Stern Matrix Logic

Theory and Applications
1. Auflage 2014
ISBN: 978-1-4832-9549-7
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 220 Seiten, Web PDF

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.

Autoren/Hrsg.

Stern, A.

Inhaltsverzeichnis

1;Front Cover;1
2;Matrix Logic;4
3;Copyright Page;5
4;Table of Contents;8
5;Acknowledgements;6
6;INTRODUCTION;10
7;CHAPTER 1. ELEMENTS OF MATRIX CALCULUS;16
7.1;1.1. Inner and outer products;16
7.2;1.2 Vector space formalism;18
7.3;1.3 Algebra of matrices;23
7.4;1.4 Orthogonal transformations;41
8;CHAPTER 2. FUNDAMENTALS OF CONVENTIONAL LOGIC;45
8.1;2.1 First-order logic;46
8.2;2.2 Higher-order logics;67
8.3;2.3 Multivalued logic;69
8.4;2.4 Quantum logic;71
9;CHAPTER 3. MATRIX FORMULATION OF LOGIC;74
9.1;3.1 Positive logic O+;74
9.2;3.2 Negative logic O-;128
9.3;3.3 Continuous logic Oe;148
9.4;3.4 Hypercube logic On;156
10;CHAPTER 4. MATRIX LOGIC AND FUNDAMENTAL PHYSICS;159
10.1;4.1 Spinor logic;161
10.2;4.2 Relativistic spinor logic;163
10.3;4.3 CPT-theorem;167
10.4;4.4 Fundamental interactions;172
11;CHAPTER 5. APPLICATION TO NEW GENERATION COMPUTING;192
11.1;5.1 Multiplicative gates;192
11.2;5.2 Hypercube group processors;197
11.3;5.3 Abelian and non-abelian machines;209
11.4;5.4 Optical computing;211
11.5;5.5 Intelligent capabilities;214
12;MATHEMATICAL RESUME;220
13;INDEX;222