generalized Boolean functions (De Morgan
functions, quasi-De Morgan functions, super-Boolean functions,
super-De Morgan functions, etc); the structural results for De
Morgan algebras, Boole-De Morgan algebras, super-Boolean algebras,
bilattices, among others.While problems of Boolean functions theory
are well known, the present book offers alternative, more general
problems, involving the concepts of De Morgan functions, quasi-De
Morgan functions, super-Boolean functions, and super-De Morgan
functions, etc. In contrast to other generalized Boolean functions
discovered and investigated so far, these functions have clearly
normal forms. This quality is of crucial importance for their
applications in pure and applied mathematics, especially in
discrete mathematics, quantum computation, quantum information
theory, quantum logic, and the theory of quantum computers.
General
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