A pragmatic uncertainty measure based on rate-distorion theory and the uncertainty of BOE's

Abstract

We discuss pragmatic information measures (hypergraph entropy and fractional entropy) inspired by source-coding theory (rate-distortion theory). We re-phrase the problem in the language of evidence theory, by expressing the pragmatic requirements of the human agent in terms of suitable bodies of evidence, or BOE's. We tackle the situation when the overall uncertainty is removed in two steps. In the case when fractional entropy measures the first-step (partial, pragmatic) uncertainty, we put forward an information measure for the uncertainty left in the second step. The results found plead in favour of uncertainty measures for BOE's obtained by maximization of Shannon entropies.