SOME BOOLEAN REPRESENTATIONS OF THE PROPOSITIONAL CALCULUS

Abstract

Boolean algebra has long played a well known role in the development of mathematical logic, but even in the propositional calculus there are many problems still to be investigated. Among these is the question of the feasibility of identifying the statement calculus with a Boolean algebra other than the (0, 1) algebra. The theory of Boolean algebra as required for a study of the algebraic aspects of logic is formulated. Characteristics of the equality relation are discussed and the propositional calculus is outlined with early emphasis on the equivalence classes, (0) and (1). The concepts of truth values, truth functions and truth sets are developed. Through these concepts, the statement calculus is identified with a Boolean algebra consisting of more than two elements.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1964
Accession Number
AD0482373

Entities

People

  • Leonard A. Snider

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boolean Algebra
  • Calculus
  • Composite Materials
  • Digital Computers
  • Functional Analysis
  • Generators
  • Identities
  • Inclusions
  • Logic
  • Materials
  • Mathematics
  • Mechanics
  • Numbers
  • Real Numbers
  • Set Theory
  • Theorems
  • United States

Readers

  • Graph Algorithms and Convex Optimization.
  • Systems Analysis and Design