The Application of Vector Formalism in Logic and Logical-Mathematical Modeling

Abstract

The article presents an overview of research related to the application of vector formalism in logical investigations. Three directions of research in this area are discussed. The first area has to deal with the complication of formalism of classical mathematical logic. It is based on the vectorization of the categories of Truth and Falsehood. This line of research is represented by a vector logic of E. Mizrahi and matrix logic of A. Stern. The second one is the vectorization of logical semantics. This approach is represented by the logic of K.I. Bakhtiyarov, neutrosophy logic of F. Smarandache and in the logics with vector semantics. The third area is devoted to vectorization syllogistics of Aristotle. Here vector representation is used for partial visualization and automation of building syllogisms. All three areas are of practical importance and can be used for the solution of applied problems, in particular, in computer science and artificial intelligence.