We address the fundamental question: what does it mean for data in a database to be of high quality? We motivate our discussion with examples, where traditional views on data quality are found to be unsatisfactory. Our work is founded on the premise that data values are primarily linguistic signs that convey meaning from their producer to their user through senses and referents. In this setting, data quality issues arise when discrepancies occur during this communication. We sketch a theory of senses for individual values in a relational table based on its semantics expressed using some ontology. We use this to offer a compositional approach, where data quality is expressed in terms of a variety of primitive relationships among values and their senses. We evaluate our approach by accounting for quality attributes in other frameworks proposed in the literature. This exercise allows us to (i) reveal and differentiate multiple, sometimes conflicting, definitions of a quality attribute, (i...