Matrix Logic (eBook)

Theory and Applications

A. Stern (Autor)

eBook Download: PDF

2014 | 1. Auflage
220 Seiten
Elsevier Science (Verlag)
978-1-4832-9549-7 (ISBN)

Infos

In this pioneering work, the author develops a fundamental formulation of logic in terms of theory of matrices and vector spaces. The discovery of matrix logic represents a landmark in the further formalization of logic. For the first time the power of direct mathematical computation is applied to the whole set of logic operations, allowing the derivation of both the classical and modal logics from the same formal base.The new formalism allows the author to enlarge the alphabet of the truth-values with negative logic antivalues and to link matrix logic descriptions with the Dirac formulation of quantum theory - a result having fundamental implications and repercussions for science as a whole.As a unified language which permits a logical examination of the underlying phenomena of quantum field theory and vice versa, matrix logic opens new avenues for the study of fundamental interactions and gives rise to a revolutionary conclusion that physics as such can be viewed and studied as a logic in the fundamental sense.Finally, modelling itself on exact sciences, matrix logic does not refute the classical logic but instead incorporates it as a special deterministic limit. The book requires multidisciplinary knowledge and will be of interest to physicists, mathematicians, computer scientists and engineers.

Inhalt

Front Cover 1
Matrix Logic 4
Copyright Page 5
Table of Contents 8
Acknowledgements 6
INTRODUCTION 10
CHAPTER 1. ELEMENTS OF MATRIX CALCULUS 16
1.1. Inner and outer products 16
1.2 Vector space formalism 18
1.3 Algebra of matrices 23
1.4 Orthogonal transformations 41
CHAPTER 2. FUNDAMENTALS OF CONVENTIONAL LOGIC 45
2.1 First-order logic 46
2.2 Higher-order logics 67
2.3 Multivalued logic 69
2.4 Quantum logic 71
CHAPTER 3. MATRIX FORMULATION OF LOGIC 74
3.1 Positive logic O+ 74
3.2 Negative logic O- 128
3.3 Continuous logic Oe 148
3.4 Hypercube logic On 156
CHAPTER 4. MATRIX LOGIC AND FUNDAMENTAL PHYSICS 159
4.1 Spinor logic 161
4.2 Relativistic spinor logic 163
4.3 CPT-theorem 167
4.4 Fundamental interactions 172
CHAPTER 5. APPLICATION TO NEW GENERATION COMPUTING 192
5.1 Multiplicative gates 192
5.2 Hypercube group processors 197
5.3 Abelian and non-abelian machines 209
5.4 Optical computing 211
5.5 Intelligent capabilities 214
MATHEMATICAL RESUME 220
INDEX 222

Produkt-Details

• Erscheint lt. Verlag: 28.6.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
• Themenwelt: Technik
• ISBN-10: 1-4832-9549-4 / 1483295494
• ISBN-13: 978-1-4832-9549-7 / 9781483295497