Classic Formal Logic and Nonclassical Logics: Basis of Research on Neural Networks

Abstract This chapter shows the logical foundation of current and future research in natural or artificial neural networks. First, nonformal logic that formed the basis for the formalization of the logic is addressed. Second, the fundamentals of classical formal logic are explained: principles, propositional logic, predicate logic, binary logic, decision-making, and system of relations. Third, the conceptual aspects of nonclassical logics that allow us to understand other forms of reasoning to solve complex problems are reviewed. They are addressed from the closest to the classical formal logic, modal logic as dynamic, relevant, deontic, epistemic, and versatile to the most dissimilar or alternatives such as intuitionistic, diffuse, dynamic, free, and quantum.