Название: The Matrix Algebra of Logic: From Logic Operators to Cellular Automata
Автор: Eduardo Mizraji
Издательство: De Gruyter
Год: 2026
Страниц: 139
Язык: английский
Формат: pdf (true), epub
Размер: 12.4 MB

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.

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