Information retrieval (IR) is driven by a process that decides whether a document is about a query. Recent attempts spawned from a logic-based information retrieval theory have formalized properties characterizing "aboutness," but no consensus has yet been reached. The proposed properties are largely determined by the underlying framework within which aboutness is defined. In addition, some properties are only sound within the context of a given IR model, but are not sound from the perspective of the user. For example, a common form of aboutness, namely overlapping aboutness, implies precision degrading properties such as compositional monotonicity. Therefore, the motivating question for this article is: independent of any given IR model, and examined within an information-based, abstract framework, what are commonsense properties of aboutness (and its dual, nonaboutness)? We propose a set of properties characterizing aboutness and nonaboutness from a commonsense perspective. Special attention is paid to the rules prescribing conservative behavior of aboutness with respect to information composition. The interaction between aboutness and nonaboutness is modeled via normative rules. The completeness, soundness, and consistency of the aboutness proof systems are analyzed and discussed. A case study based on monotonicity shows that many current IR systems are either monotonic or nonmonotonic. An interesting class of IR models, namely those that are conservatively monotonic, is identified.