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E-raamat: Matrix Logic: Theory and Applications

(Van Nijenrodeweg 912, 1081 BK Amsterdam, The Netherlands)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 28-Jun-2014
  • Kirjastus: North-Holland
  • Keel: eng
  • ISBN-13: 9781483295497
  • Formaat - PDF+DRM
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 28-Jun-2014
  • Kirjastus: North-Holland
  • Keel: eng
  • ISBN-13: 9781483295497

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In this revolutionary work, the author sets the stage for the science of
the 21st Century, pursuing an unprecedented synthesis of fields previously
considered unrelated. Beginning with simple classical concepts, he ends
with a complex multidisciplinary theory requiring a high level of
abstraction. The work progresses across the sciences in several
multidisciplinary directions: Mathematical logic, fundamental physics,
computer science and the theory of intelligence. Extraordinarily enough,
the author breaks new ground in all these fields.

In the field of
fundamental physics the author reaches the revolutionary conclusion that
physics can be viewed and studied as logic in a fundamental sense, as
compared with Einstein's view of physics as space-time geometry. This opens
new, exciting prospects for the study of fundamental interactions. A
formulation of logic in terms of matrix operators and logic vector spaces
allows the author to tackle for the first time the intractable problem of
cognition in a scientific manner. In the same way as the findings of
Heisenberg and Dirac in the 1930s provided a conceptual and mathematical
foundation for quantum physics, matrix operator logic supports an important
breakthrough in the study of the physics of the mind, which is interpreted
as a fractal of quantum mechanics. Introducing a concept of logic quantum
numbers, the author concludes that the problem of logic and the
intelligence code in general can be effectively formulated as eigenvalue
problems similar to those of theoretical physics. With this important leap
forward in the study of the mechanism of mind, the author concludes that
the latter cannot be fully understood either within classical or quantum
notions. A higher-order covariant theory is required to accommodate the
fundamental effect of high-level intelligence. The landmark results
obtained by the author will have implications and repercussions for the
very foundations of science as a whole. Moreover, Stern's Matrix Logic is
suitable for a broad spectrum of practical applications in contemporary
technologies.

Arvustused

G.J. Davis ...pioneering...an extremely interesting and compelling work. The theoretical prerequisites are mostly contained within the first two chapters, making the matrix logic concept accessible to anyone with a modest mathematical background. The material in the chapters on applications is sufficiently advanced to catch the interest of physicists and computer scientists. Those interested in logic from its foundations to its applications and limitations should be aware of this landmark work. ACM Computing Reviews D. Seese The book is well-written and easily accessible to anyone with a basic mathematical background. It opens a world of new interesting ideas and suggestions which are worth thinking about. The book can be recommended to students and researchers in mathematics, logic, computer science, physics and engineering. Biometrical Journal

1. Elements of Matrix Calculus. Inner and Outer Products. Vector Space
Formalism. Algebra of Matrices. Orthogonal Transformations.
2. Fundamentals of Conventional Logic. First-Order Logic. Higher-Order
Logics. Multivalued Logic. Quantum Logic.
3. Matrix Formulation of Logic. Positive Logic. Negative Logic. Continuous
Logic. Hypercube Logic.
4. Matrix Logic and Fundamental Physics. Spinor Logic. Relativistic Spinor
Logic. CPT-Theorem. Fundamental Interactions.
5. Application to New
Generation Computing. Multiplicative Gates. Hypercube Group Processor.
Abelian and Non-Abelian Machines. Intelligent Capabilities.
Mathematical Resume. Index.