Screen LibraryHyperidentities : Boolean and De Morgan structures /
"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 application...
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| Main Authors: | |
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| Published: |
World Scientific Publishing,
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| Publisher Address: | New Jersey : |
| Publication Dates: | [2023] |
| Literature type: | Book |
| Language: | English |
| Subjects: | |
| Summary: |
"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. This text is 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"-- |
| Carrier Form: | xxvii, 532 pages : 26 cm |
| Bibliography: | Includes bibliographical references (pages 507-525) and index. |
| ISBN: |
9789811254918 9811254915 |
| Index Number: | QA251 |
| CLC: | O187.2 |
| Call Number: | O187.2/M935 |