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Matrix Logic

Theory and Applications

A. Stern (Autor)

Buch | Hardcover

220 Seiten

1988
North-Holland (Verlag)
978-0-444-70432-0 (ISBN)

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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.

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.

Erscheint lt. Verlag	1.6.1988
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Informatik ► Theorie / Studium
	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Quantenphysik
ISBN-10	0-444-70432-9 / 0444704329
ISBN-13	978-0-444-70432-0 / 9780444704320
Zustand	Neuware