A Computer Algebra Approach to Relational Systems Using Gröbner Bases

The aim of this paper is to suggest that Grobner bases can be applied to the study of reflexive and transitive relations. To illustrate our suggestion, we consider two examples. The first example is a Rule-Based-Expert-System: the reflexive and transitive relation is the implication arrow. The second example deals with railway interlocking systems: the reflexive and transitive relation is the accessibility to sections in a railway network. The study is generic; it can be applied to any reflexive and transitive relation.