## ReAlM - a system to manipulate relations

##### Abstract

Given a heterogeneous relation algebra R, it is well known that the algebra of matrices with coefficient from R is relation algebra with relational sums that is not
necessarily finite. When a relational product exists or the point axiom is given, we
can represent the relation algebra by concrete binary relations between sets, which
means the algebra may be seen as an algebra of Boolean matrices. However, it is
not possible to represent every relation algebra. It is well known that the smallest
relation algebra that is not representable has only 16 elements. Such an algebra can
not be put in a Boolean matrix form.[15]
In [15, 16] it was shown that every relation algebra R with relational sums and
sub-objects is equivalent to an algebra of matrices over a suitable basis. This basis is
given by the integral objects of R, and is, compared to R, much smaller.
Aim of my thesis is to develop a system called ReAlM - Relation Algebra Manipulator - that is capable of visualizing computations in arbitrary relation algebras
using the matrix approach.