Semi-Boolean Algebras Empirical Logic and Rings.

Abstract

This paper presents application of semi-Boolean algebras to empirical logic and ring theory. The development of semi-Boolean algebras from subtraction algebras is shown and the identity of the two is established. Examples of subtraction algebras are given. A weakening of one of the subtraction axioms leads to a structure which is non-distributive but orthomodular. Known as orthosubtraction algebra, this structure is identical to a semi-orthomodular lattice. Since the subspaces of a Hilbert space (and thus the projections) form an orthomodular lattice they also form an orthosubtraction algebra. Examples of orthosubtraction algebra applied to Hilbert space are given. The concept of a manual and how it relates to empirical logic is introduced next. The set of events of a manual is a semi-Boolean algebra. It is atomic and dominated and has relations of operational complementation and operational perspectivity defined on it. From these relations the manual condition is defined and the semi-Boolean algebra is a DASBAM. Examples of manuals and DASBAMs are given. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1982
Accession Number
ADA124406

Entities

People

  • Peter P. Haglich

Organizations

  • United States Naval Academy

Tags

Communities of Interest

  • Air Platforms
  • Counter WMD
  • Energy and Power Technologies
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DTIC Thesaurus Topics

  • Abstracts
  • Boolean Algebra
  • Computer Science
  • District Of Columbia
  • Geometry
  • Hilbert Space
  • Maryland
  • Massachusetts
  • Mathematics
  • New York
  • Quantum Mechanics
  • Reasoning
  • Security
  • Students
  • Uncertainty Principle
  • United States
  • United States Naval Academy

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.

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  • Space