Mathematical foundations of multiple inheritance: Reflexive-transitive closure of the binary relations

Abstract

The paper is devoted to the mathematical foundations of the linearization algorithms - the method of conflict resolution that occurs in object-oriented programming languages which support multiple inheritance. The main object of study is the reflexive-transitive closure of a binary relation. The basic properties of this closure are found: the criterion to be partial order, closure is the closure operator, denotative representations of closure in terms of its properties and as the least solution of some equation (the structure of the set of all solutions of this equation is established).