Spatial Interpretation of the Notion of Relation and Its Application in the System of Artificial Intelligence

Abstract

This paper considers the point of view on relations that are interpreted as generalized spaces, in contrast to the classical definition of a relation as a subset of the Cartesian product of sets. The connection of generalized spaces with predicates and maps is also considered. Predicates accompanying generalized spaces, projection predicates are introduced. Possible interpretations of generalized spaces are presented. Looking at the attitude as a generalized space leads to the formulation of a number of interesting logical-mathematical problems and to the results that are promising for use in many areas of artificial intelligence.