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Boolean-based mathematics

  • Sergiu Rudeanu
Part of the Discrete Mathematics and Theoretical Computer Science book series (DISCMATH)

Abstract

As was seen in Chapter 12 of BFE, several Boolean-based algebraic structures have been studied, that is, algebras having as support a Boolean algebra and whose operations are Boolean functions; homomorphisms connecting such algebras and expressed by Boolean functions have also been investigated. Chapter 13 of BFE deals with Boolean arithmetic and Boolean geometry. The former means the study of divisibility between Boolean functions. In Boolean geometry the rôle of the space is played by a Boolean algebra and one looks for analogues of the basic concepts of geometry; for instance, a “good” analogue of the distance function is the symmeric difference d(x, y) = x + y. As was seen in BFE, Chapter 14, Boolean analysis replaces the real line by a Boolean algebra, while the functions dealt with are Boolean functions.

Keywords

Boolean Function Boolean Algebra Classical Propositional Calculus Deduction Theorem Boolean Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London 2001

Authors and Affiliations

  • Sergiu Rudeanu
    • 1
  1. 1.Faculty of MathematicsUniversity of BucharestBucharestRomania

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