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.
- No. of pages:
- © North Holland 1988
- 1st June 1988
- North Holland
- eBook ISBN:
Van Nijenrodeweg 912, 1081 BK Amsterdam, The Netherlands
@from:G.J. Davis @qu:...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. @source:ACM Computing Reviews @from:D. Seese @qu: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. @source:Biometrical Journal