Design in a universe of chance

An alternative representation of the binary relationship used in <I>Q</I>-analysis is presented. A unique decomposition is constructed without loss of information, and the elements of the decomposition are ordered in a Galois lattice. This lattice is an algebra identified with the intuitionistic logic of Brouwer. Comparisons are made with Boolean systems. Throughout references are made to the work of Charles Sanders Peirce who pioneered relational logic and diagrammatic methods in the nineteenth century.