On the Identification of Structures in Multivariate Data by the Spectral Analysis of Relations

Complex systems are typically manifest in multi-variate data. The analysis of such data is therefore an intrinsic effort of systems research. In this paper, a distinction is made between the logic of many-valued relations and the quantification of the strength of these relations in data. The former is unrelated to data whereas the latter is invoked in two empirical tasks: the identification of structures in data and the construction of models and theories that reproduce or explain these data at least approximately so. A unified calculus is proposed to aid both tasks. It required a third generalization of Shannon's quantity of communication. The paper presents several algebraic identities of the quantity with entropies, transmissions and interactions. These identities are intended to provide the basis of two separate identification strategies; decomposition and composition. These are exemplified. The paper concludes with pointing out several yet unresolved problems.