Tests and entity in evidence theory and quantum mechanics

Abstract

We propose a new interpretation of Dempster-Shafer theory of evidence based on a stochastic model for a quantum system developed in terms of amplitude on entities. An entity provides an axiomatic description for the set of tests and states of a physical system and an amplitude density gives a mean for computing probability and pseudo-probability within this framework. The interference and independence of tests relative to an amplitude density are formulated. Various ways of combining entities and amplitudes are presented as superpositions of amplitude. We propose to extend the theory of evidence also to the physical observable experiment in quantum mechanics. So we can use, for quantum mechanics, all the knowledge in the evidence theory. On the contrary the knowledge in the evidence theory can give new insight in the quantum mechanics uncertainty. We give a modal logic interpretation of evidence theory and entity and tests definitions. We establish a bridge between mental approach to uncertainty by evidence theory and the physical phenomena represented by quantum mechanics. When one use the amplitude density in the evidence theory one can generate a new interpretation of joint and conditional definition of the basic probability assignment ( pseudo-probability).