The interplay between models and observations

We propose a formal framework to examine the relationship between models and observations. To make our analysis precise, models are reduced to first-order theories that represent both terminological knowledge - e.g., the laws that are supposed to regulate the domain under analysis and that allow for explanations, predictions, and simulations - and assertional knowledge - e.g., information about specific entities in the domain of interest. Observations are introduced into the domain of quantification of a distinct first-order theory that describes their nature and their organization and takes track of the way they are experimentally acquired or intentionally elaborated. A model mainly represents the theoretical knowledge or hypotheses on a domain, while the theory of observations mainly represents the empirical knowledge and the given experimental practices. We propose a precise identity criterion for observations and we explore different links between models and observations by assuming a degree of independence between them. By exploiting some techniques developed in the field of social choice theory and judgment aggregation, we sketch some strategies to solve inconsistencies between a given set of observations and the assumed theoretical hypotheses. The solutions of these inconsistencies can impact both the observations - e.g., the theoretical knowledge and the analysis of the way observations are collected or produced may highlight some unreliable sources - and the models - e.g., empirical evidences may invalidate some theoretical laws.