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We consider relations with no order on their attributes as in DatabaseTheory. An independent partition of the set of attributes S of a finiterelation R is any partition X of S such that the join of the projections of Rover the elements of X yields R. Identifying independent partitions has manyapplications and corresponds conceptually to revealing orthogonality betweensets of dimensions in multidimensional point spaces. A subset of S is termedself-correlated if there is a value of each of its attributes such that notuple of R contains all those values. This paper uncovers a connection betweenindependence and self-correlation, showing that the maximum independentpartition is the least fixed point of a certain inflationary transformer alphathat operates on the finite lattice of partitions of S. alpha is defined viathe minimal self-correlated subsets of S. We use some additional properties ofalpha to show the said fixed point is still the limit of the standardapproximation sequence, just as in Kleene's well-known fixed point theorem forcontinuous functions.

Self-Correlation and Maximum Independence in Finite Relations