The notion of independence in the theory of evidence: An algebraic study

In this paper we discuss the nature of independence of sources in the theory of evidence from an algebraic point of view, starting from an analogy with projective geometries. Independence in Dempster’s rule is equivalent to independence of frames as Boolean algebras. Collection of frames, in turn, can be given several algebraic interpretations in terms of semimodular lattices, matroids, and geometric lattices. Each of those structures are endowed with a particular notion of independence, which we prove to be distinct even though related to independence of frames. We show that the latter is in fact opposed to classical linear independence, giving collection of frames the structure of “anti-matroids”.