The Matrix Algebra of Logic
About this book
In these times when matrix algebra is proving to be a fundamental tool in emerging theories such as quantum computing and the neural models that underpin generative AI, the analysis of logical operations using matrix algebra provides us with a fresh perspective on logic and opens up an approach that simultaneously proposes new ways of teaching logic and opens up new avenues for research.
- Introduces the rich versatility of matrix algebra representation of logic.
- Generates new results in basic logic, modal theory, the differential logic calculus, and logical automata.
Author / Editor information
Eduardo Mizraji is a Doctor of Medicine from the University of the Republic, Uruguay and a DEA in Applied Mathematics at the University of Paris V, France. He was Professor of Biophysics in the Faculty of Science, University of the Republic, Uruguay, until his retirement. After his retirement he received an Honorary Doctorate from the Faculty of Sciences. He is now Emeritus Researcher of the National System of Researchers and member of the National Academy of Sciences of Uruguay. His current research focuses on neural network models, information processing in biological systems and the algebra of logic.
Topics
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Frontmatter
I -
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Dedication
V -
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Acknowledgments
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Preface
IX -
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Contents
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Introduction
1 - Part 1: The foundations
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Chapter 1 The bases of logical calculation
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Chapter 2 An informal look at matrices and vectors
17 -
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Chapter 3 Neural memory models and the origin of vector logic
27 - Part 2: Vector logic
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Chapter 4 The matrix operators of logic
35 -
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Chapter 5 Binary matrix operators and uncertain logical values
55 -
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Chapter 6 The modalities and conceptualization of uncertainty
67 - Part 3: Explorations of complexity
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Chapter 7 Elements of differential and integral calculus of logical operators
81 -
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Chapter 8 Binary cellular automata and the complexity of the simple
97 -
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Chapter 9 Analyzing the internal structure of complex ECA through logical matrices: an unfinished exploration
109 -
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Index
125
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