This paper introduces a general-purpose framework aimed at capturing the elusive concept of quality of measurement information, a critical issue for both researchers and practitioners when dealing with measurement information-enabled decision making. The framework is a blueprint for the definition, assessment, communication, and improvement of measurement information quality, as analyzed through a set of general criteria, classified according to the syntactic, semantic, and pragmatic layers of semiotics, as suggested in the ISO 8000-8:2015 technical standard. The top-down analysis, where each criterion is specified in terms of characteristics and each characteristic in terms of domain-related indicators, is complemented with a bottom-up synthesis and operationalized by means of a flow chart. An application example, about the quality of information provided by the networks of measurement instruments reporting pollutants in the air, is presented to test the usefulness and the limitations of the framework.