Mizraji E. The Matrix Algebra of Logic...Logic Operators..Cellular Automata 2026

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Mizraji E. The Matrix Algebra of Logic...Logic Operators..Cellular Automata 2026

Textbook in PDF format 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. Our purpose here is to represent the algebra of logic through a theory of operators. The operators used are matrices that operate on vector truth values. These matrices allow us to represent virtually all operations of propositional calculus and prove its fundamental theorems, but operating according to the rules of matrix algebra. Likewise, various aspects of non-binary logic and modal logic can also be analyzed using this method of algebraic operators. It is important to note that in mathematical logic, an algebraic structure called a “matrix” is defined. However, these formal matrices are not the matrix operators of linear algebra that we will refer to in this book. Preface Introduction References The foundations The bases of logical calculation An informal look at matrices and vectors Neural memory models and the origin of vector logic Vector logic The matrix operators of logic Binary matrix operators and uncertain logical values The modalities and conceptualization of uncertainty Explorations of complexity Elements of differential and integral calculus of logical operators Binary cellular automata and the complexity of the simple Analyzing the internal structure of complex ECA through logical matrices: an unfinished exploration Index