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Logics and Arithmetics

In: Logic Functions and Equations

Author

Listed:
  • Christian Posthoff

    (The University of The West Indies)

  • Bernd Steinbach

    (Freiberg University of Technology)

Abstract

In this chapter we will give an outline of applications of logic functions and equations that are not directly related to the design of hardware. The applications in propositional logics are surely the oldest and reach back to the developments of science in ancient Greece. The names ”Boolean Algebra” and ”Boolean Ring” have been selected in honour of George Boole who wanted to formalize the ideas expressed by texts in natural language and to calculate the truth of complex constructions (in order to be precise and more accurate) . Naturally we already had to use logics in this sense throughout the book, however, we will go back to an introductory or elementary point of view and show that the knowledge that has been prepared up to now is fully appropriate to solve these problems. There was an enormous development of logics (in a broad mathematical sense) during the last 150 years that resulted in a highly sophisticated and specialized level, however, the propositional calculus is still the foundation of all these developments, and it is still necessary and useful to have a good understanding of these concepts.

Suggested Citation

  • Christian Posthoff & Bernd Steinbach, 2004. "Logics and Arithmetics," Springer Books, in: Logic Functions and Equations, chapter 0, pages 209-264, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4020-2938-7_6
    DOI: 10.1007/978-1-4020-2938-7_6
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