Theory Extraction in Relational Data Analysis

Abstract

From numerical mathematics we know that a linear equation Ax=b may be solved more efficiently if a reduction of A as A=$\left(\begin{array}{cc} B ~ O \\ C ~ D \\ \end{array}\right)$ is known beforehand. For the task $\left(\begin{array}{cc} B ~ O \\ C ~ D \\ \end{array}\right) \cdot \left(\begin{array}{c} y \\ z \\ \end{array}\right) = \left(\begin{array}{c} c \\ d \\ \end{array}\right)$, one will solve By=c first and then Dz=d-Cy. Having an a priori knowledge of this kind is also an advantage in many other application fields. We here deal with a diversity of techniques to decompose relations according to some criteria and embed these techniques in a common framework. The results of decompositions obtained may be used in decision making, but also as a support for teaching, as they often give visual help.