Observations and Their Explanations

We introduce a first-oder theory where observations are reified into the domain of quantification. Observations have an epistemological nature, they describe how the world appears, not as the world is. Our primitive notions allow to represent how some observations are explained in terms of more simple ones or how they are aggregated into macro-indexes. We analyze in detail the cases of measurement and testing where observations are collected through calibrated devices and eventually aggregated into scores. Our framework is based on a decoupling between the observations and the propositions that belong to the temporally qualified A-box. It allows contradictory observations, but it requires these disagreements to be resolved via a merging process that identifies, among the contradictory observations, the most plausible one that can then be safely transferred into the A-box.