Probability theory as a logic for modelling the measurement process

Abstract

The problem of the nature of probability has been drawn to the attention of the measurement community in the comparison between the frequentist and the Bayesian views, in the expression and the evaluation of measurement uncertainty. In this regard, it is here suggested that probability can be interpreted as a logic for developing models of measurement capable of accounting for uncertainty. This contributes to regard measurement theory as an autonomous discipline, rather than a mere application field for statistics. Following a previous work in this line of research, where only measurement representations, through the various kinds of scales, were considered, here the modelling of the measurement process is discussed and the validity of the approach is confirmed, which suggests that the vision of probability as a logic could be adopted for the entire measurement theory. With this approach, a deterministic model can be turned into probabilistic by simply shifting from a deterministic to a probabilistic semantic.